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Integers as Exponents

An exponent tells us how many times a number (called the base) is multiplied by itself.

Exponent वह number है जो यह बताता है कि base को अपने आप से कितनी बार multiply करना है।

For example :

  • \( 3 \times 3 \times 3 \times 3 \) can be written as \( 3^4 \).
    \( 3 \times 3 \times 3 \times 3 \) को हम लिख सकते हैं \( 3^4 \) के रूप में।
  • Here, 3 is the base and 4 is the exponent or power.
    यहाँ 3 है base और 4 है exponent
  • It is read as “3 raised to the power 4”.
    इसे पढ़ते हैं “3 raised to the power 4”

This works for any rational number, not just whole numbers.
यह किसी भी rational number के लिए काम करता है।

  • \( \frac{3}{8} \times \frac{3}{8} \times \frac{3}{8} \times \frac{3}{8} = \left( \frac{3}{8} \right)^4 \)
    \( \frac{3}{8} \) को 4 बार multiply करने पर : \( \left( \frac{3}{8} \right)^4 \)
  • \( \left( -\frac{3}{5} \right) \times \left( -\frac{3}{5} \right) \times \left( -\frac{3}{5} \right) = \left( -\frac{3}{5} \right)^3 \)
    \( -\frac{3}{5} \) को 3 बार multiply करने पर : \( \left( -\frac{3}{5} \right)^3 \)

In general:
If \( \frac{a}{b} \) is any rational number and \( n \) is a natural number, then :
\( \left( \frac{a}{b} \right)^n = \frac{a}{b} \times \frac{a}{b} \times \frac{a}{b} \times … \text{(n times)} \)

किसी भी non-zero number \( x \) के लिए,
\( x^{-n} = \frac{1}{x^n} \)
और
\( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)


Positive Integral Exponents

When the exponent (n) is a positive integer (like 1, 2, 3, 4…), it is called a positive integral exponent. It simply means repeated multiplication.

जब exponent एक positive integer होता है (जैसे 1, 2, 3…), तो उसे Positive Integral Exponent कहते हैं। इसका मतलब सिर्फ repeated multiplication है।


Negative Integral Exponents

A negative exponent means we are talking about the reciprocal of the base with a positive exponent.
Negative Exponent का मतलब होता है reciprocal लेना।

For example:

  • The reciprocal of ( 9 ) is \( \frac{1}{9} \).
    9 का reciprocal है \( \frac{1}{9} \)
  • We know \( 9 = 3^2 \), so \( \frac{1}{9} = \frac{1}{3^2} = 3^{-2} \).
    \( 9 = 3^2 \) , इसलिए \( \frac{1}{9} = \frac{1}{3^2} = 3^{-2} \)
  • \( 3^{-2} \) is read as “3 raised to the power -2”.
    \( 3^{-2} \) को पढ़ते हैं “3 raised to the power -2”

In general:
For any non-zero rational number \( x \),
\( x^{-n} = \frac{1}{x^n} \)
and
\( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

Examples:

  1. \( \frac{1}{2^5} = 2^{-5} \)
  2. \( \frac{1}{2^{-5}} = 2^{5} \)
  3. \( 3^5 = \frac{1}{3^{-5}} \)
  4. \( 3^{-4} = \frac{1}{3^4} \)

Working Rules

To convert between rational numbers and exponential form, remember these key rules:

  1. \( x^m = x \times x \times x … \) (m times)
    Exponential form में convert करने के लिए : \( x^m = x \times x \times x … \) m times
  2. \( x^{-m} = \frac{1}{x^m} \)
    Negative exponent को positive करने के लिए: \( x^{-m} = \frac{1}{x^m} \)
  3. When a Negative Rational Number is Multiplied to itself (a) Odd Times , then the Answer has Negative sign (b) Even Times, then the Answer has Positive sign.

    जब कोई Negative Rational Number अपने आप से (a) Odd times multiply होता है, तो Answer में Negative sign होती है (b) Even times multiply होता है, तो Answer में Positive sign आ जाती है .

Solved Examples at a Glance


Example 1
Express the following power notations as rational numbers:
( निम्नलिखित power notations को rational numbers के रूप में express करो : )
(i) \( \left( -\frac{3}{2} \right)^4 \)
(ii) \( (-1)^7 \)

Solution :
(i) \( \left( -\frac{3}{2} \right)^4 = \left( -\frac{3}{2} \right) \times \left( -\frac{3}{2} \right) \times \left( -\frac{3}{2} \right) \times \left( -\frac{3}{2} \right) = \frac{81}{16} \)
\( \left( -\frac{3}{2} \right)^4 \) का मतलब है \( -\frac{3}{2} \) को अपने आप से 4 बार multiply करना।
जब हम multiply करते हैं, तो negative signs cancel हो जाती हैं क्योंकि 4 एक even number है।
\( \frac{3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2} = \frac{81}{16} \)

(ii) \( (-1)^7 = (-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) = -1 \)
\( (-1)^7 \) का मतलब है -1 को 7 बार multiply करना।
7 एक odd number है, इसलिए answer negative होगा।
\( (-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) = -1 \)


Example 2

Express each of the following rational numbers in power notation:
(i) \( \frac{-27}{64} \)
(ii) \( \frac{-1}{32} \)

Solution:
(i) \( -27 = (-3)^3 \) and \( 64 = 4^3 \)
So, \( \frac{-27}{64} = \frac{(-3)^3}{4^3} = \left( -\frac{3}{4} \right)^3 \)

(ii) \( -1 = (-1)^5 \) and \( 32 = 2^5 \)
So, \( \frac{-1}{32} = \frac{(-1)^5}{2^5} = \left( -\frac{1}{2} \right)^5 \)


निम्नलिखित rational numbers को power notation में express करो:
(i) \( \frac{-27}{64} \)
(ii) \( \frac{-1}{32} \)

Solution:
(i) पहले numerator और denominator को किसी number की power के रूप में लिखो।
\( -27 \) है \( (-3) \times (-3) \times (-3) = (-3)^3 \)
\( 64 \) है \( 4 \times 4 \times 4 = 4^3 \)
इसलिए, \( \frac{-27}{64} = \frac{(-3)^3}{4^3} = \left( -\frac{3}{4} \right)^3 \)

(ii) \( -1 \) को \( (-1)^5 \) लिख सकते हैं।
\( 32 \) है \( 2 \times 2 \times 2 \times 2 \times 2 = 2^5 \)
इसलिए, \( \frac{-1}{32} = \frac{(-1)^5}{2^5} = \left( -\frac{1}{2} \right)^5 \)


Example 3
Find the value of:
(i) \( (3^2 – 2^2) \div \left( \frac{1}{5} \right)^2 \)
(ii) Reciprocal of \( \left[ \left( \frac{1}{2} \right)^2 – \left( \frac{1}{4} \right)^3 \right] \times 2^3 \)

Solution:
(i) \( (9 – 4) \div \frac{1}{25} = 5 \div \frac{1}{25} = 5 \times 25 = 125 \)

(ii) First, simplify inside the brackets:
\( \left( \frac{1}{4} – \frac{1}{64} \right) \times 8 = \left( \frac{16}{64} – \frac{1}{64} \right) \times 8 = \frac{15}{64} \times 8 = \frac{15}{8} \)
The reciprocal of \( \frac{15}{8} \) is \( \frac{8}{15} \).



निम्नलिखित का मान ज्ञात करो:
(i) \( (3^2 – 2^2) \div \left( \frac{1}{5} \right)^2 \)
(ii) \( \left[ \left( \frac{1}{2} \right)^2 – \left( \frac{1}{4} \right)^3 \right] \times 2^3 \) का reciprocal

Solution:
(i) पहले brackets को solve करो: \( 3^2 = 9 \), \( 2^2 = 4 \), so \( 9 – 4 = 5 \)
अब, \( \left( \frac{1}{5} \right)^2 = \frac{1}{25} \)
Division by a fraction is multiplication by its reciprocal : \( 5 \div \frac{1}{25} = 5 \times 25 = 125 \)

(ii) पहले brackets के अंदर solve करो :
\( \left( \frac{1}{2} \right)^2 = \frac{1}{4} ), ( \left( \frac{1}{4} \right)^3 = \frac{1}{64} \)
So, \( \frac{1}{4} – \frac{1}{64} = \frac{16}{64} – \frac{1}{64} = \frac{15}{64} \)
अब, \( \frac{15}{64} \times 2^3 = \frac{15}{64} \times 8 = \frac{15}{8} \)
Reciprocal means अंश (Numerator) और हर (Denominator) को बदलना: \( \frac{8}{15} \)


Example 4
The value of \( \left( \frac{1}{3} \right)^{-3} \) is :
(a) \( \frac{1}{27} \) (b) \( -\frac{1}{27} \) (c) -27 (d) 27

Solution :
\( \left( \frac{1}{3} \right)^{-3} = \frac{1}{\left( \frac{1}{3} \right)^3} = \frac{1}{\frac{1}{27}} = 1 \times 27 = 27 \)
So, the correct option is (d).



\( \left( \frac{1}{3} \right)^{-3} \) का मान है :
(a) \( \frac{1}{27} \) (b) \( -\frac{1}{27} \) (c) -27 (d) 27

Solution:
Negative exponent rule : \( \left( \frac{1}{3} \right)^{-3} = \frac{1}{\left( \frac{1}{3} \right)^3} \)
अब, \( \left( \frac{1}{3} \right)^3 = \frac{1}{27} \)
So, \( \frac{1}{\frac{1}{27}} = 1 \times 27 = 27 \)
सही option है (d) 27


Example 5
The value of \( (-5)^{-4} \) is :
(a) \( \frac{1}{625} \) (b) -125 (c) \( -\frac{1}{12} \) (d) -625

Solution:
\( (-5)^{-4} = \frac{1}{(-5)^4} = \frac{1}{(-5) \times (-5) \times (-5) \times (-5)} = \frac{1}{625} \)
So, the correct option is (a).



\( (-5)^{-4} \) का मान है :
(a) \( \frac{1}{625} \) (b) -125 (c) \( -\frac{1}{12} \) (d) -625

Solution :
Negative exponent rule : \( (-5)^{-4} = \frac{1}{(-5)^4} \)
अब, \( (-5)^4 = (-5) \times (-5) \times (-5) \times (-5) \)
Negative signs cancel out (even exponent), so answer positive: ( 5 \times 5 \times 5 \times 5 = 625 )
So, \( \frac{1}{625} \)
सही option है (a) \( \frac{1}{625} \)


Of course! Here are the solutions for Exercise 2.1, Question 1 (MCQ) with detailed explanations.


Exercise 2.1


Question 1 (i)
The value of \( \left( \frac{2}{5} \right)^{-4} \) is :
(a) \( \frac{16}{625} \)
(b) \( -\frac{625}{16} \)
(c) \( \frac{625}{16} \)
(d) \( -\frac{16}{625} \)

Solution:
We use the rule for negative exponents : \( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

So,\( \left( \frac{2}{5} \right)^{-4} = \left( \frac{5}{2} \right)^{4}\)
Now, calculate \( \left( \frac{5}{2} \right)^{4} \) :
\( \left( \frac{5}{2} \right)^{4} = \frac{5^4}{2^4} = \frac{5 \times 5 \times 5 \times 5}{2 \times 2 \times 2\times 2} = \frac{625}{16}\)

Therefore, the correct option is (c) \( \frac{625}{16} \) .


\( \left( \frac{2}{5} \right)^{-4} \) का मान  (value) है :
(a) \( \frac{16}{625} \)
(b) \( -\frac{625}{16} \)
(c) \( \frac{625}{16} \)
(d) \( -\frac{16}{625} \)

Solution:
हम negative exponent के rule का use करेंगे :
\( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

इसलिए,
\( \left( \frac{2}{5} \right)^{-4} = \left( \frac{5}{2} \right)^{4} \)
अब, \( \left( \frac{5}{2} \right)^{4} \) की value निकालते हैं:
\(\left( \frac{5}{2} \right)^{4} = \frac{5^4}{2^4} = \frac{5 \times 5 \times 5 \times 5}{2 \times 2 \times 2 \times 2} = \frac{625}{16} \)

इसलिए, सही option है (c) \( \frac{625}{16} \)


Question 1 (ii)

Left Side (Simple English):
The reciprocal of \( \left[ \left( \frac{1}{3} \right)^2 – \left( \frac{1}{3} \right)^3 \right] \times 3^3 \) is :
(a) \( \frac{1}{2} \)
(b) 2
(c) \( -\frac{1}{2} \)
(d) -2

Solution:
First, simplify the expression inside the brackets.

Step 1: Simplify the terms inside
\( \left( \frac{1}{3} \right)^2 = \frac{1}{9} \) \( \left( \frac{1}{3} \right)^3 = \frac{1}{27} \) \( \ left( \frac{1}{3}
\right)^2 – \left( \frac{1}{3} \right)^3 = \frac{1}{9} – \frac{1}{27} \)
Find a common denominator (which is 27) :
\( \frac{1}{9} = \frac{3}{27}, \quad \text{so} \quad \frac{3}{27} – \frac{1}{27} = \frac{2}{27} \)
So, the expression inside the brackets becomes \( \frac{2}{27} \).

Step 2: Multiply by \( 3^3 \)
\(3^3 = 27 \) \( \left[ \frac{2}{27} \right] \times 27 = 2 \)
The value of the expression is 2.

Step 3: Find the reciprocal
The reciprocal of 2 is \( \frac{1}{2} \).

Therefore, the correct option is (a) \( \frac{1}{2} \).


\( \left[ \left( \frac{1}{3} \right)^2 – \left( \frac{1}{3} \right)^3 \right] \times 3^3 \)
का reciprocal है :
(a) \( \frac{1}{2} \)
(b) 2
(c) \( -\frac{1}{2} \)
(d) -2

Solution:
सबसे पहले brackets के अंदर के expression को simplify करते हैं।

Step 1: Brackets के अंदर simplify करो
\( \left( \frac{1}{3} \right)^2 = \frac{1}{9} \) \( \left( \frac{1}{3} \right)^3
= \frac{1}{27} \) \( \left( \frac{1}{3} \right)^2 – \left( \frac{1}{3} \right)^3 = \frac{1}{9} – \frac{1}{27} \)
Common denominator 27 लो :
\( \frac{1}{9} = \frac{3}{27}, \quad \text{so} \quad \frac{3}{27} – \frac{1}{27} = \frac{2}{27} \)
तो, brackets के अंदर की value है \( \frac{2}{27} \).

Step 2: \( 3^3 \) से multiply करो
\(3^3 = 27\) \( \left[ \frac{2}{27} \right] \times 27 = 2 \)
Pure expression की value है 2.

Step 3: Reciprocal निकालो
2 का reciprocal है \( \frac{1}{2} \).

इसलिए, सही option है (a) \( \frac{1}{2}\)


Question 2 (i)


Express the following power of a rational number as a rational number :
\( \left( \frac{-4}{5} \right)^3 \)

Solution:
The expression \( \left( \frac{-4}{5} \right)^3 \) means \( \frac{-4}{5} \) multiplied by itself 3 times.
\(
\left( \frac{-4}{5} \right)^3 = \left( \frac{-4}{5} \right) \times \left( \frac{-4}{5} \right) \times \left( \frac{-4}{5} \right) \)

Step 1: Multiply the numerators :
\( (-4) \times (-4) \times (-4) \)
First, \( (-4) \times (-4) = +16 \)
Then, \( 16 \times (-4) = -64 \)
So, the numerator is -64.

Step 2: Multiply the denominators :
\( 5 \times 5 \times 5 = 125 \)
So, the denominator is 125.

Step 3: Combine the results :
\( \left( \frac{-4}{5} \right)^3 = \frac{-64}{125}\)

Final Answer : \( \frac{-64}{125} \)


निम्नलिखित power of a rational number को एक rational number के रूप में express करो :
\( \left( \frac{-4}{5} \right)^3 \)

Solution :
\( \left( \frac{-4}{5} \right)^3 \) का मतलब है \( \frac{-4}{5} \) को अपने आप से 3 बार multiply करना।
\( \left( \frac{-4}{5} \right)^3 = \left( \frac{-4}{5} \right) \times \left( \frac{-4}{5} \right) \times \left( \frac{-4}{5} \right \)

Step 1 : Numerators को multiply करो :
\( (-4) \times (-4) \times (-4) \)
पहले, \( (-4) \times (-4) = +16 \)
फिर, \( 16 \times (-4) = -64 \)
तो, numerator है -64

Step 2 : Denominators को multiply करो :
\( 5 \times 5 \times 5 = 125 \)
तो, denominator है 125

Step 3 : Results को combine करो :
\( \left( \frac{-4}{5} \right)^3 = \frac{-64}{125} \)

Final Answer : \( \frac{-64}{125} \)


Question 2 (ii)


Express the following power of a rational number as a rational number :
\( (-1)^{12} \)

Solution:
The expression \( (-1)^{12} \) means (-1) multiplied by itself 12 times.
\((-1)^{12} = \underbrace{(-1) \times (-1) \times (-1) \times \dots \times (-1)}_{12\ \text{times}} \)

Key Concept:

  • When (-1) is raised to an even power (like 2, 4, 6, … 12), the result is +1.
  • When (-1) is raised to an odd power (like 1, 3, 5, …), the result is -1.

Since 12 is an even number, the negative signs will all cancel out, and the final result will be positive.

Therefore :
\((-1)^{12} = +1\)

Final Answer: ( 1 )



निम्नलिखित power of a rational number को एक rational number के रूप में express करो :
\( (-1)^{12} \)

Solution:
\( (-1)^{12} \) का मतलब है (-1) को अपने आप से 12 बार multiply करना
\((-1)^{12} = \underbrace{(-1) \times (-1) \times (-1) \times \dots \times (-1)}_{12\ \text{बार}} \)

Important Rule:

  • जब (-1) को किसी even power (जैसे 2, 4, 6, … 12) पर raise किया जाता है, तो result +1 होता है
  • जब (-1) को किसी odd power (जैसे 1, 3, 5, …) पर raise किया जाता है, तो result -1 होता है

क्योंकि 12 एक even number है, सारे negative signs cancel हो जाएंगे, और final result positive होगा

इसलिए:
\((-1)^{12} = +1 \)

Final Answer: ( 1 )


Question 3 (i)


Express the rational number in power notation :
\( -\frac{1}{125} \)

Solution:
We need to write both the numerator and the denominator as powers.

  1. The numerator is -1. We can write \( -1 = (-1)^3 \).
  2. The denominator is 125. We know \( 125 = 5 \times 5 \times 5 = 5^3 \).

Therefore :
\( -\frac{1}{125} = \frac{-1}{5^3} = \frac{(-1)^3}{5^3} = \left( -\frac{1}{5} \right)^3\)

Final Answer : \( \left( -\frac{1}{5} \right)^3 \)


Rational number को power notation में express करो :
\( -\frac{1}{125} \)

Solution :
हमें numerator और denominator दोनों को powers के रूप में लिखना है

  1. Numerator है -1. हम लिख सकते हैं \( -1 = (-1)^3 \).
  2. Denominator है 125. हम जानते हैं \( 125 = 5 \times 5 \times 5 = 5^3 \).

इसलिए :
\( -\frac{1}{125} = \frac{-1}{5^3} = \frac{(-1)^3}{5^3} = \left( -\frac{1}{5} \right)^3 \)

Final Answer: \( \left( -\frac{1}{5} \right)^3 \)


Question 3 (ii)

Express the rational number in power notation:
\( -\frac{27}{8} \)

Solution:
We need to write both the numerator and the denominator as powers.

  1. The numerator is -27. We know \( 27 = 3 \times 3 \times 3 = 3^3 ), so ( -27 = (-3)^3 \).
  2. The denominator is 8. We know \( 8 = 2 \times 2 \times 2 = 2^3 \).

Therefore:
\( -\frac{27}{8} = \frac{(-3)^3}{2^3} = \left( -\frac{3}{2} \right)^3 \)

Final Answer: \( \left( -\frac{3}{2} \right)^3 \)


Rational number को power notation में express करो :
\( -\frac{27}{8} \)

Solution:
हमें numerator और denominator दोनों को powers के रूप में लिखना है

  1. Numerator है -27. हम जानते हैं \( 27 = 3 \times 3 \times 3 = 3^3 ), इसलिए ( -27 = (-3)^3 \).
  2. Denominator है 8. हम जानते हैं \( 8 = 2 \times 2 \times 2 = 2^3 \).

इसलिए :
\( -\frac{27}{8} = \frac{(-3)^3}{2^3} = \left( -\frac{3}{2} \right)^3 \)

Final Answer : \(\left( -\frac{3}{2} \right)^3 \)


Question 3 (iii)

Left Side (Simple English):
Express the rational number in power notation:
\( \frac{9}{25} \times \frac{64}{25} \)

Solution:
We can write each number as a square.

  1. \( 9 = 3^2 ), so ( \frac{9}{25} = \frac{3^2}{5^2} = \left( \frac{3}{5} \right)^2 \)
  2. \( 64 = 8^2 ), so ( \frac{64}{25} = \frac{8^2}{5^2} = \left( \frac{8}{5} \right)^2 \)

Now, the expression becomes :
\( \left( \frac{3}{5} \right)^2 \times \left( \frac{8}{5} \right)^2 \)
Using the law of exponents: \( a^m \times b^m = (a \times b)^m \)
\( \left( \frac{3}{5} \times \frac{8}{5} \right)^2 = \left( \frac{3 \times 8}{5 \times 5} \right)^2 = \left( \frac{24}{25} \right)^2 \)

Final Answer: \( \left( \frac{24}{25} \right)^2 \)


Rational number को power notation में express करो :
\( \frac{9}{25} \times \frac{64}{25} \)

Solution:
हम प्रत्येक number को एक square के रूप में लिख सकते हैं

  1. \( 9 = 3^2 ), इसलिए ( \frac{9}{25} = \frac{3^2}{5^2} = \left( \frac{3}{5} \right)^2 \)
  2. \( 64 = 8^2 ), इसलिए ( \frac{64}{25} = \frac{8^2}{5^2} = \left( \frac{8}{5} \right)^2 \)

अब, expression बन जाता है :
\( \left( \frac{3}{5} \right)^2 \times \left( \frac{8}{5} \right)^2 \)
Exponents के law का use करते हुए : \( a^m \times b^m = (a \times b)^m \)
\( \left( \frac{3}{5} \times \frac{8}{5} \right)^2 = \left( \frac{3 \times 8}{5 \times 5} \right)^2 = \left( \frac{24}{25} \right)^2 \)

Final Answer : \( \left( \frac{24}{25} \right)^2 \)


Question 3 (iv)

Express the rational number in power notation :
\( \frac{49}{64} \)

Solution :
We need to write both the numerator and the denominator as squares.

  1. The numerator is 49. We know \( 49 = 7 \times 7 = 7^2 \).
  2. The denominator is 64. We know \( 64 = 8 \times 8 = 8^2 \).

Therefore :
\( \frac{49}{64} = \frac{7^2}{8^2} = \left( \frac{7}{8} \right)^2 \)

Final Answer : \( \left( \frac{7}{8} \right)^2 \)


Rational number को power notation में express करो :
\( \frac{49}{64} \)

Solution:
हमें numerator और denominator दोनों को squares के रूप में लिखना है

  1. Numerator है 49. हम जानते हैं \( 49 = 7 \times 7 = 7^2 \).
  2. Denominator है 64. हम जानते हैं \( 64 = 8 \times 8 = 8^2 \).

इसलिए :
\( \frac{49}{64} = \frac{7^2}{8^2} = \left( \frac{7}{8} \right)^2 \)

Final Answer : \( \left( \frac{7}{8} \right)^2 \)


Question 3 (v)

Express the rational number in power notation :
\( 0.49 \)

Solution :
First, convert the decimal into a fraction.
\( 0.49 = \frac{49}{100} \)
Now, write both the numerator and the denominator as squares.

  1. The numerator is 49. We know \( 49 = 7 \times 7 = 7^2 \).
  2. The denominator is 100. We know \( 100 = 10 \times 10 = 10^2 \).

Therefore :
\( 0.49 = \frac{49}{100} = \frac{7^2}{10^2} = \left( \frac{7}{10} \right)^2 \)

Final Answer: \( \left( \frac{7}{10} \right)^2 \)


Rational number को power notation में express करो:
\( 0.49 \)

Solution:
सबसे पहले, decimal को fraction में convert करो।
\( 0.49 = \frac{49}{100} \)
अब, numerator और denominator दोनों को squares के रूप में लिखो

  1. Numerator है 49. हम जानते हैं \( 49 = 7 \times 7 = 7^2 \) .
  2. Denominator है 100. हम जानते हैं \( 100 = 10 \times 10 = 10^2 \).

इसलिए :
\( 0.49 = \frac{49}{100} = \frac{7^2}{10^2} = \left( \frac{7}{10} \right)^2 \)

Final Answer: \( \left( \frac{7}{10} \right)^2 \)


Question 4 Convert negative exponents to positive exponents:

Question 4 (i) \( \left( \frac{4}{5} \right)^{-5} \)

We use the rule for negative exponents : \( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

Applying the rule :
\( \left( \frac{4}{5} \right)^{-5} = \left( \frac{5}{4} \right)^{5} \)

Final Answer : \( \left( \frac{5}{4} \right)^{5} \)


Negative exponent को positive बनाने का rule है : \( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

इस rule को apply करते हैं :
\( \left( \frac{4}{5} \right)^{-5} = \left( \frac{5}{4} \right)^{5} \)

Final Answer : \( \left( \frac{5}{4} \right)^{5} \)


Question 4 (ii) \( \left( -\frac{8}{9} \right)^{-10} \)

We use the rule : \( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

Applying the rule :
\( \left( -\frac{8}{9} \right)^{-10} = \left( -\frac{9}{8} \right)^{10} \)

Important Note : The exponent 10 is even. A negative base raised to an even power results in a positive number.
So, \( \left( -\frac{9}{8} \right)^{10} = \left( \frac{9}{8} \right)^{10} \) .

Final Answer : \( \left( \frac{9}{8} \right)^{10} \)


Rule use करते हैं : \( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

Apply करने पर :
\( \left( -\frac{8}{9} \right)^{-10} = \left( -\frac{9}{8} \right)^{10} \)

Important Note : Exponent 10 एक even number है। Negative base को even power पर raise करने पर result positive होता है।
इसलिए, \( \left( -\frac{9}{8} \right)^{10} = \left( \frac{9}{8} \right)^{10} \) .

Final Answer: \( \left( \frac{9}{8} \right)^{10} \)


Question 4 (iii) \( \left( \frac{7}{8} \right)^9 \)

This expression already has a positive exponent. There is no negative exponent to convert. The expression remains unchanged.

Final Answer : \( \left( \frac{7}{8} \right)^9 \)


इस expression में पहले से ही एक positive exponent है। इसमें कोई negative exponent नहीं है जिसे convert करना हो। Expression वैसा का वैसा ही रहेगा

Final Answer : \( \left( \frac{7}{8} \right)^9 \)


Question 4 (iv) \( \left( -\frac{6}{5} \right)^{-11} \)

We use the rule : \( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

Applying the rule :
\( \left( -\frac{6}{5} \right)^{-11} = \left( -\frac{5}{6} \right)^{11} \)

Important Note : The exponent 11 is odd. A negative base raised to an odd power remains negative. So, the expression stays as \( \left( -\frac{5}{6} \right)^{11} \).

Final Answer: \( \left( -\frac{5}{6} \right)^{11} \)


Rule use करते हैं: \( \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n} \)

Apply करने पर :
\( \left( -\frac{6}{5} \right)^{-11} = \left( -\frac{5}{6} \right)^{11} \)

Important Note : Exponent 11 एक odd number है। Negative base को odd power पर raise करने पर result negative ही रहता है।
इसलिए, expression \( \left( -\frac{5}{6} \right)^{11} \) के रूप में ही रहेगा

Final Answer : \( \left( -\frac{5}{6} \right)^{11} \)


Question 5 (i)

Simplify:
\(\left[ \left( -\frac{2}{3} \right)^3 + \frac{4}{9} \right] + \left( \frac{3}{5} \right)^{-3}\)

Step 1: Simplify the first bracket.
\( \left( -\frac{2}{3} \right)^3 = \frac{(-2)^3}{(3)^3} = \frac{-8}{27} \)
So, the bracket becomes :
\(\left[ \frac{-8}{27} + \frac{4}{9} \right] \)
Find a common denominator (27) :
\( \frac{4}{9} = \frac{12}{27} \)
\( \frac{-8}{27} + \frac{12}{27} = \frac{4}{27} \)

Step 2 : Simplify the second term.
\( \left( \frac{3}{5} \right)^{-3} = \left( \frac{5}{3} \right)^{3} = \frac{125}{27} \)

Step 3 : Add the results.
\( \frac{4}{27} + \frac{125}{27} = \frac{129}{27} = \frac{43}{9} \)

Final Answer: \(\frac{43}{9}\)


Step 1: पहले हम brackets को simplify करेंगे.
\( \left( -\frac{2}{3} \right)^3 = \frac{(-2)^3}{(3)^3} = \frac{-8}{27} \)
तो , Bracket की Value होगी
:
\( \left[ \frac{-8}{27} + \frac{4}{9} \right] \)
Common denominator (27) लेते है
:
\( \frac{4}{9} = \frac{12}{27} \)
\( \frac{-8}{27} + \frac{12}{27} = \frac{4}{27} \)

Step 2: दूसरे term ko simplify करेंगे.
\( \left( \frac{3}{5} \right)^{-3} = \left( \frac{5}{3} \right)^{3} = \frac{125}{27} \)

Step 3: दोनों results को add करेंगे .
\( \frac{4}{27} + \frac{125}{27} = \frac{129}{27} = \frac{43}{9} \)

Final Answer: \(\frac{43}{9}\)


Question 5 (ii)

Simplify:
\((4)^{-3} + \left( -\frac{1}{2} \right)^3 \)

Step 1: Simplify each term.
\( (4)^{-3} = \frac{1}{4^3} = \frac{1}{64} \)
\( \left( -\frac{1}{2} \right)^3 = \frac{(-1)^3}{(2)^3} = \frac{-1}{8} \)

Step 2: Add the results.
Find a common denominator (64) :
\( \frac{-1}{8} = \frac{-8}{64} \)
\( \frac{1}{64} + \left( \frac{-8}{64} \right) = \frac{1 – 8}{64} = \frac{-7}{64} \)

Final Answer: \(\frac{-7}{64})\


Step 1: हर term को हम simplify करेंगे.
\( (4)^{-3} = \frac{1}{4^3} = \frac{1}{64} \)
\( \left( -\frac{1}{2} \right)^3 = \frac{(-1)^3}{(2)^3} = \frac{-1}{8} \)

Step 2: Results को add करेंगे.
Common denominator (64) लेते है :
\( \frac{-1}{8} = \frac{-8}{64} \)
[ \( \frac{1}{64} + \left( \frac{-8}{64} \right) = \frac{1 – 8}{64} = \frac{-7}{64} \)

Final Answer: \(\frac{-7}{64}\)


Question 5 (iii)

Simplify :
\(\left( \frac{3}{7} \right)^2 \times \frac{25}{7} \times \left( -\frac{7}{5} \right)^2 \)

Step 1: Write all terms with exponents.
\( \left( \frac{3}{7} \right)^2 = \frac{3^2}{7^2} = \frac{9}{49} \)
\( \left( -\frac{7}{5} \right)^2 = \frac{(-7)^2}{(5)^2} = \frac{49}{25} \)
The middle term is \(\frac{25}{7} \).

Step 2: Multiply all terms together.
\( \frac{9}{49} \times \frac{25}{7} \times \frac{49}{25} \)
Notice that 49 and 25 cancel out:
\( \frac{9}{\cancel{49}} \times \frac{\cancel{25}}{7} \times \frac{\cancel{49}}{\cancel{25}} = \frac{9}{7} \)

Final Answer: \( \frac{9}{7} \)


Step 1: सभी terms को Exponents के साथ लिखेंगे .
\( \left( \frac{3}{7} \right)^2 = \frac{3^2}{7^2} = \frac{9}{49} \)
\( \left( -\frac{7}{5} \right)^2 = \frac{(-7)^2}{(5)^2} = \frac{49}{25} \)
बीच वाले terms है \(\frac{25}{7}\).

Step 2: सभी terms को multiply करेंगे.
\( \frac{9}{49} \times \frac{25}{7} \times \frac{49}{25} \)
यहाँ 49 और 25 cancel हो जाते है
:
\( \frac{9}{\cancel{49}} \times \frac{\cancel{25}}{7} \times \frac{\cancel{49}}{\cancel{25}} = \frac{9}{7} \)

Final Answer: \(\frac{9}{7}\)


Question 5 (iv)

Simplify:
\(\left( -\frac{3}{4} \right)^3 \times \left[ \left( \frac{3}{4} \right)^{-3} – \left( \frac{2}{3} \right)^3 \right]\)

Step 1: Simplify each exponent.
\( \left( -\frac{3}{4} \right)^3 = \frac{-27}{64} \)
\( \left( \frac{3}{4} \right)^{-3} = \left( \frac{4}{3} \right)^{3} = \frac{64}{27} \)
\( \left( \frac{2}{3} \right)^3 = \frac{8}{27} \)

Step 2: Simplify the expression inside the bracket.
\( \left[ \frac{64}{27} – \frac{8}{27} \right] = \frac{56}{27} \)

Step 3: Multiply the results.
\( \frac{-27}{64} \times \frac{56}{27} \)
Cancel 27 and simplify 56/64 :
\( \frac{-\cancel{27}}{\cancel{64}} \times \frac{\cancel{56}^7}{\cancel{27}} = \frac{-7}{8} \)

Final Answer: \(\frac{-7}{8}\)


Step 1: हर Exponent को Simplify करेंगे.
\( \left( -\frac{3}{4} \right)^3 = \frac{-27}{64} \)
\( \left( \frac{3}{4} \right)^{-3} = \left( \frac{4}{3} \right)^{3} = \frac{64}{27} \)
\( \left( \frac{2}{3} \right)^3 = \frac{8}{27} \)

Step 2: Bracket ke andar wale expression ko simplify karenge.
\( \left[ \frac{64}{27} – \frac{8}{27} \right] = \frac{56}{27} \)

Step 3: Results ko multiply karenge.
\( \frac{-27}{64} \times \frac{56}{27} \)
27 cancel हो जायेगा और 56 & 64 को simplify करेंगे :

\( \frac{-\cancel{27}}{\cancel{64}} \times \frac{\cancel{56}^7}{\cancel{27}} = \frac{-7}{8} \)

Final Answer: \( \frac{-7}{8} \)


Question 5 (v)

Simplify:
\(\left( \frac{2}{3} \right)^4 \times \left( \frac{3}{2} \right)^5 \times \left( \frac{5}{3} \right)^{-2} \times \left( \frac{3}{5} \right)^{-3} \)

Step 1: Convert all negative exponents to positive.
\( \left( \frac{5}{3} \right)^{-2} = \left( \frac{3}{5} \right)^{2} \)
\( \left( \frac{3}{5} \right)^{-3} = \left( \frac{5}{3} \right)^{3} \)

Step 2: Rewrite the entire expression.
\( \left( \frac{2}{3} \right)^4 \times \left( \frac{3}{2} \right)^5 \times \left( \frac{3}{5} \right)^{2} \times \left( \frac{5}{3} \right)^{3} \)

Step 3: Group the same bases together.
\( = \frac{2^4}{3^4} \times \frac{3^5}{2^5} \times \frac{3^2}{5^2} \times \frac{5^3}{3^3} \)

Step 4: Combine the exponents for each base.

  • For base 2 : \(4 – 5 = -1) → (\frac{1}{2^1} \)
  • For base 3 : \(-4 + 5 + 2 – 3 = 0) → (3^0 = 1 \)
  • For base 5 : \(-2 + 3 = 1) → (5^1 \)

Step 5: Write the final expression.
\( \frac{1}{2} \times 1 \times 5 = \frac{5}{2} \)

Final Answer: \( \frac{5}{2} \)


Step 1: सभी Negative Exponents को Positive बनाएंगे .
\( \left( \frac{5}{3} \right)^{-2} = \left( \frac{3}{5} \right)^{2} \)
\( \left( \frac{3}{5} \right)^{-3} = \left( \frac{5}{3} \right)^{3} \)

Step 2: Pure expression को फिर से लिखेंगे.
\( \left( \frac{2}{3} \right)^4 \times \left( \frac{3}{2} \right)^5 \times \left( \frac{3}{5} \right)^{2} \times \left( \frac{5}{3} \right)^{3} \)

Step 3: Same bases को group करेंगे.
\( = \frac{2^4}{3^4} \times \frac{3^5}{2^5} \times \frac{3^2}{5^2} \times \frac{5^3}{3^3} \)

Step 4: हर Base के Exponents को Combine करेंगे .

  • Base 2: \(4 – 5 = -1) → (\frac{1}{2^1} \)
  • Base 3: \(-4 + 5 + 2 – 3 = 0) → (3^0 = 1 \)
  • Base 5: \(-2 + 3 = 1) → (5^1 \)

Step 5: Final expression लिखेंगे.
\( \frac{1}{2} \times 1 \times 5 = \frac{5}{2} \)

Final Answer: \(\frac{5}{2} \)


Question 6

Life Skills Problem: A gardener plants in a pattern :

  • Row 1 : 1 plant
  • Row 2 : 3 plants
  • Row 3 : 9 plants
    If this pattern continues, how many plants will be in the 9th row? Give your answer in exponential form.

Step 1: Identify the Pattern

  • Row 1 : \( 3^0 = 1 \) plant
  • Row 2 : \( 3^1 = 3 \) plants
  • Row 3 : \( 3^2 = 9 \) plants

The number of plants in each row follows powers of 3.

Step 2: Find the Formula
For the n-th row, the number of plants is :
\( 3^{(n-1)} \)

Step 3: Apply for 9th Row
For the 9th row \((n = 9) \) : \( 3^{(9-1)} = 3^8 \)

Final Answer in Exponential Form: \(3^8 \)


Step 1: Pattern को समझेंगे :

  • Row 1 : 1 plant → \(3^0 = 1 \)
  • Row 2 : 3 plants → \(3^1 = 3 \)
  • Row 3 : 9 plants → \(3^2 = 9 \)

हर Row में Plants का Number 3 के Power के हिसाब से Increase हो रहा है.

Step 2: Formula बनाएं
n-th row में plants = \(3^{(n-1)} \)

Step 3: 9th row के लिए calculate करें
9th row के लिए \((n = 9)\ ) : \( 3^{(9-1)} = 3^8 \)

Final Answer : \(3^8 \)


2.2 LAWS OF EXPONENTS WITH INTEGRAL POWERS


Law 1: Product of Powers with Same Base

If you multiply two powers with the same base, you keep the base and add the exponents.
Formula : \( x^m \times x^n = x^{m+n} \)
Example : \( 2^3 \times 2^4 = 2^{3+4} = 2^7 \)

Law 2: Power of a Power


When you raise a power to another power, you keep the base and multiply the exponents.
Formula : \( (x^m)^n = x^{m \times n} \)
Example : \( (3^2)^4 = 3^{2 \times 4} = 3^8 \)

Law 3: Quotient of Powers with Same Base


When you divide two powers with the same base, you keep the base and subtract the exponents.
Formula : \( x^m \div x^n = x^{m-n} \)

Example : \( 5^7 \div 5^2 = 5^{7-2} = 5^5 \)

Law 4: Zero Exponent Rule


Any non-zero number raised to the power of zero is always equal to 1.
Formula : \( x^0 = 1 ) (where ( x \neq 0 )\)
Example : \( 7^0 = 1 ), ( (-4)^0 = 1 ), ( \left(\frac{2}{3}\right)^0 = 1 \)


Solved Example 6

Find the value of : \( \left( -\frac{2}{3} \right)^{-3} \times \left( -\frac{2}{3} \right)^6 \)

Solution:

  • Use the law : \( x^m \times x^n = x^{m+n} \)
  • Here, base = \( -\frac{2}{3} \), exponents = -3 and 6
  • Add exponents: -3 + 6 = 3
  • So : \( \left( -\frac{2}{3} \right)^3 = \frac{-8}{27} \)

Final Answer : \( -\frac{8}{27} \)


Solved Example 7

Express as a single exponential form:

(i) \( \left( -\frac{4}{5} \right)^{-10} \times \left( -\frac{4}{5} \right)^{15} \div \left( -\frac{4}{5} \right)^9 \)

  • Multiply = add exponents, Divide = subtract exponents
  • Combine : \( (-10) + 15 – 9 = -4 \)
  • So : \( \left( -\frac{4}{5} \right)^{-4} \)

(ii) \( \left( \frac{3}{2} \right)^{33} \div \left( \frac{2}{3} \right)^{-35} \)

  • First : \( \left( \frac{2}{3} \right)^{-35} = \left( \frac{3}{2} \right)^{35} \)
  • Now : \( \left( \frac{3}{2} \right)^{33} \div \left( \frac{3}{2} \right)^{35} = \left( \frac{3}{2} \right)^{-2} \)

Final Answers:
(i) \( \left( -\frac{4}{5} \right)^{-4} \)
(ii) \( \left( \frac{3}{2} \right)^{-2} \)


Solved Example 8

Simplify :

(i) \( \left( 4^{-1} + 8^{-1} \right) \div \frac{1}{\left( \frac{3}{2} \right)^{-2}} \)

  • \( 4^{-1} = \frac{1}{4} ), ( 8^{-1} = \frac{1}{8} \)
  • Sum : \( \frac{1}{4} + \frac{1}{8} = \frac{3}{8} \)
  • \( \frac{1}{\left( \frac{3}{2} \right)^{-2}} = \left( \frac{3}{2} \right)^2 = \frac{9}{4} \)
  • Now : \( \frac{3}{8} \div \frac{9}{4} = \frac{3}{8} \times \frac{4}{9} = \frac{1}{6} \)

(ii) \( \left( 5^{-1} \times 5^{-19} \right)^2 \times \left( -\frac{5}{2} \right)^{40} \)

  • \( 5^{-1} \times 5^{-19} = 5^{-20} \)
  • \( (5^{-20})^2 = 5^{-40} \)
  • \( \left( -\frac{5}{2} \right)^{40} = \frac{5^{40}}{2^{40}} \) (since exponent is even)
  • Multiply : \( 5^{-40} \times \frac{5^{40}}{2^{40}} = \frac{1}{2^{40}} = \left( \frac{1}{2} \right)^{40} \)

(iii) \( \left[ \left( -\frac{3}{2} \right)^{20} \right]^{20} \)

  • Power of a power: multiply exponents : \( 20 \times 20 = 400 \)
  • So : \( \left( -\frac{3}{2} \right)^{400} \)
  • Since 400 is even : \( \left( \frac{3}{2} \right)^{400} \)

Final Answers:
(i) \( \frac{1}{6} \)
(ii) \( \left( \frac{1}{2} \right)^{40} \)
(iii) \( \left( \frac{3}{2} \right)^{400} \)


Solved Example 9

By what number should \( (-9)^{-1} ) be multiplied to get ( (-12)^{-1} \) ?

  • Let the number be \( x \)
  • Equation : \( (-9)^{-1} \times x = (-12)^{-1} \)
  • So : \( x = (-12)^{-1} \div (-9)^{-1} \)
  • \( x = \left( -\frac{1}{12} \right) \div \left( -\frac{1}{9} \right) = \left( -\frac{1}{12} \right) \times (-9) = \frac{9}{12} = \frac{3}{4} \)

Final Answer : \( \frac{3}{4} \)


Solved Example 10

If \( \left( \frac{3}{4} \right)^{-6} \times \left( \frac{4}{3} \right)^{-8} = \left( \frac{3}{4} \right)^n \), find \(n\)

  • \( \left( \frac{4}{3} \right)^{-8} = \left( \frac{3}{4} \right)^{8} \)
  • So : \( \left( \frac{3}{4} \right)^{-6} \times \left( \frac{3}{4} \right)^{8} = \left( \frac{3}{4} \right)^n \)
  • Add exponents : \( -6 + 8 = 2 \)
  • So : \( \left( \frac{3}{4} \right)^{2} = \left( \frac{3}{4} \right)^n \)
  • Therefore : \( n = 2 \)

Final Answer : \( n = 2 \)


Exercise 2.2


Question 1 (i) Find the value of :
\(\left[ \left( \left( -\frac{1}{2} \right)^2 \right)^{-2} \right]^{-1} \)

Step-by-step solution using Power of a Power Law :

Law Used : \((x^m)^n = x^{m \times n} \)

1. Multiply all exponents :
\( 2 \times (-2) \times (-1) = 4 \)

2. Raise the base to the resulting power : \( \left( -\frac{1}{2} \right)^4 = \frac{(-1)^4}{2^4} = \frac{1}{16} \)

\( \left( -\frac{1}{2} \right)^4 = \frac{(-1)^4}{2^4} = \frac{1}{16} \)

Final Answer : \(\frac{1}{16} \)


Question 1 (ii)

Find the value of :
\( left{ \left( \frac{1}{4} \right)^{-3} – \left( \frac{1}{2} \right)^{-3} \right} \div \left( \frac{1}{4} \right)^{-3} \)

Step-by-step solution:

  1. Simplify each term using \( a^{-m} = \frac{1}{a^m} \) :
    \( \left( \frac{1}{4} \right)^{-3} = 4^3 = 64 \)
    \( \left( \frac{1}{2} \right)^{-3} = 2^3 = 8 \)
  2. Substitute into the expression:
    \( \left{ 64 – 8 \right} \div 64 = 56 \div 64 \)
  3. Simplify the division:
    \( \frac{56}{64} = \frac{7}{8} \)

Final Answer: \(\frac{7}{8} \)

Exercise 2.2 Question 1 (ii)

Find the value of : \( \left{ \left( \frac{1}{4} \right)^{-3} – \left( \frac{1}{2} \right)^{-3} \right} \div \left( \frac{1}{4} \right)^{-3} \)

Step-by-step solution :

  1. Simplify each term using \( a^{-m} = \frac{1}{a^m} \) :
    \( \left( \frac{1}{4} \right)^{-3} = 4^3 = 64 \)
    \( \left( \frac{1}{2} \right)^{-3} = 2^3 = 8 \)
  2. Substitute into the expression :
    \( \left{ 64 – 8 \right} \div 64 = 56 \div 64 \)
  3. Simplify the division :
    \( \frac{56}{64} = \frac{7}{8} \)

Final Answer : \(\frac{7}{8}\)


Question 1 (iii)

By what number should \( \left( \frac{1}{-2} \right)^{-1} \) be multiplied so that the product equals \( \left( \frac{4}{7} \right)^{-1} \) ?

Step-by-step solution :

Let the required number be \( x \).

  1. Set up the equation :
    \( \left( \frac{1}{-2} \right)^{-1} \times x = \left( \frac{4}{7} \right)^{-1} \)
  2. Simplify both sides :
    \( \left( \frac{1}{-2} \right)^{-1} = (-2)^1 = -2 \)
    \( \left( \frac{4}{7} \right)^{-1} = \frac{7}{4} \)
  3. Substitute into the equation :
    \( -2 \times x = \frac{7}{4} \)
  4. Solve for \( x \) :
    \( x = \frac{7}{4} \div (-2) = \frac{7}{4} \times \left( -\frac{1}{2} \right) = -\frac{7}{8} \)

Final Answer : \( -\frac{7}{8} \)



Question 2 (i)

Express the following into a single exponential form :
\( \left( \frac{2}{3} \right)^{-5} \times \left( \frac{2}{3} \right)^6 \times \left( \frac{2}{3} \right)^2 \)

Step-by-step solution :

Law Used : \( x^m \times x^n \times x^p = x^{m+n+p} \)

  1. Identify the base : \( \frac{2}{3} \)
  2. Add the exponents :
    \( -5 + 6 + 2 = 3 \)
  3. Write in single exponential form :
    \( \left( \frac{2}{3} \right)^3 \)

Final Answer : \( \left( \frac{2}{3} \right)^3 \)


Question 2 (ii)

Express the following into a single exponential form :
\( \left( \frac{-6}{7} \right)^{10} \times \left( \frac{-6}{7} \right)^{-15} \times \left( \frac{-6}{7} \right)^2 \)

Step-by-step solution :

Law Used : \( x^m \times x^n \times x^p = x^{m+n+p} \)

  1. Identify the base : \( \frac{-6}{7} \)
  2. Add the exponents : \(10 + (-15) + 2 = -3 \)
  3. Write in single exponential form : \( \left( \frac{-6}{7} \right)^{-3} \)

Final Answer : \( \left( \frac{-6}{7} \right)^{-3} \)



Question 3 (i)

Express the following into a single exponential form :
\( \left( -\frac{2}{3} \right)^{10} \times \left( -\frac{2}{3} \right)^{-15} \div \left( -\frac{2}{3} \right)^{25} \)

Step-by-step solution :

Laws Used :

  • Multiplication : \( x^m \times x^n = x^{m+n} \)
  • Division : \( x^m \div x^n = x^{m-n} \)
  1. Combine all operations :
    \( \left( -\frac{2}{3} \right)^{10 + (-15) – 25} \)
  2. Simplify the exponent :
    \( 10 – 15 – 25 = -30 \)
  3. Write in single exponential form :
    \( \left( -\frac{2}{3} \right)^{-30} \)

Final Answer : \( \left( -\frac{2}{3} \right)^{-30} \)


Search Results for:

Introduction


  1. What is Matter?
    • Anything that has mass and takes up space is called matter.
    • Everything around us (like a book, water, or air) is matter.
  2. Three States of Matter:
    • Solid: (e.g., Wood, Ice)
      • Has a fixed shape and fixed volume.
      • Particles are tightly packed with strong forces between them.
      • They cannot be compressed and do not flow.
    • Liquid: (e.g., Milk, Water)
      • Has a fixed volume but no fixed shape. It takes the shape of its container.
      • Particles are less tightly packed than solids. Forces are weaker, so liquids can flow.
      • They cannot be compressed easily.
    • Gas: (e.g., Oxygen, Smoke)
      • Has no fixed shape and no fixed volume. It fills the entire container.
      • Particles are very far apart with very weak forces between them.
      • Gases can be compressed easily and flow in all directions.
  3. Recall and Unwind (Answers):
    Let’s fill the blanks using > (greater than) for more, and < (less than) for less.
    1. Intermolecular Force: Solids > Liquids > Gases
    2. Intermolecular Space: Solids < Liquids < Gases
    3. Compressibility: Solids < Liquids < Gases
    4. Rigidity: Solids > Liquids > Gases

  1. Matter क्या है?
    • जिस भी चीज़ का द्रव्यमान (mass) होता है और जो जगह घेरती है (occupies space) , उसे matter कहते हैं।
    • हमारे आस-पास की हर चीज़ (जैसे किताब, पानी, हवा) matter है।
  2. Matter की तीन States (अवस्थाएं):
    • ठोस (Solid): (जैसे- लकड़ी, बर्फ)
      • इनका एक fixed shape ( निश्चित आकार ) और fixed volume ( निश्चित आयतन ) होता है।
      • इनके particles आपस में बहुत पास-पास होते हैं और उनके बीच force बहुत strong होता है।
      • ये दबाए नहीं जा सकते (incompressible) और बहते नहीं (cannot flow) हैं।
    • तरल (Liquid): (जैसे- दूध, पानी)
      • इनका fixed volume (निश्चित आयतन) होता है लेकिन fixed shape नहीं होता। ये जिस बर्तन में डाले जाते हैं उसी का आकार ले लेते हैं।
      • इनके particles solids के मुकाबले थोड़े दूर-दूर होते हैं। Forces कमजोर होते हैं, इसलिए liquids बह सकते (flow) हैं।
      • ये भी दबाए नहीं जा सकते
    • गैस (Gas): (जैसे- ऑक्सीजन, धुआं)
      • इनका ना कोई fixed shape होता है ना fixed volume। ये पूरे container में फैल जाती हैं।
      • इनके particles बहुत ज्यादा दूर-दूर होते हैं और उनके बीच force बहुत weak होता है।
      • Gases आसानी से दबाई (compressible) जा सकती हैं और हर दिशा में flow करती हैं।
  3. Recall and Unwind (जवाब):
    चलिए खाली जगह को > (greater than/ज्यादा) और < (less than/कम) से भरते हैं।
    1. Intermolecular Force (आकर्षण बल): Solids > Liquids > Gases
    2. Intermolecular Space (रिक्त स्थान): Solids < Liquids < Gases
    3. Compressibility ( संपीड्यता ): Solids < Liquids < Gases
    4. Rigidity ( कठोरता ): Solids > Liquids > Gases


Kinetic Molecular Theory of Matter


Imagine you are trying to understand why ice is hard, water flows, and air is all around us. The Kinetic Molecular Theory is like a set of rules that scientists use to explain this.

  1. What is it?
    It is a theory (a well-explained idea) that tells us what matter is made of and how it behaves.
  2. The Main Idea:
    • All matter (everything around us) is made up of very, very tiny particles. These particles can be atoms or molecules.
    • These tiny particles are always moving. Because they are moving, they have energy. This energy of movement is called kinetic energy.
  3. The Rules (Postulates) of the Theory:
    • Rule 1: Matter is made of a huge number of tiny particles (atoms or molecules).
    • Rule 2: These particles are always moving. They never sit completely still. This movement gives them kinetic energy.
    • Rule 3: The particles move in random directions (everywhere!). They keep bumping into each other and when they collide, they transfer energy to each other.
    • Rule 4: When particles gain or lose a lot of energy (like when we heat or cool something), it can cause a change of state (e.g., solid ice can become liquid water).
    • Rule 5: There is empty space between these particles. This space is called intermolecular space.
    • Rule 6: There is an invisible force of attraction that pulls the particles towards each other. This is called intermolecular force of attraction.
      • This force becomes weaker if the space between particles is large.
      • This force becomes stronger if the space between particles is small.

चलो एक कहानी की तरह समझते हैं। यह theory हमें बताती है कि ठोस, तरल, गैस अलग-अलग क्यों दिखते और अलग – अलग behave क्यों करते हैं।

  1. यह क्या है?
    यह एक सिद्धांत (theory) है जो हमें बताता है कि matter किससे बना होता है और उसके छोटे-छोटे particles कैसे behave करते हैं।
  2. मुख्य बात:
    • सारा matter (हमारे आस-पास की सभी चीज़ें) बहुत ही छोटे-छोटे particles से मिलकर बना होता है। ये particles atoms या molecules होते हैं।
    • ये tiny particles हमेशा हिलते-डुलते (move) रहते हैं। क्योंकि वे move कर रहे हैं, उनमें energy होती है। इस movement की energy को kinetic energy कहते हैं।
  3. सिद्धांत के नियम (Postulates):
    • नियम 1: Matter बहुत सारे tiny particles (atoms or molecules) से मिलकर बना होता है।
    • नियम 2: ये particles लगातार motion में रहते हैं। वे कभी पूरी तरह still नहीं बैठते। इस movement के कारण उनमें kinetic energy होती है।
    • नियम 3: Particles random directions में चलते हैं (इधर-उधर!)। वे एक-दूसरे से टकराते (collide) रहते हैं और जब टकराते हैं, तो वे एक-दूसरे को energy transfer करते हैं।
    • नियम 4: जब particles बहुत ज़्यादा energy gain या lose करते हैं (जैसे किसी चीज़ को गर्म या ठंडा करने पर), तो इससे उसकी state change हो सकती है (जैसे, बर्फ पिघलकर पानी बन जाती है)।
    • नियम 5: इन particles के बीच में खाली जगह (empty space) होती है। इस space को intermolecular space कहते हैं।
    • नियम 6: Particles के बीच एक अदृश्य आकर्षण बल (invisible force of attraction) होता है जो उन्हें एक-दूसरे की तरफ खींचता है। इसे intermolecular force of attraction कहते हैं।
      • अगर particles के बीच की space ज़्यादा है तो यह force कमज़ोर हो जाता है।
      • अगर particles के बीच की space कम है तो यह force मजबूत होता है।


Brownian Motion


Brownian motion is the name given to the random, zig-zag movement of tiny particles floating in a liquid or a gas.

A Scottish scientist named Robert Brown was looking at tiny pollen grains in water under a microscope. He noticed that the grains were not staying still. They were constantly jiggling and moving in a random, shaky path, like they were being bumped by invisible things.

We now know that this movement happens because the particles are constantly being bumped and hit by the even smaller, fast-moving molecules of the water (or air) they are floating in. These molecules are always moving (as per the Kinetic Theory) and their collisions push the larger pollen grains around, causing the zig-zag motion.



Diffusion


What is Diffusion?
Diffusion is the process where particles of a substance automatically spread out from a place where there are many of them (high concentration) to a place where there are few of them (low concentration). They do this until they are evenly mixed everywhere.

A Simple Example:
Imagine you open a bottle of perfume at one end of a room. Slowly, the smell spreads to the entire room. This is because the perfume particles move from the bottle (where they are crowded) into the air of the room (where there are none) until the smell is equally strong everywhere.

Diffusion in Different States:

  • In Gases: Gases diffuse very fast and easily. Why? Because their particles have a lot of space between them and move very quickly in all directions.
    • Example: The smell of cooking food reaches you quickly.
  • In Liquids: Liquids also diffuse, but slower than gases. Their particles are closer but can still move around and mix.
    • There are two types of liquids:
      • Miscible Liquids: Liquids that can mix completely with each other. E.g., Milk and water, lemon juice in water.
      • Immiscible Liquids: Liquids that do not mix with each other. E.g., Oil and water.
  • In Solids: Solids do not show diffusion easily (or show it very, very slowly). Why? Because their particles are packed tightly together and can only vibrate in their fixed positions. They cannot move around to mix.
    • Example: If you put two different metal blocks together, their atoms will not mix for a very long time.

Diffusion क्या है?
Diffusion एक ऐसी process है जिसमें किसी substance के particles अपने आप फैल जाते हैं,  उस जगह से जहाँ उनकी संख्या ज़्यादा (high concentration) है वहाँ से उस जगह की तरफ जहाँ उनकी संख्या कम (low concentration) है। वह ऐसा तब तक करते हैं जब तक वह हर जगह एक जैसे (evenly mixed) नहीं मिल  जाते।

एक आसान Example:
मान लो तुम किसी एक room के एक कोने में perfume की bottle खोलते हो। धीरे-धीरे, उसकी खुशबू पूरे room में फैल जाती है। ऐसा इसलिए होता है क्योंकि perfume के particles bottle (जहाँ वे crowded हैं) से room की हवा में (जहाँ शुरू में कोई नहीं हैं) फैलते हैं जब तक खुशबू हर जगह एक जैसी नहीं हो जाती।

अलग-अलग States में Diffusion:

  • Gases में : Gases बहुत तेज़ी और आसानी से diffuse होती हैं। क्यों? क्योंकि उनके particles के बीच बहुत ज़्यादा space होता है और वे बहुत तेज़ी से हर दिशा में move करते हैं।
    • Example : खाना बनने की smell तुरंत तुम तक पहुँच जाती है।
  • Liquids में : Liquids भी diffuse होते हैं, लेकिन gases से धीमी गति से। उनके particles पास-पास होते हैं लेकिन फिर भी इधर-उधर move करके mix हो सकते हैं।
    • Liquids दो तरह के होते हैं:
      • Miscible Liquids: वे liquids जो एक-दूसरे में पूरी तरह mix हो जाते हैं। जैसे- दूध और पानी, नींबू का रस पानी में।
      • Immiscible Liquids: वे liquids जो एक-दूसरे में mix नहीं होते। जैसे- तेल और पानी
  • Solids में: Solids आसानी से diffusion नहीं दिखाते (या बहुत बहुत धीमी गति से दिखाते हैं)। क्यों? क्योंकि उनके particles बहुत टाइट पैक रहते हैं और सिर्फ अपनी जगह पर vibrate कर सकते हैं। वे इधर-उधर move होकर mix नहीं हो पाते।
    • Example: अगर तुम दो अलग-अलग metal के blocks आपस में जोड़ोगे, उनके atoms बहुत लंबे time तक mix नहीं होंगे।

Answers to “Think about it”

Question: Which of these substances will exhibit Brownian movement? Give reason for each.

  1. Pen or juice
    • Answer: Juice
    • Reason: Juice is a liquid. Its particles are moving and can be bumped by smaller water molecules, showing Brownian motion. A pen is a solid. Its particles are fixed and only vibrate, so we cannot see Brownian motion in it.
  2. Carbon dioxide or paper
    • Answer: Carbon dioxide
    • Reason: Carbon dioxide is a gas. Its particles move very fast and freely, constantly colliding and showing Brownian motion. Paper is a solid, so its particles cannot move around freely.
  3. Steam or honey
    • Answer: Steam
    • Reason: Steam is water in its gaseous state. The fast-moving gas particles will show Brownian motion. Honey is a very thick (viscous) liquid. Its particles move very slowly, so Brownian motion is very hard to see compared to a gas.


States of Matter Based on Kinetic Molecular Theory


How do we decide the State of Matter?

The state of matter (solid, liquid, or gas) depends on two main things:

  1. Intermolecular Force of Attraction : How strongly the particles attract each other.
  2. Intermolecular Space : How much empty space is between the particles.

The Kinetic Molecular Theory uses these two ideas to explain why solids, liquids, and gases behave so differently.

1. Solids (ठोस)

  • Packing of Particles: The molecules are very, very close together (closely packed). There is almost no space between them.
  • Force of Attraction: Because the particles are so close, the force that pulls them together is the strongest.
  • Movement: The particles cannot move from their positions. They don’t have enough energy to break the strong force. They can only vibrate (shake) in their fixed spots.
  • Result: This is why solids are hard, have a fixed shape, and a fixed volume.

  • Particles की स्थिति: Solids के molecules बहुत ही पास-पास (closely packed) होते हैं। उनके बीच लगभग कोई space  नहीं होता (negligible space)
  • आकर्षण बल (Force of Attraction) : क्योंकि particles बहुत पास होते हैं, इसलिए उनके बीच का आपस में खिचाव का बल (Force of Attraction) सबसे मजबूत (strongest) होता है।
  • Movement : Particles अपनी जगह से move नहीं कर सकते। उनमें इतनी energy नहीं होती कि वह इस strong force को तोड़ सकें। वे सिर्फ अपनी fixed जगह पर काँप (vibrate) सकते हैं।
  • नतीजा (Result): इसीलिए solids hard होते हैं, और उनका एक fixed shape और fixed volume होता है।


Question: Match the following.

Column AColumn B
(a) Tiffin box(i) Highest intermolecular force
(b) Cough syrup(ii) Highest intermolecular space
(c) Smoke(iii) Molecules of similar type
(d) Cohesion(iv) Molecules of different type
(e) Adhesion(v) Fixed volume

Answers and Explanations

1. (a) Tiffin box → (i) Highest intermolecular force

  • Explanation: A tiffin box is made of metal or plastic, which is a solid. In solids, the molecules are packed very tightly together. This means the force of attraction between the molecules (intermolecular force) is the strongest.
  • Tiffin box metal या plastic का बना होता है, जो एक solid (ठोस) है। Solids में molecules बहुत Tight Pack रहते हैं। इसका मतलब है कि molecules के बीच का आकर्षण बल (Force of Attraction) सबसे मजबूत (strongest) होता है।

2. (b) Cough syrup → (v) Fixed volume

  • Explanation: Cough syrup is a liquid. A key property of liquids is that they have a fixed volume. Even though they take the shape of their container, the amount of space they occupy (their volume) does not change easily.
  • Cough syrup एक liquid (तरल) है। Liquids की एक मुख्य property यह है कि उनका एक fixed volume (निश्चित आयतन) होता है। भले ही वे अपने container का आकार ले लें, लेकिन उनके द्वारा घेरी गई जगह (volume) आसानी से नहीं बदलती।

3. (c) Smoke → (ii) Highest intermolecular space

  • Explanation: Smoke is a gas. In gases, the molecules are very far apart from each other. This means the empty space between the molecules (intermolecular space) is the largest compared to solids and liquids.
  • Smoke एक gas (गैस) है। Gases में molecules एक-दूसरे से बहुत दूर होते हैं। इसका मतलब है कि molecules के बीच की खाली जगह (intermolecular space) solids और liquids की तुलना में सबसे ज़्यादा (largest) होती है।

4. (d) Cohesion → (iii) Molecules of similar type

  • Explanation: Cohesion is the force of attraction that acts between molecules of the same kind of substance. For example, it is the force that holds water molecules together to form a drop.
  • Cohesion (संसजन बल) वह आकर्षण बल है जो एक ही तरह (similar type) के molecules के बीच काम करता है। उदाहरण के लिए, यही बल पानी के molecules को आपस में जोड़कर एक बूंद बनाता है।

5. (e) Adhesion → (iv) Molecules of different type

  • Explanation: Adhesion is the force of attraction that acts between molecules of different substances. For example, it is the force that makes water stick to the glass of a window.
  • Adhesion (आसंजन बल) वह आकर्षण बल है जो अलग-अलग तरह (different type) के molecules के बीच काम करता है। उदाहरण के लिए, यही बल पानी को किसी शीशे की खिड़की पर चिपकाए रखता है।


Properties of States of Matter & Kinetic Energy


This part of the chapter tells us two main things:

1. What decides if matter will change its state?
The change of state (like solid ice melting into liquid water) depends on two things:

  • Intermolecular Space: The amount of empty space between the particles.
  • Intermolecular Force: The strength of the invisible force that pulls the particles together.

When we heat or cool a substance, we are changing these two things. For example:

  • On Heating: Particles get more energy, start moving faster, need more space, and the force between them becomes weaker. This can change a solid to a liquid or a liquid to a gas.
  • On Cooling: Particles lose energy, move slower, need less space, and the force between them becomes stronger. This can change a gas to a liquid or a liquid to a solid.

2. The link between Temperature and Kinetic Energy

  • Kinetic Energy is the energy of movement. Particles that are moving have kinetic energy.
  • Temperature is a measure of how fast the particles of a substance are moving on average.

The important rule is:

As the temperature increases, the kinetic energy of the particles also increases.


यह हिस्सा हमें दो मुख्य बातें बताता है:

1. Matter की state कब बदलती है?
Matter की state का बदलना ( जैसे ठोस बर्फ का पिघलकर तरल पानी बनना ) दो चीज़ों पर निर्भर करता है:

  • Intermolecular Space : Particles के बीच की खाली जगह।
  • Intermolecular Force : Particles को आपस में खींचने वाला अदृश्य बल।

जब हम किसी चीज़ को गर्म या ठंडा करते हैं, तो हम इन दोनों चीज़ों को बदल रहे होते हैं। जैसे :

  • गर्म करने पर : Particles को ज़्यादा energy मिलती है, वे तेज़ी से हिलने लगते हैं, उन्हें ज़्यादा जगह चाहिए होती है, और उनके बीच का Force कमज़ोर पड़ जाता है। इससे Solids चीज़ें Liquids बन सकती है या Liquid चीज़ें Gases बन सकती है।
  • ठंडा करने पर : Particles की energy कम हो जाती है, वे धीरे चलते हैं, उन्हें कम जगह चाहिए होती है, और उनके बीच का Force मजबूत हो जाता है। इससे Gases convert Liquid हो सकते है या Liquids convert हो सकते है Solids में।

2. Temperature और Kinetic Energy का कनेक्शन

  • Kinetic Energy : movement की energy है। जो particles move कर रहे हैं, उनमें kinetic energy होती है।
  • Temperature : यह मापता है कि किसी substance के particles औसतन कितनी तेज़ी से move कर रहे हैं।

यहाँ महत्वपूर्ण नियम है:

जैसे-जैसे temperature बढ़ता है, वैसे-वैसे particles की kinetic energy भी बढ़ती है।



Properties of Solids, Liquids, and Gases


1. Properties of SOLIDS

  • Shape and Volume: Solids have a fixed shape and a fixed volume.
  • Particles: The molecules are closely packed with very little space between them.
  • Movement: The particles cannot move from their spots. They only vibrate in their fixed positions.
  • Force: The intermolecular force is very strong.
  • Energy: They have low kinetic energy.
  • Effect of Temperature: When temperature changes, the kinetic energy of the particles changes.

  • Shape और Volume: Solids का एक fixed shape होता है और एक fixed volume होता है।
  • Particles: Solid के molecules बहुत पास-पास (closely packed) होते हैं। उनके बीच बहुत कम space होता है।
  • Movement: ये particles अपनी जगह से move नहीं कर सकते। वे सिर्फ अपनी जगह पर काँपते (vibrate) रहते हैं।
  • Force: Particles के बीच जो intermolecular force है, वह बहुत strong होता है।
  • Energy: उनमें kinetic energy बहुत कम होती है।
  • Temperature का effect: जब temperature बदलती है, तो particles की kinetic energy बदल जाती है।

2. Properties of LIQUIDS

  • Shape and Volume: Liquids have no fixed shape but they have a fixed volume. They take the shape of their container.
  • Particles: The molecules are less closely packed than in solids. There is more space between them.
  • Movement: The particles can move around and slide past each other. This is why liquids flow.
  • Force: The intermolecular force is weaker than in solids.
  • Effect of Temperature: When temperature changes, the kinetic energy of the particles changes.

  • Shape और Volume: Liquids का कोई fixed shape नहीं होता, लेकिन उनका एक fixed volume होता है। वे अपने container का shape ले लेते हैं।
  • Particles: Liquid के molecules solid के मुकाबले थोड़े दूर (less closely packed) होते हैं। उनके बीच ज़्यादा space होता है।
  • Movement: Particles इधर-उधर move कर सकते हैं और एक-दूसरे के पास से slide कर सकते हैं। इसीलिए liquids flow कर सकते हैं।
  • Force: Particles के बीच जो intermolecular force है, वह solid से weaker होता है।
  • Temperature का effect: जब temperature बदलती है, तो particles की kinetic energy बदल जाती है।

3. Properties of GASES

  • Shape and Volume: Gases have no fixed shape and no fixed volume. They fill their entire container.
  • Particles: The molecules are very far apart. The intermolecular space is the maximum.
  • Movement: The particles move very fast and randomly in all directions.
  • Force: The intermolecular force is very weak (almost zero).
  • Collisions: When they collide, it is elastic (no loss of energy).
  • Effect of Temperature: When temperature changes, the kinetic energy of the particles changes.

  • Shape और Volume: Gases का ना कोई fixed shape होता है ना fixed volume। वे पूरे container को भर देती हैं।
  • Particles: Gas के molecules बहुत दूर-दूर (very far apart) होते हैं। उनके बीच की space सबसे ज़्यादा (maximum) होती है।
  • Movement: Particles बहुत तेज़ और अनियमित (randomly) तरीके से हर direction में move करते हैं।
  • Force: Particles के बीच जो intermolecular force है, वह बहुत weak होता है।
  • Collisions: जब वे आपस में टकराते (collide) हैं, तो वह elastic होता है (energy loss नहीं होता)।
  • Temperature का effect: जब temperature बदलती है, तो particles की kinetic energy बदल जाती है।


Change of State of Matter


What is Change of State?
It is when a substance changes from one physical state to another. For example, when solid ice changes to liquid water.

Why does this happen?
This change happens because of two things:

  1. The movement of its molecules.
  2. The force that holds the molecules together.

What happens when we HEAT a substance? (Adding Energy)

Example: Solid Ice to Liquid Water to Water Vapour

  1. Heating a Solid:
    • When we heat a solid, its molecules gain energy (kinetic energy).
    • They start vibrating faster.
    • They try to overcome the force holding them together.
    • The space between molecules increases.
    • The force between molecules becomes weaker.
    • Finally, the solid melts and becomes a liquid.
  2. Heating a Liquid:
    • On further heating, the liquid molecules gain even more energy.
    • They start moving around randomly very fast.
    • The space between them increases even more.
    • The force between them becomes very weak.
    • Finally, the liquid boils and becomes a gas.

गर्म करने पर क्या होता है? (Adding Energy)

  1. Solid को गर्म करना:
    • जब हम solid को गर्म करते हैं, उसके molecules energy gain करते हैं।
    • वे तेज़ हिलने लगते हैं।
    • वे उन्हें पकड़ कर रखने वाले force को overcome करने की कोशिश करते हैं।
    • Molecules के बीच का space बढ़ जाता है।
    • Molecules के बीच का force कमज़ोर हो जाता है।
    • आखिर में, solid पिघल कर liquid बन जाता है।
  2. Liquid को गर्म करना:
    • ज़्यादा गर्म करने पर, liquid के molecules और भी ज़्यादा energy gain करते हैं।
    • वे बहुत तेज़ और randomly move करने लगते हैं।
    • उनके बीच का space और बढ़ जाता है।
    • उनके बीच का force बहुत weak हो जाता है।
    • आखिर में, liquid उबल कर gas बन जाती है।

What happens when we COOL a substance? (Removing Energy)

Example: Water Vapour to Liquid Water to Solid Ice

  • When we cool a substance, its molecules lose energy.
  • They start moving slower.
  • The force of attraction between them increases.
  • The molecules come closer together, so the space between them decreases.
  • With more cooling, a gas changes to a liquid (like steam becoming water droplets).
  • With even more cooling, the liquid changes to a solid (like water freezing into ice).

ठंडा करने पर क्या होता है? (Removing Energy)

  • जब हम किसी चीज़ को ठंडा करते हैं, उसके molecules energy lose करते हैं।
  • वे धीमे move करने लगते हैं।
  • उनके बीच का आकर्षण बल (force of attraction) बढ़ जाता है।
  • Molecules एक-दूसरे के पास आने लगते हैं, इसलिए उनके बीच का space कम हो जाता है।
  • ज़्यादा cooling से, gas liquid बन जाती है (जैसे steam के water की बूंदें बन जाना)।
  • और ज़्यादा cooling से, liquid solid बन जाता है (जैसे पानी freeze होकर बर्फ बन जाना)।



1. Fusion (Melting)

  • What it is: The process where a solid changes into a liquid by absorbing heat.
  • Important Point: During melting, the temperature does not change until all the solid has become liquid.
  • Melting Point: The fixed temperature at which a solid melts.
    • Example: Ice (solid) melts into water (liquid) at 0°C.

  • यह क्या है : वह process जहाँ एक solidheat सोखकर (absorbing heat)liquid में बदल जाता है।
  • महत्वपूर्ण बात : पिघलने के दौरान, temperature नहीं बदलती जब तक सारा solid liquid नहीं बन जाता।
  • Melting Point : वह fixed temperature जिस पर solid पिघलता है।
    • उदाहरण : बर्फ (solid) पिघलकर पानी (liquid) 0°C पर बनती है।

2. Vaporisation (Boiling)

  • What it is : The process where a liquid changes into its vapour or gas by absorbing heat at a constant temperature.
  • How it happens : This happens through boiling.
  • Boiling Point : The fixed temperature at which a liquid starts to boil.
    • Example : Water (liquid) boils and becomes steam (gas) at 100°C.

  • यह क्या है : वह process जहाँ एक liquidheat सोखकर, एक constant temperature पर अपनी gas अवस्था में बदल जाता है।
  • यह कैसे होता है : यह उबालने (boiling) से होता है।
  • Boiling Point : वह fixed temperature जिस पर liquid उबलना शुरू करता है।
    • उदाहरण : पानी (liquid) उबलकर भाप (gas) 100°C पर बनता है।

3. Solidification (Freezing)

  • What it is: The process where a liquid changes into a solid by releasing heat at a constant temperature.
  • Freezing Point: The constant temperature at which a liquid changes into a solid.
    • Example: Water (liquid) freezes and becomes ice (solid) at 0°C.
  • Note: The melting point of a solid is the same as the freezing point of its liquid.

  • यह क्या है: वह process जहाँ एक liquidheat छोड़कर (releasing heat), एक constant temperature पर solid में बदल जाता है।
  • Freezing Point: वह constant temperature जिस पर liquid solid बन जाता है।
    • उदाहरण: पानी (liquid) जमकर बर्फ (solid) 0°C पर बनता है।
  • नोट: एक solid का melting point उसके liquid के freezing point के बराबर होता है।

4. Condensation

  • What it is: The process where a gas changes into its liquid state at a particular temperature.
  • Condensation Point: The fixed temperature at which a gas changes to a liquid.
  • Important Point: For most substances, the condensation point and boiling point are the same. The difference is that heat is absorbed during boiling, but heat is released during condensation.
    • Example: Steam (gas) cools down and condenses into water droplets (liquid).

  • यह क्या है: वह process जहाँ एक gas एक particular temperature पर अपनी liquid अवस्था में बदल जाता है।
  • Condensation Point: वह fixed temperature जिस पर gas liquid बन जाती है।
  • महत्वपूर्ण बात: ज़्यादातर substances के लिए, condensation point और boiling point एक ही होते हैं। फर्क सिर्फ इतना है कि उबालने पर heat सोखी जाती है, लेकिन condensation पर heat छोड़ी जाती है
    • उदाहरण: भाप (gas) ठंडी होकर घन्नीभूत (condenses) होकर पानी की बूंदों (liquid) में बदल जाती है।

5. Sublimation

  • What it is: The process where a substance directly changes from its solid state to its gaseous state without becoming a liquid in between.
  • Example: Camphor (solid) slowly changes into gaseous form at room temperature.

  • यह क्या है: वह process जहाँ एक substance बीच में liquid बने बिना, सीधे अपनी solid अवस्था से gaseous अवस्था में बदल जाता है।
  • उदाहरण: कपूर (solid) room temperature पर ही धीरे-धीरे gaseous form में बदल जाता है।

6. Deposition

  • What it is: The process where a substance directly changes from its gaseous state into its solid state without becoming a liquid in between.
  • Example: On cooling, the vapour from naphthalene balls (used in toilets) directly changes back into solid naphthalene.

  • यह क्या है: वह process जहाँ एक substance बीच में liquid बने बिना, सीधे अपनी gaseous अवस्था से solid अवस्था में बदल जाता है।
  • उदाहरण: ठंडा करने पर, नेफ्थलीन बॉल्स (toilets में use होती हैं) की vapour सीधे solid नेफ्थलीन में बदल जाती है।


Evaporation

What is Evaporation?
Evaporation is the process where a liquid slowly changes into its gaseous state (vapour) without boiling.

Key Point: This happens below the boiling point of the liquid. The liquid does not need to be heated until it boils to turn into vapour.

Everyday Example:
Have you noticed that wet utensils dry up on their own after you wash them? This is because of evaporation. The water on the utensils slowly turns into water vapour and disappears into the air, without anyone boiling it.

Evaporation vs. Boiling (Vaporisation):

FeatureEvaporationBoiling (Vaporisation)
TemperatureHappens below the boiling point, at any temperature.Happens only at the boiling point.
SpeedA slow process.A fast and rapid process.
LocationHappens only from the surface of the liquid.Happens from all parts of the liquid, forming bubbles.

यह क्या है?
Evaporation वह process है जहाँ एक liquid धीरे-धीरे अपनी gaseous state (vapour) में बदल जाता है बिना उबले

मुख्य बात: यह liquid के boiling point से नीचे के temperature पर होता है। Liquid को vapour में बदलने के लिए उबालना ज़रूरी नहीं है।

रोज़मर्रा का उदाहरण:
क्या तुमने गौर किया है कि बर्तन धोने के बाद वे अपने आप सूख जाते हैं? यह evaporation की वजह से होता है। बर्तनों पर का पानी धीरे-धीरे water vapour में बदलकर हवा में मिल जाता है, बिना उबाले।

Evaporation और Boiling (Vaporisation) में अंतर:

FeatureEvaporationBoiling (Vaporisation)
TemperatureBoiling point से नीचे किसी भी temperature पर होता है।सिर्फ boiling point पर होता है।
Speedएक धीमी (slow) process है।एक तेज़ और rapid process है।
Locationसिर्फ liquid की सतह (surface) से होता है।Liquid के सभी हिस्सों से होता है, bubbles बनते हैं।

Of course! Here is a simple explanation of the Law of Conservation of Mass.


Topic: Law of Conservation of Mass


What is the Law?
The Law of Conservation of Mass states a very simple but important rule:

Mass can neither be created nor destroyed.

This means that in any change—whether it’s physical (like melting ice) or chemical (like burning wood)—the total mass of all substances involved stays the same before and after the change.

  • The shape, size, or volume of matter may change.
  • But the total mass always remains constant.

Why is this true?
This law holds true because the atoms that make up everything are stable. They are not created or destroyed in a change; they are just rearranged.

Scientist: Antoine Lavoisier
He is the scientist who clearly stated this law in the 18th century. He is often called the “Father of Modern Chemistry.”


Examples to Understand the Law

Example 1: Melting Ice (Physical Change)

  • What you do: Add 30 grams of ice to 50 grams of water in a glass.
  • Mass before melting: 30 g (ice) + 50 g (water) = 80 grams
  • What happens: The ice melts and turns into water.
  • Mass after melting: The total water in the glass = 80 grams

Conclusion: The mass before and after the change is the same. Mass was conserved.

Example 2: Burning Wood (Chemical Change)

  • What you see: When wood burns, it leaves behind only a little ash. It seems like mass is lost.
  • What actually happens:
    • The wood reacts with oxygen from the air.
    • The burnt wood (ash) has less mass, but the missing mass has not disappeared!
    • It has escaped into the air as gases like carbon dioxide (CO₂), carbon monoxide (CO), and water vapour.
  • Mass before burning = Mass of wood + Mass of oxygen used from the air
  • Mass after burning = Mass of ash + Mass of gases produced (CO₂, CO, etc.)

Conclusion: If you could collect and measure all the substances (the ash AND the gases), the total mass would be equal to the mass of the wood and oxygen before burning.

Example 3: Burning Magnesium (Chemical Reaction)

  • Reaction: Magnesium + Oxygen → Magnesium Oxide
  • Mass of Reactants: 48 g of Magnesium + ? g of Oxygen
  • Mass of Product: 80 g of Magnesium Oxide
  • To find the mass of oxygen used: 80 g (product) – 48 g (magnesium) = 32 g of oxygen.
  • So, 48 g + 32 g = 80 g. The total mass of reactants equals the total mass of the product.

The Key Idea in a Chemical Reaction:

  • The reactants (starting substances) break apart into atoms.
  • These atoms then rearrange themselves to form new products (new substances).
  • No atoms are lost or gained. The same atoms are just used to make different molecules.
  • Therefore, Total Mass of Reactants = Total Mass of Products.

यह नियम क्या है?
द्रव्यमान के संरक्षण का नियम (Law of Conservation of Mass) एक बहुत Simple नियम बताता है:

न तो द्रव्यमान(Mass) बनाया जा सकता है ; और न ही नष्ट किया जा सकता है।

इसका मतलब है कि किसी भी बदलाव में—चाहे वह physical हो (जैसे बर्फ पिघलना) या chemical हो (जैसे लकड़ी जलना)—शामिल सभी पदार्थों का कुल द्रव्यमान (total mass) बदलाव से पहले और बाद में एक समान रहता है

  • Matter का आकार, shape, या volume बदल सकता है।
  • लेकिन कुल द्रव्यमान हमेशा constant रहता है।

वैज्ञानिक: एंटोनी लवॉइजियर
यह वह scientist हैं जिन्होंने 18वीं सदी में इस नियम को स्पष्ट किया। उन्हें “आधुनिक रसायन विज्ञान का जनक” कहा जाता है।


उदाहरण (Examples)

उदाहरण 1: बर्फ का पिघलना (Physical Change)

  • आप क्या करते हैं: एक glass में 30 grams बर्फ और 50 grams पानी मिलाइए।
  • पिघलने से पहले mass: 30 g (बर्फ) + 50 g (पानी) = 80 grams
  • क्या होता है: बर्फ पिघलकर पानी बन जाती है।
  • पिघलने के बाद mass: glass में कुल पानी = 80 grams

निष्कर्ष: बदलाव से पहले और बाद में mass एक जैसी है। Mass संरक्षित (conserved) रही।

उदाहरण 2: लकड़ी का जलना (Chemical Change)

  • आप क्या देखते हैं: लकड़ी जलने पर सिर्फ थोड़ी सी राख बचती है। ऐसा लगता है mass कम हो गई।
  • वास्तव में क्या होता है:
    • लकड़ी हवा से oxygen के साथ reaction करती है।
    • जली हुई लकड़ी (राख) का mass कम है, लेकिन गायब mass गायब नहीं हुई है!
    • यह carbon dioxide (CO₂), carbon monoxide (CO), और water vapour जैसी gases के रूप में हवा में मिल गई है।
  • जलने से पहले mass = लकड़ी का mass + हवा से ली गई oxygen का mass
  • जलने के बाद mass = राख का mass + बनी gases का mass (CO₂, CO, आदि)

निष्कर्ष: अगर आप सभी पदार्थों (राख और gases दोनों) को इकट्ठा करके तौल सकें, तो कुल mass लकड़ी और oxygen के पहले के mass के बराबर होगी।

उदाहरण 3: मैग्नीशियम का जलना (Chemical Reaction)

  • अभिक्रिया (Reaction): मैग्नीशियम + ऑक्सीजन → मैग्नीशियम ऑक्साइड
  • अभिकारकों का mass (Reactants): 48 g मैग्नीशियम + ? g ऑक्सीजन
  • उत्पाद का mass (Product): 80 g मैग्नीशियम ऑक्साइड
  • ऑक्सीजन का mass पता करने के लिए: 80 g (उत्पाद) – 48 g (मैग्नीशियम) = 32 g ऑक्सीजन
  • इसलिए, 48 g + 32 g = 80 g। अभिकारकों का कुल mass उत्पाद के कुल mass के बराबर है।

Chemical Reaction का मुख्य विचार:

  • अभिकारक (reactants) टूटकर atoms में बदल जाते हैं।
  • यह atoms फिर rearrange होकर नए उत्पाद (products) बनाते हैं।
  • कोई atoms खोती या बनती नहीं है। एक ही atoms अलग molecules बनाने के लिए इस्तेमाल होते हैं।
  • इसलिए, अभिकारकों का कुल द्रव्यमान = उत्पादों का कुल द्रव्यमान


Of course! Here is a simple summary of the chapter’s main points.


Chapter Summary

Let’s quickly revise everything we learned in this chapter.

1. What is Matter?

  • Matter is anything that has mass and occupies space.
  • It exists in three main states: Solid, Liquid, and Gas.

2. States of Matter & Their Properties:

  • Solids: Have a fixed shape and a fixed volume.
  • Liquids: Have a fixed volume but no fixed shape. They take the shape of their container.
  • Gases: Have no fixed shape and no fixed volume. They fill their entire container.

3. Kinetic Molecular Theory:

  • This theory explains why matter has different states.
  • It says that all matter is made of very tiny particles (molecules) that are always moving.
  • This movement gives them energy called kinetic energy.
  • There is a force of attraction between these particles.
  • There is space between these particles.

4. What Decides the State?

  • The state of matter (solid, liquid, gas) depends on two things:
    1. The strength of the force between the particles.
    2. The amount of space between the particles.

5. Law of Conservation of Mass:

  • This is a very important law.
  • It states that mass can neither be created nor destroyed.
  • In any physical change (like melting ice) or chemical change (like burning wood), the total mass always remains the same.
  • In a chemical reaction: Total mass of reactants = Total mass of products.

चलिए इस chapter की सभी मुख्य बातों को quickly revise करते हैं।

1. Matter क्या है?

  • Matter वह सब कुछ है जिसका mass (द्रव्यमान) होता है और जो space (जगह) घेरता है।
  • यह तीन main states में मिलता है: Solid, Liquid, और Gas

2. States of Matter और उनके गुण:

  • Solids: इनका एक fixed shape और एक fixed volume होता है।
  • Liquids: इनका एक fixed volume होता है लेकिन कोई fixed shape नहीं होता। ये अपने container का shape ले लेते हैं।
  • Gases: इनका ना कोई fixed shape होता है ना fixed volume। ये अपने पूरे container को भर देती हैं।

3. Kinetic Molecular Theory:

  • यह theory समझाती है कि matter के अलग-अलग states क्यों होते हैं।
  • यह कहती है कि सारा matter बहुत छोटे particles (molecules) से बना है जो हमेशा move करते रहते हैं।
  • इस movement से उन्हें kinetic energy नामक energy मिलती है।
  • इन particles के बीच एक आकर्षण बल (force of attraction) होता है।
  • इन particles के बीच space होता है।

4. State क्या तय करता है?

  • Matter की state (solid, liquid, gas) दो चीज़ों पर निर्भर करती है:
    1. Particles के बीच के बल की strength
    2. Particles के बीच के space की मात्रा

5. द्रव्यमान के संरक्षण का नियम (Law of Conservation of Mass):

  • यह एक बहुत important law है।
  • यह बताती है कि न तो mass बनाया जा सकता है और न ही नष्ट किया जा सकता है
  • किसी भी physical change (जैसे बर्फ पिघलना) या chemical change (जैसे लकड़ी जलना) में, कुल mass हमेशा एक जैसी रहती है
  • एक chemical reaction में: अभिकारकों का कुल mass = उत्पादों का कुल mass


Exercise – Question & Answers



Reference Exercise Questions and Answers of VIVA Publication



A. Fill in the blanks.

  1. The intermolecular attraction is weaker in gases compared to liquids.
    • Explanation: In gases, the particles are far apart, so the force of attraction between them is very weak.
  2. The kinetic energy of molecules increases as temperature increases.
    • Explanation: When you heat something, you give its particles more energy, making them move faster.
  3. Liquids have a fixed volume but do not have a fixed shape.
    • Explanation: A liquid will always take the shape of its container, but the amount of liquid (its volume) stays the same.
  4. Change in temperature results in change of state of matter.
    • Explanation: Heating or cooling a substance can make it change from solid to liquid, liquid to gas, etc.
  5. The intermolecular spaces are maximum in gases.
    • Explanation: Gas particles are spread far apart from each other, with a lot of empty space between them.

B. State whether the following statements are true (T) or false (F).

  1. Brownian movement is maximum in solids.
    • Answer: F (False)
    • Explanation: Brownian movement is maximum in gases because their particles move freely and randomly. In solids, particles only vibrate in place.
  2. The molecules of solids only vibrate at their fixed positions.
    • Answer: T (True)
    • Explanation: The molecules in a solid are held in place by strong forces, so they cannot move around and can only vibrate.
  3. The process of converting ice to water is called solidification.
    • Answer: F (False)
    • Explanation: The process of converting ice to water is called melting or fusion. Solidification is the opposite process, where a liquid turns into a solid.
  4. The mass of wood and mass of ash after burning remains the same.
    • Answer: F (False)
    • Explanation: The mass of the ash is less than the mass of the wood because the carbon in the wood combines with oxygen from the air to form gases like carbon dioxide, which escape into the atmosphere.
  5. Barium chloride is safe to use with bare hands.
    • Answer: F (False)
    • Explanation: The chapter specifically states that “Barium chloride is a toxic chemical and direct contact with barium chloride should be avoided.”

C. Write down the changes in kinetic energy, intermolecular attraction and intermolecular spaces that will occur in the following.

  1. When water is frozen to ice
    • Kinetic Energy: Decreases
    • Intermolecular Attraction: Increases
    • Intermolecular Spaces: Decreases
    • Explanation: When water is frozen, energy is removed. The particles slow down, come closer together, and the forces between them become stronger, forming a solid structure.
  2. When gas is compressed to liquid
    • Kinetic Energy: Decreases
    • Intermolecular Attraction: Increases
    • Intermolecular Spaces: Decreases
    • Explanation: Compressing a gas and cooling it removes energy from the particles. They slow down, get closer together, and the forces of attraction become strong enough to hold them together as a liquid.
  3. When camphor changes to gaseous state
    • Kinetic Energy: Increases
    • Intermolecular Attraction: Decreases
    • Intermolecular Spaces: Increases
    • Explanation: This process is called sublimation. The solid camphor particles gain energy, start moving very fast, overcome the forces of attraction, and spread far apart to become a gas.

D. Choose the correct answer.

  1. Which is a property of solids?
    (a) Large intermolecular spaces
    (b) Compressible
    (c) High kinetic energy
    (d) Rigid
    • Explanation: Solids are rigid, meaning they have a fixed shape and are hard to change. The other options are properties of gases.
  2. Which is a property of liquids?
    (a) Fixed shape
    (b) Very low intermolecular attraction
    (c) Fixed volume
    (d) Compressible
    • Explanation: Liquids have a fixed volume but take the shape of their container. They are not easily compressible.
  3. Which is a property of gases?
    (a) Fixed shape
    (b) Fixed volume
    (c) Rigid
    (d) Lowest force of attraction
    • Explanation: The particles in a gas are very far apart, so the intermolecular force of attraction is the lowest among the three states of matter.
  4. Which of the following is the process by which gas changes to liquid?
    (a) Solidification
    (b) Sublimation
    (c) Condensation
    (d) Vaporisation
    • Explanation: Condensation is the process where a gas turns into a liquid, like when water vapour forms dew.
  5. What is the mass of product(s), if the mass of reactants is 10 g and 40 g each?
    (a) 10 g
    (b) 40 g
    (c) 50 g
    (d) 60 g
    • Explanation: According to the Law of Conservation of Mass, the total mass of the reactants (10 g + 40 g = 50 g) is equal to the total mass of the products.

E. Match the columns.

Column AColumn B
1. Change of phase(a) Loosely held molecules
2. Solids(b) Change in kinetic energy
3. Gases(c) Naphthalene
4. Liquids(d) Tightly packed molecules
5. Sublimation(e) Shape of container

Answer:

Column AColumn B
1. Change of phase(b) Change in kinetic energy
2. Solids(d) Tightly packed molecules
3. Gases(a) Loosely held molecules
4. Liquids(e) Shape of container
5. Sublimation(c) Naphthalene

Explanation of Matches:

  1. Change of phase happens when particles gain or lose kinetic energy, changing their motion and arrangement.
  2. Solids have molecules that are tightly packed together in a fixed structure.
  3. Gases have molecules that are very far apart and are loosely held, moving freely.
  4. Liquids take the shape of their container because they can flow.
  5. Sublimation is when a solid turns directly into a gas. Naphthalene balls are a common example of this.

F. Give reasons for the following statements.

  1. The particles in a solid remain in fixed positions.
    • Reason: In solids, the intermolecular force of attraction is the strongest and the intermolecular space is negligible. The molecules are arranged in a well-defined order and the kinetic energy is not enough to break the strong force, so they only vibrate at their fixed positions.
  2. Increase in temperature causes increase in kinetic energy.
    • Reason: The kinetic molecular theory states that particles possess kinetic energy due to their constant motion. As temperature increases, the particles gain energy and move faster, which means their kinetic energy increases.
  3. The intermolecular spaces in liquids is more than that in solids.
    • Reason: The molecules in liquids are less closely packed compared to solids. Therefore, the intermolecular space in liquids is more than in solids, which allows the molecules to move from one position to another.
  4. The mass of reactants is equal to the mass of products.
    • Reason: This is due to the Law of Conservation of Mass, which states that mass can neither be created nor destroyed. The atoms in the reactants are the same as the ones present in the products, only rearranged, thus conserving the total mass.
  5. Liquids evaporate when heated.
    • Reason: When a liquid is heated, its molecules gain kinetic energy. This energy enables them to overcome the intermolecular force of attraction, and they escape from the liquid’s surface, changing into vapour.

H. Differentiate between the following. Give examples wherever applicable.

1. Solids, liquids and gases

PropertySolidsLiquidsGases
Shape & VolumeHave fixed shape and volume.Have fixed volume but no fixed shape. They take the shape of the container.Have no fixed shape or volume. They take the shape and volume of the container.
Intermolecular ForceStrongestWeaker than solids, but stronger than gases.Negligible (weakest)
Intermolecular SpaceNegligible (very less)More than solidsMaximum
CompressibilityIncompressibleIncompressibleHighly compressible
Movement of ParticlesParticles only vibrate at fixed positions.Particles can move and slide past each other.Particles move randomly and freely in all directions.
ExampleWood, iceMilk, waterOxygen, smoke

2. Conservation of mass during a physical change and conservation of mass during a chemical change

AspectConservation of Mass in a Physical ChangeConservation of Mass in a Chemical Change
DefinitionThe total mass of the substance remains the same before and after a change in its physical state.The total mass of the reactants is equal to the total mass of the products formed.
Nature of ChangeInvolves a change in physical properties like size, shape, or state. No new substance is formed.Involves the formation of new substances with different properties.
What happens to particles?The molecules remain the same; only their arrangement, motion, or space changes.The atoms of the reactants rearrange themselves to form molecules of new products.
ExampleMelting 30 g of ice in 50 g of water gives 80 g of water.Burning magnesium (48g) in oxygen (32g) produces 80g of magnesium oxide.

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Introduction


Plants prepare their own food in their leaves through the process of photosynthesis. This food, mainly glucose, is produced using sunlight, water, and carbon dioxide. However, the food made in the leaves is not just used there—it needs to be supplied to every part of the plant, like roots, stem, flowers, and fruits. This transportation of food is crucial because all plant parts need energy and nutrients to function properly and grow. The movement of food from the leaves to the rest of the plant is what keeps the plant healthy and alive. The main system involved in this transportation is the plant’s vascular system, especially the phloem tissue, which distributes food prepared in the leaves to all plant parts.


प्लांट्स अपना food leaves में बनाते हैं photosynthesis process से. Photosynthesis में sunlight, water और carbon dioxide लगते हैं, और glucose या food तैयार होता है. Food सिर्फ leaves को नहीं चाहिए, बल्कि roots, stem, branches, flowers, fruits – सबको energy और growth के लिए food चाहिए. जब leaves में food बन जाता है, तो वह food पूरे plant के हर part तक जाना चाहिए, ताकि हर part active और healthy रह सके. Food का movement leaves से बाकी plant parts में बहुत जरूरी process है, जिससे पूरा plant survive और grow करता है. इसमें plant का vascular system, यानी phloem tissue, सबसे important role play करता है.



Transportation


Transportation is the process of moving water, minerals, and food from one part of the plant to another. Plants have a specialized system called the vascular system that helps in this transport. The vascular system mainly consists of two types of tissues: xylem and phloem.

  • Xylem is responsible for transporting water and minerals absorbed by the roots from the soil to different parts of the plant. This movement of water and minerals in xylem is usually in one direction—upwards from roots to leaves.
  • Phloem transports food made in the leaves (mainly glucose) to all other parts of the plant, including roots, stem, flowers, and fruits. This transport of food in the phloem can happen in both upward and downward directions based on the plant’s needs.

The main function of transportation in plants is to ensure that all parts of the plant receive the water, minerals, and food necessary for their growth, development, and proper functioning. Without this transport system, plants cannot survive as the roots may have water and minerals but the leaves have food; they need to share these substances efficiently.



Transportation एक ऐसा process है जिसमें पानी, minerals और food plant के एक part से दूसरे part में move होते हैं। Plants में एक special system होता है जिसे vascular system कहते हैं, जो transportation में मदद करता है। इस vascular system में दो important tissues होते हैं: xylem और phloem।

  • Xylem roots से soil से absorbed पानी और minerals को plant के अलग-अलग हिस्सों तक पहुँचाता है। यह पानी और minerals का movement एक direction में होता है, यानी roots से ऊपर यानी leaves तक।
  • Phloem leaves में बनाये गए food (ज्यादातर glucose) को plant के बाकी हिस्सों जैसे roots, stem, flowers और fruits तक पहुँचाता है। Food का transport phloem में दोनों direction में हो सकता है, ऊपर और नीचे, जो plant की जरूरत पर depend करता है।

Transportation का main function यह है कि plant के हर part को पानी, minerals और food मिल सके, ताकि वे सही से grow, develop और function कर सकें। बिना transportation system के, plants survive नहीं कर सकते क्योंकि roots में पानी और minerals हैं, और leaves में food है, इन्हें efficiently share करना जरूरी है।



Xylem


Functions: Xylem is a vascular tissue that extends from the roots to the leaves through the stem. Its main function is to transport water and dissolved minerals absorbed by the roots from the soil to all parts of the plant. Water moves through the xylem in only one direction—upwards.

Structure and Types: Xylem consists mainly of dead cells forming long tubes that help in this upward water movement. These tubes include:

  • Vessels: Long, tube-like structures open at both ends, joined end to end to form continuous channels. These have thick cellulose walls and a hollow center called the lumen.
  • Tracheids: Narrow, long cells with tapering ends. They are also dead cells and help in supporting the plant.

There are also living components like xylem parenchyma, which store food materials such as starch and fat. Xylem sclerenchyma are dead, narrow, thick-walled cells that provide structural support to the plant.

An Inquiring Mind

This section highlights that vessels in the xylem are continuous channels formed by joining individual vessel elements. The thick cellulose cell walls of vessels strengthen these channels and allow water to flow easily. Tracheids and vessels together help in water conduction and provide mechanical support. The only living cells in the xylem tissue are xylem parenchyma, which serve to store food.


Functions: Xylem एक vascular tissue है जो roots से लेकर leaves तक stem के अंदर extend करता है। इसका main काम roots से soil से absorbed पानी और soluble minerals को plant के हर हिस्से तक पहुँचाना होता है। Xylem में पानी सिर्फ ऊपर की ओर ही flow करता है।

Structure and Types: Xylem मुख्यतः dead cells से बना होता है, जो लंबे tubes बनाते हैं, जिससे पानी ऊपर की तरफ आसानी से move कर पाता है। इन tubes में शामिल हैं:

  • Vessels: लंबे, tube जैसे structures जो दोनों ends पर open होते हैं और end to end जुड़कर continuous channels बनाते हैं। इनके thick cellulose walls होते हैं और अंदर hollow भाग जिसे lumen कहते हैं।
  • Tracheids: पतले, लंबे cells होते हैं जिनके ends taper करते हैं। ये भी dead cells होते हैं और plant को support करते हैं।

इसके अलावा, xylem में living cells भी होते हैं जैसे कि xylem parenchyma, जो food materials जैसे starch और fat store करते हैं। Xylem sclerenchyma narrow, dead और thick-walled cells होते हैं जो plant को structural support देते हैं।

An Inquiring Mind

इस section में बताया गया है कि vessels xylem के individual vessel elements से बने continuous channels होते हैं। इनकी thick cellulose walls water flow को मजबूत और smooth बनाती हैं। Tracheids और vessels मिलकर water conduction और mechanical support का काम करते हैं। Xylem में केवल xylem parenchyma ही living cells होते हैं, जो food store करते हैं।



Phloem


Function: Phloem is the vascular tissue responsible for transporting food from the leaves, where it is made, to all other parts of the plant such as roots, stems, flowers, and fruits. This transportation of food is called translocation.

Structure: Phloem runs alongside the xylem and is made up of four main types of cells:

  • Sieve tubes: Long, narrow tubes with perforated sieve plates that allow food material to pass from one sieve tube to another. These cells are alive but lack nuclei in mature form.
  • Companion cells: These are living cells with nuclei and are found adjacent to sieve tubes. They don’t transport food directly but help in maintaining the sieve tubes by controlling their metabolic functions.
  • Phloem fibers: Composed of dead cells with thick walls, they provide mechanical support to the plant.
  • Phloem parenchyma: These thin-walled cells store food and also help transport it within the plant.
Explore More

The Explore More section encourages students to observe different plants under a microscope to identify the presence or absence of conducting tissues like xylem and phloem. Simple plants like Chlamydomonas and Spirogyra do not have these tissues, but higher plants such as Petunia, Vinca, Mustard, Balsam, Mango, and Neem have well-developed vascular systems. This comparison helps understand the evolutionary advancement of plants and their ability to transport food and minerals efficiently.


Function: Phloem वह vascular tissue है जो leaves से बनाये गए food को plant के बाकी parts जैसे roots, stem, flowers और fruits तक पहुँचाता है। इस process को translocation कहा जाता है।

Structure: Phloem xylem के पास चलता है और चार मुख्य प्रकार के cells से बना होता है:

  • Sieve tubes: लंबे, पतले tubes होते हैं जिनमें perforated sieve plates होती हैं जो food materials को एक sieve tube से दूसरे sieve tube तक जाने देती हैं। ये cells जिंदा होते हैं लेकिन mature stage में nuclei नहीं होती।
  • Companion cells: ये living cells होते हैं जिनमें nuclei होती है और ये sieve tubes के पास होते हैं। ये cells सीधे food transport नहीं करते लेकिन sieve tubes के लिए जरूरी metabolic activities को control करते हैं।
  • Phloem fibers: ये dead cells होते हैं जिनकी दीवारें thick होती हैं और plant को mechanical support देते हैं।
  • Phloem parenchyma: ये thin-walled cells food store करते हैं और इसके अलावा food transport में मदद करते हैं।

Explore More

Explore More section में students को encourage किया जाता है कि वे microscope की मदद से विभिन्न plants की जांच करें और देखें कि conducting tissues जैसे xylem और phloem होते हैं या नहीं। Simple plants जैसे Chlamydomonas और Spirogyra में ये tissues नहीं होते जबकि higher plants जैसे Petunia, Vinca, Mustard, Balsam, Mango और Neem में well-developed vascular system होता है। इससे plants के evolutionary development और उनके द्वारा food और minerals transport करने की क्षमता को समझने में मदद मिलती है।



Absorption of Water


The root system of plants consists of a main root from which smaller lateral roots arise. These lateral roots have tiny hair-like outgrowths called root hairs. Each root hair is an extension of an epidermal cell and is unicellular, delicate, and easily damaged. Root hairs increase the surface area of the root, helping the plant absorb more water and minerals from the soil.

Each root hair has a permeable outer cell wall and a semipermeable inner cell membrane. The permeable cell wall allows all molecules to pass through, but the semipermeable cell membrane allows only certain substances to enter or leave the cell.

Water moves from the soil, where it is in higher concentration, into the root hair through the process of osmosis. Osmosis is the movement of water molecules from an area of higher water concentration to an area of lower water concentration through a semipermeable membrane. This absorption of water through root hairs is the first step in the transportation of water within the plant.


Plant की root system main root से बनती है, जिससे छोटे lateral roots निकलते हैं। इन lateral roots पर छोटे छोटे root hairs होते हैं जो hair जैसे दिखते हैं। हर root hair epidermal cell का extension होता है, यह unicellular होता है, delicate होता है और आसानी से damage हो सकता है। Root hairs root का surface area बढ़ाते हैं जिससे plant ज्यादा water और minerals soil से absorb कर पाता है।

हर root hair का outer cell wall permeable होता है, जिसका मतलब है कि यह सब molecules को pass करने देता है। Inner cell membrane semipermeable होती है, यानी यह केवल कुछ खास substances को ही अंदर या बाहर जाने देती है।

Water soil से, जहाँ water concentration ज्यादा होता है, root hair में osmosis के process से जाता है। Osmosis वह process है जिसमें water molecules एक semipermeable membrane के जरिए ज्यादा water वाला area से कम water वाले area में move करते हैं। Root hairs के through water का absorption plant में पानी के transportation का पहला step होता है।



Osmosis


Osmosis is the process in which water molecules move from an area where they are more in number (higher concentration) to an area where they are fewer in number (lower concentration) through a semipermeable membrane. This process allows only certain molecules, like water, to pass through while blocking others. Osmosis is essential in plants as it helps in the absorption of water through root hairs from the soil where water concentration is higher.

1. Conduction of Water through Osmosis

Water absorbed by root hairs moves into adjacent root cells by osmosis because the concentration of water in the soil is higher than inside the root hairs. As root hairs take in water, they become swollen or turgid. Water then moves from one cell to another by osmosis, gradually reaching the inner parts of the root and then moving into the xylem vessels. This movement helps in the upward transport of water and minerals from roots to different parts of the plant.

2. Diffusion

Diffusion is the movement of molecules from an area of higher concentration to an area of lower concentration without the need for a semipermeable membrane. It continues until the concentration becomes uniform throughout. Diffusion helps in the exchange of gases like oxygen and carbon dioxide in and out of leaves. In plants, water vapor also diffuses from leaf cells to the atmosphere during transpiration.


Osmosis एक process है जिसमें पानी के molecules एक ऐसे area से दूसरे area में move करते हैं जहाँ उनकी संख्या ज्यादा होती है (higher concentration) से वहाँ जहाँ उनकी संख्या कम होती है (lower concentration) through एक semipermeable membrane। यह membrane केवल कुछ खास molecules जैसे पानी को पास होने देता है, बाकी molecules को रोका जाता है। Plants में osmosis important है क्योंकि इसके माध्यम से roots के root hairs soil से पानी absorb करते हैं जहाँ पानी की मात्रा ज्यादा होती है।

1. Conduction of Water through Osmosis

Roots के root hairs soil से पानी osmosis द्वारा absorb करते हैं क्योंकि soil में पानी की concentration roots से ज्यादा होती है। Root hairs पानी लेने पर swollen या turgid हो जाते हैं। इसके बाद पानी एक cell से दूसरे cell में osmosis से move करता है, धीरे धीरे root के अंदर के हिस्सों तक पहुँचता है और फिर xylem vessels में जाता है। यह प्रक्रिया पानी और minerals को roots से plant के दूसरे parts तक ऊपर transport करने में मदद करती है।

2. Diffusion

Diffusion एक process है जिसमें molecules higher concentration वाले area से lower concentration वाले area में बिना semipermeable membrane के move करते हैं। यह process तब तक चलता है जब तक दोनों areas में concentration equal नहीं हो जाता। Plants में diffusion gases जैसे oxygen और carbon dioxide के leaves के अंदर और बाहर exchange के लिए जरूरी है। Water vapor भी leaf cells से atmosphere में transpiration के दौरान diffuse होता है।



Differences Between Osmosis and Diffusion


Osmosis and diffusion are both processes by which molecules move from one place to another, but they differ in several key ways:

FeatureOsmosisDiffusion
MovementMovement of water moleculesMovement of molecules of any substance
ConcentrationFrom higher water concentration to lower through a semipermeable membraneFrom higher concentration to lower concentration without a membrane requirement
MembraneRequires a semipermeable membraneDoes not require a semipermeable membrane
MediumOccurs in liquid mediumOccurs in solid (slowly), liquid, or gas
DirectionMovement is unidirectional (one way)Movement occurs in all directions

Osmosis specifically involves the movement of water across a semipermeable membrane, important for water absorption in plants. Diffusion is more general and includes movement of gases, liquids, or solids until the molecules are evenly spread out.


Osmosis और diffusion दोनों processes हैं जिनमें molecules एक जगह से दूसरी जगह move करते हैं, पर इन में कुछ महत्वपूर्ण अंतर होते हैं:

FeatureOsmosisDiffusion
MovementWater molecules का movement होता हैकिसी भी substance के molecules का movement होता है
ConcentrationHigh water concentration से low water concentration की तरफ semipermeable membrane के throughHigh concentration से low concentration की ओर बिना किसी membrane की जरूरत के
MembraneSemipermeable membrane जरूरी होता हैSemipermeable membrane की जरूरत नहीं होती
Mediumकेवल liquid medium में होता हैSolid (धीरे), liquid, या gas medium में होता है
DirectionMovement एक दिशा में होता है (one way)Movement सब directions में होता है

Osmosis खासकर पानी के movement के लिए है जो plants में water absorption में जरूरी है। Diffusion general process है जिसमें gases, liquids, और solids के molecules फैलते हैं जब तक वे बराबर नहीं हो जाते।



Absorption of Minerals


Plants absorb minerals from the soil which are essential for their growth and development. Minerals like potassium, calcium, nitrogen, and magnesium dissolve in soil water and are taken up by plants through their roots.

There are two main methods by which minerals are absorbed:

  • Active Transport: Often, the concentration of minerals inside root hairs is higher than in the soil. To absorb minerals against this concentration gradient, plants use energy to actively transport minerals from areas of low concentration (soil) to high concentration (root hairs). This process requires energy because it moves minerals against their natural flow.
  • Diffusion: When the concentration of minerals is higher in the soil than inside the root hairs, minerals move naturally from high to low concentration areas by diffusion, which does not require energy. However, this is less common since minerals are usually more concentrated inside the root hairs.

The minerals absorbed through these methods are essential for various functions such as enzyme activation, formation of proteins, and other physiological processes in plants.


Plants soil से जरूरी minerals absorb करते हैं, जो उनके growth और development के लिए जरूरी होते हैं। Minerals जैसे potassium, calcium, nitrogen, और magnesium soil water में dissolve होते हैं और plant के roots से लिए जाते हैं।

Minerals को absorb करने के दो main तरीके होते हैं:

  • Active Transport: अक्सर minerals की concentration roots के अंदर root hairs में soil की तुलना में ज्यादा होती है। Minerals को concentration gradient के opposite direction में लेना होता है, इसलिए plants energy का use करते हैं ताकि low concentration (soil) से high concentration (root hairs) में minerals ले जा सकें। यह process energy मांगता है क्योंकि minerals अपने natural flow के opposite जाते हैं।
  • Diffusion: जब soil में minerals की concentration root hairs से ज्यादा होती है, तब minerals अपने आप high concentration से low concentration वाली जगह diffuse हो जाते हैं। यह process बिना energy के होता है। लेकिन ये कम होता है क्योंकि minerals आमतौर पर root hairs में ज्यादा concentration में होते हैं।

ये absorbed minerals plant के लिए enzymes activate करने, protein बनाने और अन्य physiological कामों के लिए जरूरी होते हैं।



Transport of Water and Minerals


The transport of water and minerals in plants is a vital process that ensures all parts of the plant receive the necessary nutrients and hydration for growth and survival. Water is absorbed by the root hairs from the soil through osmosis, and minerals are taken in by active transport and diffusion. Once inside the roots, water and minerals move from one cell to another, eventually reaching the xylem vessels.

The pressure created by the continuous entry of water into the roots is called root pressure. This root pressure helps to push water and dissolved minerals upwards from the roots through the stem to the leaves and other parts of the plant. The movement of this mixture (called sap) from the roots to the upper parts of the plant is referred to as the “ascent of sap.”

Additionally, transpiration—the loss of water as vapor from the leaves—creates a pulling force called transpirational pull, which further helps in moving water and minerals upward through the plant. Together, root pressure and transpirational pull ensure effective and continuous transport of water and minerals throughout the plant.


Plants में पानी और minerals का transport बहुत जरूरी process है जिससे plant के हर हिस्से को सही nutrition और hydration मिलता है, और जिससे growth और survival possible होता है। Roots के root hairs soil से पानी osmosis के जरिए absorb करते हैं, और minerals active transport और diffusion के जरिए अंदर लेते हैं। एक बार पानी और minerals roots के अंदर पहुंच जाते हैं, तो ये cell से cell में move करते हुए xylem vessels तक पहुँचते हैं।

Roots में लगातार पानी आने से जो pressure बनता है उसे root pressure कहते हैं। यही root pressure पानी और dissolved minerals को roots से stem के जरिए leaves और बाकी plant parts तक ऊपर की ओर push करता है। इस mixture (जिसे sap कहते हैं) का roots से plant के ऊपरी हिस्सों तक जाना ascent of sap कहलाता है।

साथ ही, leaves से पानी का vapor के रूप में loss होना (transpiration) एक pulling force बनाता है जिसे transpirational pull कहते हैं, जो पानी और minerals को plant में ऊपर की ओर खींचने में मदद करता है। Root pressure और transpirational pull दोनों मिलकर plant में पानी और minerals का effective, continuous transport करते हैं।



Importance of Water for Plants


Water is essential for plants and plays several vital roles in their survival and growth:

  • Transport of Nutrients: Water helps in carrying minerals and nutrients from the soil throughout the plant, ensuring every part gets what it needs for healthy growth.
  • Photosynthesis: Water is one of the key ingredients in photosynthesis, the process by which plants make food using sunlight, carbon dioxide, and water in their leaves.
  • Cooling Effect: Water evaporates from the surface of leaves during transpiration, which helps to cool down the plant, especially in hot weather.
  • Maintaining Cell Structure: Water keeps plant cells turgid (firm and swollen), providing structure and preventing wilting.
  • Metabolic Processes: Most chemical reactions inside a plant—including energy release, nutrient assimilation, and growth—take place in the presence of water.

Without sufficient water, plants cannot perform these functions effectively, which leads to poor growth, wilting, and even death.


पानी plants के लिए बहुत जरूरी है और इनके survival और growth में कई vital roles निभाता है :-

  • Nutrients का Transport : पानी soil से minerals और nutrients लेकर पूरे plant में distribute करता है, जिससे हर पार्ट को सही nutrition मिलता है।
  • Photosynthesis : पानी photosynthesis process में एक main ingredient है, जिसमें plants अपने leaves में sunlight, carbon dioxide और पानी से food बनाते हैं।
  • Cooling Effect : Transpiration के दौरान leaves की surface से पानी evaporate होता है, जिससे plant को गर्मी में ठंडा रहने में help मिलती है।
  • Cell Structure Maintain करना : पानी plant cells को turgid रखता है, यानी cells firm और swollen रहते हैं, जिससे plant को structure मिलती है और wilting नहीं होती।
  • Metabolic Processes : Plants के अंदर होने वाले ज्यादातर chemical reactions—जैसे energy मिलना, nutrients absorb होना, और growth—पानी की presence में होते हैं।

अगर plant को सही से पानी न मिले, तो ये सारे functions ठीक तरह से नहीं हो पाते, जिससे growth कम हो जाती है, plant wilt होने लगता है या मर भी सकता है।



Transpiration


Transpiration is the process by which plants lose excess water in the form of water vapor. This happens mainly through tiny pores called stomata on the surfaces of leaves and other aerial parts. The water absorbed by the roots travels through the plant and eventually evaporates from the leaf surface into the atmosphere.

Transpiration plays several important roles:

  • Cooling effect: As water vaporizes from the leaves, it cools the plant, protecting it from overheating.
  • Continuous water flow: It creates a suction force (transpirational pull) that helps move water and dissolved minerals from roots to upper parts of the plant.
  • Maintaining water balance: It helps in the movement and distribution of minerals and nutrients within the plant.
  • Regulation of water content: If plants lose more water by transpiration than they absorb, leaves and other parts can wilt.

Transpiration is affected by factors such as temperature, humidity, wind, and sunlight, being faster in hot and dry conditions.


Transpiration वह process है जिसमें plants अपने अंदर से extra पानी को water vapor के रूप में खो देते हैं। यह मुख्य रूप से leaves और दूसरी ऊपर की surfaces पर मौजूद छोटे pores, जिन्हें stomata कहते हैं, के जरिए होता है। Roots से absorb हुआ पानी plant के अंदर move करता है और आखिर में leaves की surface से atmosphere में evaporate हो जाता है।

Transpiration कई important roles play करता है :

  • Cooling effect : जब पानी leaves से vapor बन कर उड़ता है, तो plant ठंडा रहता है और overheat नहीं होता।
  • Continuous water flow : यह एक suction force (transpirational pull) बनाता है जो roots से पानी और dissolved minerals को ऊपर की तरफ move करने में मदद करता है।
  • Water balance maintain करना : यह plant के अंदर minerals और nutrients के movement और distribution में help करता है।
  • Water content control करना : अगर plants transpiration से ज्यादा पानी खो दें जितना absorb करते हैं, तो leaves और दूसरे parts wilt (मुरझा) हो सकते हैं।

Transpiration का rate temperature, humidity, wind, और sunlight जैसे factors पर depend करता है, और यह गरम और dry conditions में fastest होता है।



Factors Affecting the Rate of Transpiration


The rate at which transpiration occurs in plants depends on several environmental factors:

  • Sunlight/Time of the Day: Transpiration increases with sunlight because light causes stomata to open. During the daytime, when the sun is out, the rate is higher, and it is lower at night when the stomata close.
  • Temperature: Higher temperatures speed up the evaporation of water from leaf surfaces, increasing transpiration. Plants lose more water on hot days compared to cool days.
  • Humidity: When the air around the plant is humid (contains more moisture), transpiration slows down because the concentration gradient for water vapor between the leaf and air is weaker.
  • Wind: Wind removes the moisture-laden air near the leaf surface, allowing more water vapor to escape from the stomata. Hence, transpiration is higher on windy days.

All these factors together determine how much water a plant loses to the environment via transpiration.


Transpiration की speed या rate plants में कई environmental factors पर depend करती है :

  • Sunlight / Time of the Day : Transpiration sunlight के साथ बढ़ जाता है क्योंकि light stomata को open कर देती है। Daytime में rate ज्यादा होता है और night में, जब stomata बंद होते हैं, rate कम हो जाता है।
  • Temperature : High temperature leaves से पानी के evaporation को तेज कर देता है, जिससे transpiration बढ़ता है। गरम दिनों में plants ज्यादा पानी खोते हैं।
  • Humidity : अगर air में already ज्यादा moisture है (high humidity), तो transpiration slow हो जाता है क्योंकि leaf और air के बीच water vapor का concentration difference कम होता है।
  • Wind : Wind leaf surface के पास की moist हवा को हटा देती है, जिससे stomata से ज्यादा water vapor escape कर सकता है। Windy days में transpiration बहुत हाइ रहता है।

इन सभी factors का मिलकर plants में transpiration के rate पर सीधा असर होता है।



Importance of Transpiration


Transpiration is extremely important for plants and plays several critical roles:

  • Cooling Effect: As water evaporates from the surface of leaves, it helps cool down the plant, preventing it from overheating, especially on hot days.
  • Uptake and Transport of Water and Minerals: Transpiration creates a pulling force (transpirational pull) that helps move water and dissolved minerals from the roots to the upper parts of the plant.
  • Maintaining Water Balance: By removing excess water, transpiration helps maintain the right water balance inside the plant and prevents cells from bursting due to too much water.
  • Continued Nutrient Flow: Transpiration ensures the continuous supply of water and dissolved nutrients throughout the plant, necessary for photosynthesis and other vital functions.

Without transpiration, plants would not be able to efficiently transport water and minerals, regulate temperature, or maintain proper nutrition.


Transpiration plants के लिए बहुत important है और इसके कई फायदे हैं :

  • Cooling Effect : Leaves की surface से water vapor बनने पर plant को ठंडा रखने में मदद मिलती है, जिससे वो गर्म दिनों में overheat नहीं होता।
  • Water और Minerals का Uptake and Transport : Transpiration एक pulling force (transpirational pull) बनाता है जिससे roots से लेकर leaves तक पानी और minerals आसानी से move होते हैं।
  • Water Balance Maintain करना : Extra पानी को remove करके transpiration plant के अंदर सही water balance बनाए रखता है और cells को ज्यादा पानी की वजह से burst होने से बचाता है।
  • Nutrients का Continuous Flow : Transpiration plant में water और nutrients का continuous supply बनाए रखता है, जो photosynthesis और दूसरे important functions के लिए जरूरी है।

अगर transpiration नहीं हो, तो plant efficiently पानी और minerals transport नहीं कर पाएगा, temperature control नहीं कर पाएगा, और सही nutrition भी नहीं मिल पाएगा।



Translocation of Food


Translocation of food in plants is the process by which food made in the leaves (mainly glucose produced during photosynthesis) is transported to all other parts of the plant, such as roots, stems, flowers, and fruits. This transportation happens through the vascular tissue called phloem.

Unlike water movement in the xylem (which only goes upwards), food movement in the phloem can take place in both upward and downward directions, depending on where the food is needed. The main components of phloem involved in translocation are sieve tubes, which act like pipelines for food to move. This process is essential because different parts of the plant need energy and nutrients for growth, storage, and development. For example, roots and fruits do not perform photosynthesis but need food supplied from the leaves.

Translocation helps in distributing the energy resources throughout the plant, making sure every part remains healthy and active.


Translocation of food plants में एक process है जिसमें leaves में बना food (mainly glucose, जो photosynthesis के दौरान बनता है) plant के बाकी parts जैसे roots, stem, flowers और fruits तक पहुंचता है। यह transport एक special vascular tissue, जिसे phloem कहते हैं, के जरिए होता है।

Xylem में पानी सिर्फ ऊपर की तरफ जाता है, लेकिन phloem में food का movement ऊपर और नीचे दोनों directions में हो सकता है, जो plant की जरूरत पर depend करता है। Translocation में phloem के मुख्य part sieve tubes होते हैं, जो pipes जैसे food को transport करते हैं। यह process जरूरी है क्योंकि plant के अलग-अलग parts को energy और nutrients चाहिए होते हैं—जैसे roots और fruits खुद food नहीं बनाते, मगर उन्हें energy चाहिए।

Translocation plant के हर हिस्से में energy resources distribute करने में help करता है, जिससे plant healthy और active रहता है।



Nutrients Required by Plants


Plants need different nutrients for their growth, development, and survival. These nutrients are absorbed from the soil, air, and water and are essential for various processes like photosynthesis, energy production, and building plant structures.

Nutrients needed by plants are divided into two main groups :

  • Macronutrients: These are nutrients needed in large quantities. Examples include nitrogen, phosphorus, potassium, calcium, magnesium, and sulfur. Macronutrients help in building proteins, nucleic acids, chlorophyll, and also help with overall plant growth and metabolism.
  • Micronutrients: These are required in very small amounts but are equally essential. Examples include iron, manganese, zinc, copper, boron, and chlorine. Micronutrients play a major role in specific biochemical and physiological functions such as enzyme activation and hormone production.

A shortage of any essential nutrient can lead to poor growth, development issues, and even diseases in plants. That’s why maintaining the right nutrient balance is very important for healthy plants.


Plants के सही growth, development और survival के लिए कई तरह के nutrients चाहिए होते हैं। ये nutrients plant soil, air और water से absorb करते हैं और ये अलग-अलग important processes जैसे photosynthesis, energy production और plant structures बनाने में जरूरी होते हैं।

Plants को चाहिए दो main type के nutrients :

  • Macronutrients : ये वो nutrients हैं जो plant को बड़ी मात्रा में चाहिए होते हैं। Examples हैं nitrogen, phosphorus, potassium, calcium, magnesium और sulfur। Macronutrients proteins, nucleic acids, chlorophyll बनाने, और plant growth व metabolism में मदद करते हैं।
  • Micronutrients : ये nutrients बहुत कम मात्रा में चाहिए, मगर उतने ही important होते हैं। Examples हैं iron, manganese, zinc, copper, boron और chlorine। Micronutrients खास biochemical और physiological functions जैसे enzyme activation और hormone production में काम आते हैं।

अगर plant को कोई जरूरी nutrient ठीक से ना मिले, तो growth slow हो जाती है, development में problems आती हैं और diseases भी हो सकते हैं। इसलिए सही nutrient balance plant के लिए बहुत जरूरी है।



Deficiency Diseases


Deficiency diseases in plants occur when they do not receive enough of essential nutrients needed for healthy growth and development. These nutrients include macronutrients like nitrogen, phosphorus, potassium, and micronutrients like iron, zinc, manganese, and others. When a specific nutrient is missing, plants show specific symptoms called deficiency symptoms.

Some common deficiency diseases and symptoms include:

  • Nitrogen deficiency: Plants show slow growth and yellow leaves.
  • Phosphorus deficiency: Stems may turn purple, and roots and overall growth become weak.
  • Potassium deficiency: Leaves are dark green, plants become weak, and leaves may fall early.
  • Magnesium deficiency: Leaves may have pale areas, and stems lose strength.
  • Iron deficiency: Yellowing of leaves, poor growth, and plants may not stay healthy.
  • Zinc and manganese deficiency: Leaves become yellow, plants are stunted, and spots may appear.

Deficiency diseases can stunt plant growth, affect flowering and fruit formation, and reduce crop yield. Treating these problems usually involves adding the required nutrients to the soil for healthy plant recovery.


अगर plants को उनके healthy growth और development के लिए जरूरी nutrients पूरी मात्रा में नहीं मिल पाते, तो deficiency diseases हो सकती हैं। इनमें macronutrients जैसे nitrogen, phosphorus, potassium और micronutrients जैसे iron, zinc, manganese वगैरह शामिल हैं। खास nutrient की कमी से plant में खास symptoms नजर आते हैं, जिन्हें deficiency symptoms कहते हैं।

कुछ आम deficiency diseases और उनके symptoms :

  • Nitrogen deficiency : Plant की growth slow हो जाती है और leaves yellow हो जाती हैं।
  • Phosphorus deficiency : Stem purple हो सकता है, roots और overall growth कमजोर हो जाती है।
  • Potassium deficiency : Leaves बहुत dark green हो जाती हैं, plant weak हो जाता है और leaves जल्दी गिर सकती हैं।
  • Magnesium deficiency : Leaves पर pale area आ सकता है और stem में strength कम हो जाती है।
  • Iron deficiency : Leaves yellow हो जाती हैं, growth खराब रहती है और plant unhealthy हो सकता है।
  • Zinc और manganese deficiency : Leaves yellow हो जाती हैं, plant छोटा रह जाता है और spots भी आ सकते हैं।

Deficiency diseases की वजह से plant की growth रुक सकती है, flowers और fruits कम बन सकते हैं, और crop yield भी कम हो सकती है। इन problems को ठीक करने के लिए soil में जरूरी nutrients add करना होता है, जिससे plant healthy हो सके।



Fact Check 


  1. What is the function of xylem in plants?
    The xylem transports water and dissolved minerals from the roots to the rest of the plant.
  2. What is translocation in plants?
    Translocation is the process of movement of food prepared in the leaves to all other parts of the plant through the phloem.
  3. Give one symptom of nitrogen deficiency in plants.
    Yellowing of leaves is a main symptom of nitrogen deficiency.
  4. Which process helps in absorption of water by roots?
    Osmosis helps roots absorb water from the soil.
  5. Name any two macronutrients required by plants.
    Nitrogen and phosphorus are two examples of macronutrients required by plants.

  1. Plant में xylem का क्या function है?
    Xylem roots से पानी और minerals पूरे plant तक पहुँचाता है।
  2. Plants में translocation क्या है?
    Translocation leaves में बने हुए food को phloem के through plant के बाकी parts तक ले जाने की process है।
  3. Nitrogen deficiency का एक symptom बताइए।
    Leaves का yellow होना nitrogen deficiency का main symptom है।
  4. Roots पानी absorb करने के लिए कौन सा process help करता है?
    Osmosis process roots को soil से पानी absorb करने में मदद करता है।
  5. Plants को चाहिए दो macronutrients के नाम बताइए।
    Nitrogen और phosphorus plant के लिए जरूरी macronutrients हैं।


  1. Which tissue transports food in plants?
    Phloem transports food from the leaves to all other parts of the plant.
  2. What are root hairs?
    Root hairs are thin, hair-like extensions of root cells that increase the surface area for absorption of water and minerals from the soil.
  3. Name the process of movement of molecules from higher concentration to lower concentration.
    Diffusion is the process by which molecules move from an area of higher concentration to an area of lower concentration.
  4. Which mineral is needed for chlorophyll formation?
    Magnesium is essential for the formation of chlorophyll in plants.
  5. State one function of transpiration.
    Transpiration cools the plant by evaporating water from the leaves.

  1. Plants में food transport करने वाला tissue कौन सा है?
    Phloem leaves से बने food को plant के बाकी parts तक transport करता है।
  2. Root hairs क्या हैं?
    Root hairs बहुत पतले, hair जैसे extensions होते हैं जो soil से पानी और minerals absorb करने के लिए surface area बढ़ाते हैं।
  3. Molecules के higher concentration से lower concentration में जाने की process का नाम बताइए।
    Diffusion process में molecules higher concentration वाली जगह से lower concentration वाली जगह move करते हैं।
  4. Chlorophyll बनने के लिए कौन सा mineral चाहिए?
    Magnesium chlorophyll बनने के लिए जरूरी है।
  5. Transpiration का एक function बताइए।
    Transpiration leaves से पानी evaporate करके plant को ठंडा रखता है।


Tick (✓) the Correct Facts and Cross (✗) the Incorrect Facts

  1. Root pressure helps to push plant sap upwards into the stem.
    ✓ Correct — Root pressure pushes water and minerals upwards through the xylem.
  2. The downward movement of sap containing water and minerals is called ascent of sap.
    ✗ Incorrect — Ascent of sap refers to the upward movement of water and minerals, not downward.
  3. Transpiration provides a cooling effect to the plant.
    ✓ Correct — Transpiration cools the plant by evaporating water from leaves.
  4. Higher the temperature, slower is the rate of transpiration.
    ✗ Incorrect — Higher temperature increases the rate of transpiration by increasing evaporation.
  5. Zinc is a macronutrient.
    ✗ Incorrect — Zinc is a micronutrient, needed in small quantities.

सही facts पर ✓ लगाएँ और गलत facts पर ✗

  1. Root pressure plant sap को stem के अंदर ऊपर की ओर push करता है।
    ✓ सही — Root pressure पानी और minerals को xylem के through ऊपर push करता है।
  2. Sap का downward movement जिसमें पानी और minerals होते हैं उसे ascent of sap कहते हैं।
    ✗ गलत — Ascent of sap, पानी और minerals का ऊपर की ओर movement है, downward नहीं।
  3. Transpiration plant को ठंडा करता है।
    ✓ सही — Transpiration के दौरान leaves से पानी evaporate होता है जिससे plant cool होता है।
  4. Temperature जितना ज्यादा होगा, transpiration rate उतना ही धीमा होगा।
    ✗ गलत — Temperature बढ़ने से transpiration तेज होता है।
  5. Zinc macronutrient है।
    ✗ गलत — Zinc micronutrient होता है, जो plant को कम मात्रा में चाहिए।


Time to Summarise (Point-wise)


  • Plants transport water, minerals, and food to different parts through xylem and phloem.
  • Xylem carries water and minerals from roots to leaves; phloem transports food from leaves to other parts.
  • Roots absorb water mainly through root hairs by osmosis.
  • Minerals are absorbed by roots through active transport and diffusion.
  • Transpiration is the process of water loss from leaves, helping in cooling and water movement.
  • Root pressure and transpirational pull help water move upwards in plants.
  • Nutrients are essential for plant growth; deficiency leads to specific symptoms.
  • Translocation is the movement of food in plants through phloem.
  • Plants require macronutrients and micronutrients for various functions.
  • Maintaining balanced nutrition is important for healthy plants.

  • Plants पानी, minerals और food को xylem और phloem के through अपने अलग अलग parts तक transport करते हैं।
  • Xylem roots से पानी और minerals leaves तक पहुँचाता है; phloem leaves से food plant के बाकी parts तक ले जाता है।
  • Roots मुख्य रूप से root hairs के द्वारा osmosis से पानी absorb करते हैं।
  • Minerals roots active transport और diffusion से absorb करते हैं।
  • Transpiration leaves से पानी के evaporation की process है, जो plant को ठंडा रखने और पानी के movement में मदद करती है।
  • Root pressure और transpirational pull पानी को plants में ऊपर की तरफ move करने में मदद करते हैं।
  • Nutrients plant growth के लिए जरूरी होते हैं; कमी से specific symptoms होते हैं।
  • Translocation food का movement है जो phloem के through plant में होता है।
  • Plants को macronutrients और micronutrients दोनों की जरूरत होती है।
  • Balanced nutrition से plants healthy रहते हैं।


Search Results for:

Introduction to Matter    

Everything around us – the air we breathe, the water we drink, even our own bodies – is made of matter. But what exactly is the matter?“In a world of atoms, big and small,
Matter exists, embracing all.
Solid, liquid, gas they take,
Changing form, but never break.”

What You’ll Discover in This Chapter:


The Particle Nature of Matter
How tiny atoms and molecules form everything we see
The revolutionary kinetic theory explaining particle behavior
Three States of Matter
Why solids hold their shape while liquids flow
What makes gases fill any space
Phase Changes
The science behind melting, boiling, and freezing
Real-world examples like ice → water → steam
Special Phenomena
Why naphthalene balls disappear over time (sublimation!)
How frost forms without becoming liquid first (deposition)


Chapter Contents at a Glance

TopicKey ConceptsReal-World Example
Kinetic TheoryParticle motion, intermolecular forcesPerfume spreading in a room
SolidsFixed shape, high densityIron rod, ice cube
LiquidsFlowing, surface tensionMercury droplets, water waves
GasesCompressibility, pressureBalloon inflation, LPG cylinders
Melting/FreezingLatent heat, temperature plateausIce cream melting, water freezing
Evaporation/CondensationSurface phenomenon, cooling effectWet clothes drying, dew formation
Sublimation/DepositionDirect solid-gas transitionDry ice fog, frost formation

Did You Know? (Fun Facts from Both Textbooks)

🔬 A single grain of salt contains about 1.2×10¹⁸ atoms – that’s 1,200,000,000,000,000,000 particles!
🌡 Water is special – it expands when freezing (why ice floats)!
🔍 Robert Brown discovered particle motion by watching pollen grains jiggle in water!


Quick Pre-Chapter Quiz

  1. Matter is anything that has ______ and occupies ______.
    (Answer: mass, space)
  2. The three common states of matter are ______, ______, and ______.
    (Answer: solid, liquid, gas)
  3. When solid changes directly to gas, it’s called ______.
    (Answer: sublimation)

Kinetic Theory of Matter

Why Particles Never Sit Still
The Core Idea

The kinetic theory of matter (proposed in 1860) states that:

“All matter is composed of particles in constant motion, and this motion determines the substance’s state.”

5 Key Postulates


Particle Composition
Matter is made of atoms/molecules (size: 10⁻⁸ to 10⁻¹⁰ m)
Example: A sugar crystal contains ~1 sextillion molecules!
Perpetual Motion
Particles always move (vibrate in solids, slide in liquids, zoom in gases)
Proof: Brownian motion (random zigzag movement of pollen grains in water)
Energy-Temperature Link
Kinetic energy ∝ Temperature
Heating = Faster particles | Cooling = Slower particles
Intermolecular Forces
Cohesion (same-particle attraction)
Adhesion (different-particle attraction)
Space-Force Relationship
Force ↑ as Distance ↓ (strongest in solids, weakest in gases)

Evidence in Daily Life
PhenomenonKinetic Theory Explanation
Perfume spreadingGas particles move randomly, colliding with air molecules
Ice meltingHeat energy overcomes rigid bonds between water molecules
Balloon inflationGas particles fill all available space by moving freely

Classroom Activity (From Viva Education Textbook):
Dissolve potassium permanganate in water → Even after 5 dilutions, color persists, proving molecules are incredibly small!


Science Snacks

🔬 Fun Fact: Air molecules move at ~500 m/s (faster than jet planes!) at room temperature.
🌡 Demo: Blow up a balloon, then cool it – the shriveling shows gas particles slow down when chilled.


Quick Quiz
  1. The jiggling of dust particles in sunlight demonstrates ______ motion.
    (Answer: Brownian)
  2. Intermolecular forces are strongest in ______.
    (Answer: solids)
  3. When heated, particles gain ______ energy.
    (Answer: kinetic)


Molecular Arrangements

How Particles Organize in Solids, Liquids & Gases

What is Molecular Arrangement?

The specific pattern in which atoms/molecules are organized in a substance, determined by:

  • Intermolecular forces (attraction between particles)
  • Kinetic energy (energy of motion)

(“Solids have orderly arrangements while gases show chaos.”)


Comparison of States

PropertySolids 🧊Liquids 💧Gases ☁️
Particle PackingTightly packedLoosely packedVery far apart
Interparticle SpaceMinimal (0.1 nm)ModerateLarge (>10x solids)
Particle MotionVibrate in placeSlide past each otherMove freely at high speed
Shape/VolumeFixedFixed volume, no fixed shapeNo fixed shape/volume
CompressibilityNearly impossibleSlightly compressibleHighly compressible
Energy LevelLowestModerateHighest


1. Solids: Nature’s Lego Blocks

Characteristics:

  • Definite shape/volume (e.g., iron rod, ice cube)
  • Strong cohesion (why diamonds are hard)
  • Vibrational motion only (like students seated in class)

Science Snack:
Why can’t you compress a book?
→ Particles are already shoulder-to-shoulder (intermolecular space ≈ particle size).


2. Liquids: The Flexible Middle

Characteristics:

  • Take container’s shape (e.g., water in a bottle vs. bowl)
  • Moderate cohesion (forms droplets but still flows)
  • Diffusion slower than gases (particles slide, not zoom)

Real-World Example:
Mercury in thermometers – flows like liquid but forms rounded drops due to high cohesion.


3. Gases: The Ultimate Freestylers

Characteristics:

  • Fill any space (e.g., perfume spreads in a room)
  • Negligible cohesion (particles rarely interact)
  • High compressibility (LPG cylinders hold 250x compressed gas!)

Fun Fact:
If a gas molecule were a tennis ball, its neighbor would be 5 km away!


Quick Quiz

  1. ______ have particles that only vibrate in fixed positions.
    (Answer: Solids)
  2. Liquids take the shape of their container because particles can ______.
    (Answer: slide past each other)
  3. The empty space between gas particles is about ______ times their size.
    (Answer: 10)

Hands-On Activity :
Dissolve salt in water → No volume change proves intermolecular spaces exist in liquids!


States of Matter: Solids, Liquids & Gases


What Are the States of Matter?

Matter exists in three primary states, each with unique properties due to differences in:
Particle arrangement
Energy levels
Intermolecular forces

(“Solids are rigid, liquids flow, and gases fill all available space.”)



Comparison of Solids, Liquids & Gases

PropertySolids 🧊Liquids 💧Gases ☁️
ShapeFixedTakes container shapeFills entire container
VolumeFixedFixedExpands to fill space
Particle MotionVibrate in placeSlide past each otherMove freely at high speed
DensityHighModerateVery low
CompressibilityAlmost incompressibleSlightly compressibleHighly compressible
ExamplesIce, iron, woodWater, oil, mercuryAir, oxygen, steam


1. Solids: The Structured State

Key Features:

  • Particles: Tightly packed in fixed positions
  • Forces: Strong intermolecular attraction
  • Behavior: Definite shape and volume
  • Real-World Example: Diamond – hardest natural solid due to rigid carbon structure

Science Snack:
Why does a rubber band stretch but still behave like a solid?
→ Its molecules are still connected but can temporarily shift under force.


2. Liquids: The Flowing State

Key Features:

  • Particles: Close but can move past each other
  • Forces: Moderate attraction (weaker than solids)
  • Behavior: Fixed volume but no fixed shape
  • Real-World Example: Mercury – forms droplets due to strong cohesion

Did You Know?
Liquids have surface tension – a “skin” effect caused by cohesive forces (e.g., water droplets on leaves).


3. Gases: The Free-Moving State

Key Features:

  • Particles: Far apart with rapid, random motion
  • Forces: Negligible attraction
  • Behavior: No fixed shape or volume
  • Real-World Example: Helium balloons – rise because gas is lighter than air

Fun Fact:
If a gas molecule were the size of a marble, its nearest neighbor would be a football field away!


Quick Quiz

  1. Which state has particles that vibrate but don’t change position? (Answer: Solid)
  2. Why can gases be compressed easily? (Answer: Large spaces between particles)
  3. Name a liquid that forms spherical droplets. (Answer: Mercury)

Hands-On Activity:
Observe Brownian Motion – Shine a flashlight in a dusty room to see tiny particles jiggling (proof of gas molecule collisions).



Changes in States of Matter: The Molecular Transformation

Discover how matter transforms between states through heating and cooling, explained using the kinetic theory of molecules with real-world examples.


How Matter Changes State

Matter transitions between solid, liquid, and gas when energy is added or removed. The kinetic theory explains these changes through molecular motion:

“Heat makes particles dance faster, cold makes them slow down.”

Key Concepts

Energy Absorption/Release – Heating adds energy; cooling removes it
Temperature Plateaus – Phase changes occur at fixed temperatures
Molecular Rearrangement – Particles reorganize during transitions


Phase Changes Explained

ProcessMolecular Change 🧪Real-World Example 🌍Energy Change
Melting (Fusion)Solid → Liquid (bonds break)Ice → Water at 0°CAbsorbs heat
FreezingLiquid → Solid (bonds form)Water → Ice at 0°CReleases heat
Boiling (Vaporization)Liquid → Gas (particles escape)Water → Steam at 100°CAbsorbs heat
CondensationGas → Liquid (particles clump)Dew forming on grassReleases heat
SublimationSolid → Gas (skips liquid)Dry ice → FogAbsorbs heat
DepositionGas → Solid (skips liquid)Frost on windowsReleases heat

Why Temperature Stays Constant During Phase Changes

  • Hidden Energy (Latent Heat):
    • Energy is used to break/form bonds rather than raise temperature
    • Example: Ice at 0°C stays at 0°C until fully melted

Science Snack:
Place ice and thermometer in water → Temperature won’t rise above 0°C until all ice melts!


Kinetic Theory in Action

1. Melting Ice (Solid → Liquid)

  1. Heat makes water molecules vibrate violently
  2. At 0°C, vibrations overcome crystalline bonds
  3. Molecules break free but stay close (liquid form)

2. Boiling Water (Liquid → Gas)

  1. Heat gives molecules enough energy to escape liquid
  2. At 100°C, bubbles form as water becomes steam
  3. Fun Fact: Steam at 100°C burns worse than boiling water (extra latent heat!)

3. Frost Formation (Gas → Solid)

  1. Water vapor loses energy on cold surfaces
  2. Molecules slow down and lock into ice crystals
  3. No liquid stage (deposition)

Quick Quiz

  1. What is the reverse process of sublimation? (Answer: Deposition)
  2. Why does steam cause severe burns? (Answer: Releases latent heat)
  3. During melting, heat energy is used to ______. (Answer: Break bonds)

Hands-On Activity (From Viva Textbook):
Heat wax while measuring temperature → Observe the plateau at its melting point!


Melting/Fusion: The Science Behind Solids Turning to Liquids

Discover why ice melts at 0°C and how all solids transform into liquids through the fascinating process of fusion, explained with simple science experiments.


What is Melting (Fusion)?

Melting, also called fusion, is the process where a solid absorbs heat energy and transforms into a liquid at a specific temperature called its melting point.

“At 0°C, ice becomes water without getting hotter – magic? No, science!”

Key Features of Melting

Fixed Temperature: Each solid melts at a unique melting point
Energy Absorption: Heat breaks rigid molecular bonds
No Temperature Rise: Energy goes into changing state, not raising temperature


Melting Points of Common Substances

SubstanceMelting Point (°C)Real-World Observation
Ice (H₂O)0Snow melting in sunlight
Wax37Candle dripping in heat
Aluminum660Metal smelting in factories
Iron1538Steel production

Why Does Temperature Stay Constant During Melting?

The kinetic theory explains this plateau:

  1. Heat makes particles vibrate faster
  2. At melting point, energy breaks bonds instead of increasing motion
  3. All energy goes into changing state (latent heat of fusion)

Science Snack:
Try This:

  • Heat ice while measuring temperature → Stays at 0°C until fully melted
  • Then watch the temperature rise again!

Molecular View of Melting

In Solids:

  • Particles vibrate in fixed positions (ordered structure)
    At Melting Point:
  • Vibrations overcome intermolecular forces
  • Structure collapses into liquid (disordered but still dense)

Real-World Example:
Why does chocolate melt in your hand?
→ Body heat (37°C) > Chocolate’s melting point (~30°C)


Search Results for:

In this chapter, learn:

  • to identify the subject and the predicate
  • about the predicate and the elements that can occur in the predicate of a sentence
  • about the subject word and its attributes

Introduction:

Understanding the subject and predicate is fundamental to mastering English grammar. The subject tells us who or what the sentence is about, while the predicate provides information about the subject, such as actions or descriptions. This chapter will guide you through identifying these key components, exploring the elements within the predicate, and understanding the subject word along with its attributes. Whether you’re a student, teacher, or language enthusiast, this knowledge will enhance your writing and communication skills. Dive in to build a strong grammatical foundation!

A sentence is a meaningful group of words that expresses a complete thought. Consider these examples:

  • Murali likes to act in plays.
  • Dona’s sister lives in Paris.
  • My friend Saeed works for a fashion studio.
  • Amanpreet is good at tennis.

The subject of a sentence refers to the person, thing, idea, or place that the sentence is about or that performs the action of the verb. The predicate, on the other hand, provides information about the subject, such as what it does or what describes it.

In the sentences above:

  • The subjects are Murali, Dona’s sister, My friend Saeed, and Amanpreet.
  • The predicates are likes to act in plays, lives in Paris, works for a fashion studio, and is good at tennis.

This distinction helps in analyzing and constructing clear, grammatically correct sentences.


Subject Word and its Attributes

words. When the subject contains multiple words, they form the complete subject, with the most important word being the subject word.

Consider these sentences:

  • The three sisters lived happily with their parents.
  • My friend Nikhil is a TV journalist.
  • Excessive exercise is not good for the heart.

In these examples:

  • Sisters is the subject word in the first sentence.
  • Nikhil is the subject word in the second sentence.
  • Exercise is the subject word in the third sentence.

Notice that the subject word is always a noun, serving as the core of the complete subject. This distinction helps clarify the structure and meaning of sentences.



The Subject Word Attribute

In a sentence, the subject word is frequently described or modified by an adjective (or adjective-like words). This descriptive element is known as its attribute.



The Subject Word Attribute

An attribute can take various forms, including adjectives, participles, participial adjectives, infinitives, pronouns, articles, or even phrases. A single subject word may have multiple attributes modifying it. Observe these examples:

  • The girl stopped at the door.
  • Nelson Mandela, the first black president of South Africa, was awarded the Bharat Ratna.
  • The speeding train made a lot of noise.
  • Her willingness to help others made her popular.
  • He himself sent the invitation.
  • Fresh vegetable juice is good for skin.

In each sentence, the highlighted phrases function as attributes, providing additional details about the subject word.


SubjectSubject WordAttribute
The girlgirlthe – definite article
Nelson Mandela, the first black president of South AfricaNelson Mandelathe first black president of South Africa – noun phrase
The speeding traintrainthe – indefinite articlespeeding – participial adjective
Her willingness to help otherswillingnessher – possessive adjectiveto help others – infinitive
He himselfhehimself – emphatic pronoun
Fresh vegetable juicejuicefresh – adjectivevegetable – noun doing the work of an adjective

Grammar Exercise: Subject Analysis

Underline the subject in each of these sentences. Then write the subject word and its attributes for each subject. Also, mention the type of the attribute.

  1. The boy was thrilled to see the dragon.
  2. His refusal to give up is the secret of his success.
  3. The smiling baby looked very cute.
  4. Boiled water is good for health.
  5. His advice has been very useful for us.
  6. Ms Nupur, the English teacher of Class VI, was felicitated by the principal.
  7. Ms Hema herself called to enquire about the matter.

Answers:

SentenceSubject (Underlined)Subject WordAttribute(s)Type of Attribute
1.The boy was thrilled to see the dragon.boy“The”definite article
2.His refusal to give up is the secret of his success.refusal“His” (possessive adjective), “to give up” (infinitive phrase)possessive adjective + infinitive
3.The smiling baby looked very cute.baby“The” (article), “smiling” (present participle)article + participial adjective
4.Boiled water is good for health.water“Boiled” (past participle)participial adjective
5.His advice has been very useful for us.advice“His”possessive adjective
6.Ms Nupur, the English teacher of Class VI, was felicitated by the principal.Ms Nupur“the English teacher of Class VI” (appositive phrase)noun phrase
7.Ms Hema herself called to enquire about the matter.Ms Hema“herself” (emphatic pronoun)emphatic pronoun

Extra Practice Questions (with Answers):

Questions:

  • The old library books were donated to charity.
  • Her determination to win inspired everyone.
  • The running athlete broke the world record.
  • Cooked vegetables retain more nutrients.
  • Mr. Sharma, our school principal, announced a holiday.
  • The students themselves organized the event.

Answers:

SentenceSubject (Underlined)Subject WordAttribute(s)Type of Attribute
8.The old library books were donated to charity.books“The” (article), “old” (adjective), “library” (noun as adjective)article + adjective + noun modifier
9.Her determination to win inspired everyone.determination“Her” (possessive adjective), “to win” (infinitive)possessive adjective + infinitive
10.The running athlete broke the world record.athlete“The” (article), “running” (present participle)article + participial adjective
11.Cooked vegetables retain more nutrients.vegetables“Cooked” (past participle)participial adjective
12.Mr. Sharma, our school principal, announced a holiday.Mr. Sharma“our school principal” (appositive phrase)noun phrase
13.The students themselves organized the event.students“The” (article), “themselves” (emphatic pronoun)article + emphatic pronoun

Understanding Predicates and Adverbial Qualifications

A predicate can range from a single word to multiple words that complete the meaning of a sentence. For example:

  • Tulika paints. (predicate with one word)
  • The leopard chases the deer. (predicate with three words)

Within the predicate, verbs may be modified by adverbs or adverb-equivalent constructions, known as adverbial qualifications. Consider these examples:

  1. The children ran upstairs. (adverb modifying the verb)
  2. Aneesh came home. (noun functioning as an adverb of place)
  3. He jogs to keep himself fit. (infinitive phrase acting as an adverb of purpose)
  4. The birds chirped in the garden. (prepositional phrase serving as an adverbial modifier)

Grammar Exercise: Identifying Sentence Components

Read each of the sentences given below and identify:
a. The subject word and its attributes.
b. The verb and its adverbial qualification.

  1. The young professor spoke eloquently.
  2. The carefree birds were playing in the water.
  3. My friends are going to the beach.
  4. The new actors acted very well.
  5. The old lady returned home.
  6. The wrinkled old man smiled faintly.
  7. The migrant workers struggled to survive.
  8. The last train to Kalka comes mostly on time.

Answers:

SentenceSubject WordAttributesVerbAdverbial Qualification
1. The young professor spoke eloquently.professor“The” (article), “young” (adjective)spoke“eloquently” (adverb of manner)
2. The carefree birds were playing in the water.birds“The” (article), “carefree” (adjective)were playing“in the water” (prepositional phrase, adverb of place)
3. My friends are going to the beach.friends“My” (possessive adjective)are going“to the beach” (prepositional phrase, adverb of place)
4. The new actors acted very well.actors“The” (article), “new” (adjective)acted“very well” (adverb phrase of manner)
5. The old lady returned home.lady“The” (article), “old” (adjective)returned“home” (noun as adverb of place)
6. The wrinkled old man smiled faintly.man“The” (article), “wrinkled” (adjective), “old” (adjective)smiled“faintly” (adverb of manner)
7. The migrant workers struggled to survive.workers“The” (article), “migrant” (adjective)struggled“to survive” (infinitive phrase, adverb of purpose)
8. The last train to Kalka comes mostly on time.train“The” (article), “last” (adjective), “to Kalka” (prepositional phrase)comes“mostly on time” (adverb phrase of frequency)

Extra Practice Questions (with Answers):

Questions:

  • The excited children ran quickly to the park.
  • Her younger brother studies diligently every night.
  • The exhausted soldiers marched through the desert.
  • Our neighbor’s dog barks loudly at strangers.
  • The famous singer performed beautifully on stage.

Answers:

SentenceSubject WordAttributesVerbAdverbial Qualification
9. The excited children ran quickly to the park.children“The” (article), “excited” (adjective)ran“quickly” (adverb of manner), “to the park” (prepositional phrase, adverb of place)
10. Her younger brother studies diligently every night.brother“Her” (possessive adjective), “younger” (adjective)studies“diligently” (adverb of manner), “every night” (adverb phrase of frequency)
11. The exhausted soldiers marched through the desert.soldiers“The” (article), “exhausted” (adjective)marched“through the desert” (prepositional phrase, adverb of place)
12. Our neighbor’s dog barks loudly at strangers.dog“Our neighbor’s” (possessive noun phrase)barks“loudly” (adverb of manner), “at strangers” (prepositional phrase, adverb of target)
13. The famous singer performed beautifully on stage.singer“The” (article), “famous” (adjective)performed“beautifully” (adverb of manner), “on stage” (prepositional phrase, adverb of place)

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LEARNING OBJECTIVES

Understanding the representation of geographical features is fundamental in geography, as it helps visualize Earth’s diverse landscapes through maps and symbols. Topographical maps serve as essential tools, using contour lines to depict elevation, relief, and landforms like mountains, plateaus, and valleys. These maps also highlight human settlements—whether nucleated, dispersed, or linear—providing insights into how people interact with their environment. By studying the spacing, shape, and colors of contours, one can interpret slope steepness, identify ridges, and distinguish between temporary and permanent settlements. This guide explores how geographical features are accurately represented, making complex terrain easy to analyze for students, planners, and explorers alike.

Children will be able to:

  • Read contours on toposheets;
  • Distinguish between steep and gentle slopes through contours;
  • Identify landforms through contours on the toposheet;
  • Differentiate patterns of settlements on the toposheet;
  • Draw contours and related landforms on plain paper;
  • Interpret and analyse the toposheets.

LEARNING TERMS

Contour: A contour is an imaginary line joining places having the same height above sea level.
Contour Interval: The space between the contour line represents a set distance, called the contour interval.
Mountain: It is an elevation which rises abruptly above the surrounding areas.
Plateau: It is an elevated plain with a relatively level surface which falls down rapidly.
Col or Pass: A col is a short steep-sided depression on the ridge.
Temporary Settlements: The settlements which are occupied for a short period are called temporary settlements.
Permanent Settlements: The settlements which are occupied for a long period are called permanent settlements.
Nucleated or Compact Pattern: Nucleated settlements have a number of houses built close to one another along narrow streets.


Topographical Maps & Contours

Topographical Maps


These are large-scale maps showing elevation, relief, drainage, vegetation, and man-made features like roads and settlements. Used in engineering, defense, and urban planning, they help study Earth’s physical and human features.

Relief on Toposheets

Relief includes mountains, plateaus, plains, and slopes. Contours (brown lines) join points of equal height, helping visualize 3D landforms on 2D maps.

Contour Lines & Intervals

Contours indicate elevation, slope steepness, and land shape. Close contours = steep slope;

wide contours = gentle slope. The fixed height difference between lines is the CONTOUR INTERVALS.

Gentle vs. Steep Slopes

  • Gentle Slope: Contours are far apart, indicating a gradual rise.
    • Steep Slope: Contours are close, showing a rapid elevation change.

Key Features of Contours

  • Always continuous, curved, and brown.
    • Spacing shows slope steepness.
    • Values are labeled on the higher side.
    • Their shape mimics the landform.

Quiz Time! 🌍

1. What do closely spaced contour lines indicate?
a) Gentle slope
b) Steep slope
c) Flat land
Answer: b) Steep slope. Explanation: Tight spacing means a sharp elevation change.*

2. Which color are contours usually drawn in on maps?
a) Blue
b) Green
c) Brown
Answer: c) Brown. Explanation: Contours are brown to stand out from other features.*

3. What does a contour interval represent?
a) Distance between two roads
b) Height difference between two contours
c) Depth of a river
Answer: b) Height difference. Explanation: It’s the fixed elevation gap between lines.*

4. Widely spaced contours suggest:
a) A cliff
b) A gentle hill
c) A volcano
Answer: b) Gentle hill. Explanation: Gradual slopes = more space between lines.*


Jokes ! 😄

  1. Why did the contour line break up with the mountain?
    It needed space.
  2. What’s a cartographer’s favorite type of music?
    Map-hop!
  3. Why was the geography book so confident?
    It knew all the layers of the Earth.
  4. How do you spot a steep slope in a crowd?
    It’s always contour-tight!

Keep studying! 🗺️✨

Contours & Landforms

Mountain

A steep elevation rising sharply above its surroundings. On maps, closely spaced contours with increasing values show mountains, often with multiple summits.

Conical Hill

A smaller, naturally rounded elevation with a broad base and narrow peak. Its circular contours are evenly spaced, centered around the hilltop.

Plateau (Tableland)

A flat-topped elevated area with steep sides. Contours cluster at the edges, while the central plateau area has few or no contours.

Ridge

A long, narrow hill with a high elevation. Elongated, closely spaced contours form its spine, sometimes interrupted by peaks or passes.

Col/Pass

A steep-sided dip in a ridge, often used for roads. It’s a low point between two peaks, acting as a natural passage.

Saddle

A wide, shallow depression between peaks, shaped like a horse’s saddle. Less steep than a col but serves a similar purpose.

Gap

A pass eroded by water, creating a lower, wider opening in a mountain range.


    Quiz Time! 🏔️

    1. How are mountains represented on contour maps?
    a) Widely spaced circular lines
    b) Closely spaced lines with increasing values
    c) No contours at all
    Answer: b) Closely spaced lines show steep elevation changes.

    2. What shape do contours of a conical hill make?
    a) Straight lines
    b) Circular lines centered around a peak
    c) Random zigzags
    Answer: b) Circular contours indicate a rounded hill.

    3. A plateau’s contours are mostly found:
    a) Only in the center
    b) Along its edges
    c) Nowhere—it’s flat!
    Answer: b) Contours cluster at the steep sides.

    4. What’s the difference between a col and a saddle?
    a) A col is broader; a saddle is steeper
    b) A saddle is wider and shallower
    c) They’re the same thing
    Answer: b) Saddles are flatter, like a horse’s saddle.


    Jokes ! 😆

    1. Why did the geographer bring a ladder to the mountain?
      To study the high points of contour lines!
    2. What’s a plateau’s favorite song?
      “Ain’t No Mountain High Enough” (because it’s flat on top!).
    3. Why did the contour lines break up?
      They needed space—some were too close!
    4. How do you spot a ridge in a crowd?
      It’s always the high-spirited one!

    Happy mapping! 🗺️✏️

    Settlements & Topographical Maps

    Settlements

    Places where people live and work, shown in red on toposheets. Include buildings like houses, temples, and post offices. Can be temporary (short-term) or permanent (long-term).

    Nucleated/Compact Settlements

    Houses clustered close together, often near water or fertile soil. Found in both old (irregular) and new (geometric) towns. Common in resource-rich areas.

    Dispersed/Scattered Settlements

    Houses spread far apart, found in harsh areas like highlands or poor soil. Caused by limited water or tough climates. Example: Ikapura on toposheets.

    Topographical Maps

    Show land features like hills, rivers, and man-made structures (roads, settlements). Use contour lines (brown) to indicate elevation, with fixed gaps called contour intervals.


    Quiz Time! 🏡

    1. What color represents settlements on toposheets?
    a) Blue
    b) Green
    c) Red
    Answer: c) Red marks all settlement features.

    2. Nucleated settlements are typically found near:
    a) Deserts
    b) Fertile soil/water sources
    c) Volcanoes
    Answer: b) Resources encourage clustered living.

    3. Dispersed settlements occur due to:
    a) Poor soil and scarce water
    b) Too many shops
    c) Flat terrain
    Answer: a) Harsh conditions force people to spread out.

    4. Contour intervals show:
    a) Road widths
    b) Height differences between lines
    c) Population density
    Answer: b) They measure elevation changes.


    Jokes 😄

    1. Why did the settlement break up?
      It needed more space—it was too nucleated!
    2. What’s a contour line’s favorite game?
      “Follow the Leader” (because they never cross!)
    3. Why did the geographer get lost in a dispersed settlement?
      They couldn’t find a neighbor to ask directions!
    4. How do you organize a topographical map party?
      Invite all the key features—but keep the contours spaced out!

    Keep exploring! 🌍✏️

    Assessment on the chapter


    (A) Answer the following questions briefly :

    Which type of settlement is your city/village have? Give reason.

    My city has a nucleated settlement pattern. This is evident from the closely built houses and compact urban layout visible on maps. The settlement likely developed near a water source or fertile land, which encouraged people to cluster together for shared resources and community living, forming the dense, red-colored area visible on the topographical map.

    Define a topographical map.

    A topographical map is a large-scale map that shows both natural and man-made features of an area. It represents elevation and relief through contour lines, displays drainage systems like rivers, shows vegetation cover, and includes human-made features such as roads, railways, and settlements. These maps are extensively used for engineering projects, urban planning, and military purposes because they provide detailed and accurate geographical information.

    ‘Topographical maps are very important.’ Give reason.

    Topographical maps are crucial because they serve multiple essential functions. They are used by engineers for construction projects, by urban planners for residential and commercial development, and by defense forces for strategic planning. The maps provide vital information about terrain, elevation, and land features that help in navigation, resource management, and infrastructure development. Their detailed representation makes them indispensable tools for geographical studies and practical applications.

    How can physical features be represented on a map?

    Physical features on a map are represented using various symbols and colors. Contour lines in brown indicate elevation and relief, with their spacing showing slope steepness. Water bodies like rivers and lakes are shown in blue. Vegetation is represented using green shades or symbols. Man-made features such as roads and buildings are marked in black or red. This systematic representation helps in accurately depicting the physical characteristics of an area.

    Define contour.

    A contour is an imaginary line on a map that connects points of equal elevation above sea level. These lines are typically drawn in brown and help visualize the three-dimensional shape of the land on a two-dimensional map. Contours provide information about the height, slope, and terrain of an area, making them essential for understanding geographical features.

    What is contour interval?

    The contour interval is the constant vertical distance between two consecutive contour lines on a map. This fixed difference in elevation helps in determining the steepness or gentleness of slopes. For example, closely spaced contours indicate a steep slope, while widely spaced contours suggest a gentle slope. The interval is chosen based on the map’s scale and the terrain’s complexity.

    What is a mountain?

    A mountain is a significant natural elevation of the Earth’s surface that rises abruptly from the surrounding area. On a topographical map, mountains are represented by closely spaced contour lines with increasing values, indicating rapid elevation changes. Mountains often have multiple summits and are prominent features in rugged terrain.

    What is nucleated settlement?

    Nucleated settlements are compact clusters of houses built close together, often along narrow streets. These settlements are typically found near vital resources like water sources, fertile soil, or industrial sites. They can have irregular patterns in older towns or more regular, geometric layouts in modern planned towns. On maps, they appear as dense red areas.

    What is dispersed settlement?

    Dispersed settlements consist of isolated dwellings scattered over a wide area. These are common in regions with poor soil, limited water supply, or harsh climatic conditions, such as highlands. Unlike nucleated settlements, houses in dispersed settlements are far apart, resulting in low population density. On maps, they appear as sparse red dots.

    What is linear settlement?

    Linear settlements are arranged in a line, typically along roads, rivers, or coastlines. This pattern develops due to the convenience of transportation and access to resources. Houses and buildings are aligned in a straight or slightly curved line, following the natural or man-made linear feature that supports the settlement.

    What is difference between temporary and permanent settlement?

    Temporary settlements are occupied for short periods and are often associated with nomadic lifestyles or seasonal activities. Examples include campsites or pastoral settlements. Permanent settlements, on the other hand, are established for long-term habitation, featuring fixed structures like houses, schools, and hospitals. These are continuously inhabited and developed over time.

    (B) Answer the following questions in detail :

    1. Mention any four features of contours.

    Contours have several distinctive features that help in understanding terrain representation:

    • Continuous Lines: Contours are unbroken, curved lines that never cross each other, connecting points of equal elevation across the map.
    • Uniform Interval: The vertical distance between two consecutive contours, called the contour interval, remains constant throughout the map, allowing consistent measurement of elevation changes.
    • Slope Indication: Closely spaced contours indicate steep slopes, while widely spaced contours show gentle slopes, helping visualize terrain steepness.
    • Landform Representation: The shape of contour lines mirrors the actual landform – circular patterns may indicate hills or depressions, while V-shaped contours point to valleys.

    2. Analyse various types of settlements.

    Settlements can be categorized based on their patterns and distribution:

    • Nucleated/Compact Settlements: Characterized by closely built houses clustered together, typically found near water sources or fertile lands. These show dense red areas on toposheets with irregular patterns in old towns and geometric layouts in planned areas.
    • Dispersed Settlements: Feature isolated dwellings spread over large areas, common in regions with poor resources like highlands or deserts, appearing as scattered red dots on maps.
    • Linear Settlements: Develop along transportation routes like roads or rivers, with buildings arranged in linear patterns following these features.
    • Temporary vs Permanent: Temporary settlements are short-term (nomadic camps), while permanent ones have fixed structures for long-term habitation.

    3. Carefully study the given contour and comment on relief of the area.

    Based on contour characteristics:

    • Closely Spaced Contours: Indicate steep terrain features like mountains or escarpments, suggesting rapid elevation changes over short distances.
    • Widely Spaced Contours: Show gentle slopes or flat areas such as plains or plateaus, where elevation changes gradually.
    • Circular Patterns: Concentric circles with increasing values denote conical hills or mountains, while depressed contours indicate basins.
    • Irregular Shapes: Elongated contours suggest ridges or valleys, with V-shaped patterns pointing uphill in valleys. The overall relief can be determined by analyzing contour spacing, shape and values – for instance, alternating steep and gentle areas would show varying contour spacing across the map.

    (C) Read the statement and identify the term :



    Imaginary line joining places having the same height.
    Answer: Contour
    Explanation: A contour is defined as an imaginary line on a map that connects points of equal elevation above sea level, used to represent relief and landforms.


    An elevated plain with relatively level surface which falls down rapidly.
    Answer: Plateau (or Tableland)
    Explanation: A plateau is an elevated flat area with a relatively level surface that drops sharply at its edges, represented on maps by contours concentrated along its sides.


    A high elongated hill represented on the map by elliptical contours.
    Answer: Ridge
    Explanation: A ridge is a long, narrow elevation of land shown by elongated, closely spaced contour lines that form an elliptical pattern on the map.


    It is a short steep sided depression on the ridge.
    Answer: Col (or Pass)
    Explanation: A col is a sharp depression between two peaks along a ridge, often used as a natural passageway, represented by a break in contour lines.


    A pass which has been lowered by the action of running water.
    Answer: Gap
    Explanation: A gap is a type of pass that has been eroded and widened by water flow, creating a lower, more open passage through mountainous terrain.

    (D) Fill in the blank with suitable word/words :

     
    Contours are drawn in ______ colour on the toposheet.
    Answer: brown
    Explanation: Contour lines are always represented in brown on topographical maps to distinguish them from other features.


    The spacing of the contours expresses the ______ of the slope.
    Answer: steepness
    Explanation: Closely spaced contours indicate steep slopes, while widely spaced contours show gentle slopes.


    On a coloured toposheet, all types of settlements are shown in ______ colour.
    Answer: red
    Explanation: Settlements, including buildings, roads, and landmarks, are marked in red for easy identification.


    ______ type of settlement is found in sparsely populated areas.
    Answer: Dispersed (or Scattered)
    Explanation: Dispersed settlements consist of isolated houses spread over large areas, common in regions with poor resources or harsh conditions.


    ______ type of settlement can be seen along the perennial source of water.
    Answer: Nucleated (or Compact)
    Explanation: Nucleated settlements develop near reliable water sources, fertile land, or trade routes, resulting in clustered housing.

    (E) Multiple choice questions :

    It is a large-scale map which shows elevation, relief, drainage, vegetation, man-made features like roads, railways, settlements etc.
    (a) Atlas
    (b) Physical map
    (c) Political map
    (d) Topographical map
    Explanation: Topographical maps provide detailed representations of both natural and human-made features on the Earth’s surface.

    On a topographical map relief is shown with the help of ______.
    (a) Contours
    (b) Parallel lines
    (c) Triangles
    (d) Circles
    Explanation: Contours (brown lines) connect points of equal elevation, showing relief and landforms.

    The space between the contour line represents a set distance, called the ______.
    (a) Contour difference
    (b) Contour gap
    (c) Contour interval
    (d) Gradient
    Explanation: The fixed vertical distance between two consecutive contours is the contour interval.

    Which of the following is not TRUE for contour lines?
    (i) These show elevation of land.
    (ii) These represent steepness of the slope.
    (a) Only (i)
    (b) Only (ii)
    (c) Both (i) & (ii)
    (d) Neither (i) Nor (ii)
    Explanation: Both statements are true—contours indicate elevation and slope steepness.

    Crowded together contours represent ______.
    (a) Steep slope
    (b) Gentle steep
    (c) Zero slope
    (d) Level ground
    Explanation: Closely spaced contours mean rapid elevation change, indicating steep terrain.

    Contours are shown in ______ colour.
    (a) Yellow
    (b) Green
    (c) Brown
    (d) Red
    Explanation: Contours are always brown on topographical maps.

    It is a high elongated hill represented on the map by elliptical contours.
    (a) Ridge
    (b) Plateau
    (c) Mountain
    (d) Conical Hill
    Explanation: Ridges appear as elongated, elliptical contours on maps.

    ______ have a number of houses built close to one another along narrow streets.
    (a) Nucleated or Compact Pattern
    (b) Dispersed or Scattered Settlement
    (c) Linear or Ribboned Pattern
    (d) Rural Settlement
    Explanation: Nucleated settlements feature clustered housing, often near resources.

    ______ is an imaginary line joining places having the same height above sea level.
    (a) Contour
    (b) Toposheet
    (c) Isotherm
    (d) Latitude
    Explanation: Contours connect points of equal elevation.


    Answers are bolded for clarity.

    (F) Read the extract and answer the following questions :

    Extract: “These are large-scale maps which show elevation, relief, drainage, vegetation, man-made features like roads, railways, settlements etc. These are used for engineering, public works, commercial and residential planning. Information from such maps is used extensively in the field of defense and navigation.”

    Questions and Answers:


    Identify the type of map explained in the extract.
    Answer: Topographical map
    Explanation: The description matches topographical maps which show both natural features (elevation, relief, drainage, vegetation) and man-made features (roads, railways, settlements) at large scales for various practical applications.


    How is elevation or relief shown on such maps?
    Answer: Through contour lines
    Explanation: Contour lines (brown colored) are the primary method used on topographical maps to show elevation and relief. These imaginary lines connect points of equal elevation, with their spacing indicating slope steepness.


    What is a large-scale map?
    Answer: A map that represents a small area with great detail
    Explanation: Large-scale maps (e.g., 1:50,000) show smaller geographic areas but with more detailed information compared to small-scale maps. They are essential for precise planning and analysis of specific locations.

    (G) Mark True or False against the statements given below

     
    A toposheet is a small scale map.
    False
    Correction: A toposheet is a large-scale map that shows detailed features like elevation, settlements, and drainage.


    A contour is an imaginary line joining places having the same temperature.
    False
    Correction: A contour joins places of the same height above sea level, not temperature. (Isotherms show temperature.)


    On a coloured toposheet, all types of settlements are shown in brown colour.
    False
    Correction: Settlements are shown in red, while contours are brown.


    Dispersed settlements have a number of houses built close to one another.
    False
    Correction: Dispersed settlements have isolated houses spread far apart. Nucleated settlements have closely built houses.


    Nucleated settlements develop along the rivers.
    True
    Explanation: Nucleated settlements often form near resources like rivers, fertile soil, or roads, with houses clustered together.

    (H) Match the column A with column B :

    Matching Question:

    Column AColumn B
    1. Topographical map(a) Steep slope
    2. Contours are spaced together(b) Ridge
    3. Contours are widely spaced(c) Mountain
    4. Elongated and closely spaced contours(d) Gentle slope
    5. Contours are closely spaced with increase in the contour value(e) Large scale map

    Correct Answers:

    Column AColumn B
    1. Topographical map(e) Large scale map
    2. Contours are spaced together(a) Steep slope
    3. Contours are widely spaced(d) Gentle slope
    4. Elongated and closely spaced contours(b) Ridge
    5. Contours are closely spaced with increase in the contour value(c) Mountain

    Explanation of Matches:

    Increasing, close contour values depict mountains

    Topographical maps are large-scale maps showing detailed terrain features

    Closely spaced contours indicate steep slopes

    Widely spaced contours show gentle slopes

    Elongated, close contours represent ridges

    1. What is a topographical map?

    A topographical map is a large-scale map that shows elevation, relief, drainage, vegetation, and man-made features like roads and settlements. It uses contour lines to represent terrain and is essential for engineering, defense, and urban planning.

    2. How are geographical features represented on maps?

    Features like mountains, valleys, and plateaus are shown using contour lines (brown), water bodies (blue), and settlements (red). Contour spacing indicates slope steepness, while colors/symbols mark vegetation and infrastructure.

    3. What do closely spaced contour lines indicate?

    Closely spaced contours represent a steep slope (e.g., mountains), while widely spaced lines show gentle slopes (e.g., plains).

    4. What is the difference between a mountain and a plateau on a map?

    Mountain: Closely spaced contours with increasing values.
    Plateau: Concentrated contours at edges, flat center (few contours).

    5. How are settlements classified on topographical maps?

    Nucleated: Clustered houses (red, dense pattern).
    Dispersed: Scattered homes (sparse red dots).
    Linear: Along roads/rivers (line-shaped).

    6. What is a contour interval?

    The fixed vertical distance between two contour lines, showing elevation difference (e.g., 20 meters). It helps measure slope steepness.

    7. What do elliptical contours on a map represent?

    They indicate a ridge—a long, narrow hill with a high elevation.

    8. How can you identify a col or pass on a map?

    col appears as a short, steep-sided depression between two peaks, often marked by a break in contour lines.

    9. Why are topographical maps important?

    They aid in navigation, urban planning, military strategy, and disaster management by providing accurate terrain details.

    10. What colors are used for contours and settlements on toposheets?

    Contours: Brown
    Settlements: Red
    Water bodies: Blue

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    Table of Contents

    Deadpool’s Guide to Plant Tissues: Because Even Plants Have Drama!

    “Tissues are a group of similar cells which perform specific functions. Think of them like the Avengers—each has a role, but some are dead(wood) and others are just clingy (looking at you, phloem). Let’s dissect this leafy soap opera, shall we?”

    Pop Quiz, Hotshot! (Don’t worry, I’ll answer for you.)

    1. What are the different types of plant tissues?
      (Meristematic, permanent, xylem, phloem—like a plant’s version of “The Breakfast Club.”)
    2. Write two characteristics of meristematic tissues.
      (They’re the overachievers: always dividing and never mature. Basically, plant teenagers.)
    3. Identify the images of tissues below and name them.
    • (a) Food-storing tissue? Parenchyma (the snack drawer).
    • (b) Living cells? Phloem (the drama queens).
    • (c) Dead cells? Xylem (the plant’s skeleton crew).
    1. What are complex permanent tissues?
      (Xylem and phloem—the plant’s Uber and Postmates, delivering water and tacos… I mean, food.)

    The Plant’s Delivery System: Two Types of Drama

    Plants don’t have DoorDash, so they move stuff themselves:

    1. Water & Minerals: Sucked up from roots to leaves like a lazy frat bro with a straw.
    2. Food: Phloem ships sugar from leaves to the rest of the plant—basically a photosynthesis Uber Eats.

    “Xylem’s the deadbeat dad (literally, it’s made of dead cells), and phloem’s the overworked mom juggling snacks. Family goals, amirite?”

    SEO Bonus: How do plants eat? What’s xylem? Why is phloem lazy? Find out why your ficus is judging your life choices. 🌿💀

    (Stay tuned for Deadpool’s next lesson: “Transpiration—Why Plants Sweat More Than You in a Job Interview.”)

    Deadpool’s Guide to Plant Plumbing: Xylem & Phloem’s Dysfunctional Roommate Drama

    “Alright, photosynthesis fanboys and girls, let’s get into the nitty-gritty of plant logistics. These green guys don’t have veins—they’ve got a gnarly internal subway system made of deadbeat cells and sugar pushers. Buckle up, buttercups!”


    Xylem: The Plant’s Skeleton Crew (Literally)

    “Xylem is like that one goth kid in high school—mostly dead inside but weirdly essential to the ecosystem.”

    Structure:

    • Occupies the VIP center of the vascular bundle (because dead cells have seniority, apparently).
    • Four types of cells, because plants love bureaucracy:
    1. Tracheids – Long, dead, and full of holes (kinda like my morals). They’re like straws, but less useful for milkshakes.
    2. Vessels – Open-ended dead tubes stacked like a Jenga tower of poor life choices.
    3. Parenchyma – The only living part, hoarding snacks (starch & fat) like a doomsday prepper.
    4. Sclerenchyma – Thick-walled, dead, and rigid—basically the plant’s version of my ex.

    *”Xylem’s motto: ‘We move water up, and *nothing else.’ No refunds.”


    Phloem: The Plant’s Overworked Uber Eats Driver

    “Phloem is the plant’s sugar highway, and it’s got more layers than my emotional damage.”

    Structure:

    • Runs alongside xylem like a clingy sidekick (think Robin to Batman, if Robin was made of sucrose).
    • Four cell types, because why keep it simple?
    1. Sieve Tubes – Living cells without brains (no nuclei). Basically interns.
    2. Companion Cells – The micromanaging bosses keeping sieve tubes alive (Karens of the plant world).
    3. Phloem Fibres – Dead, stringy, and useless—like my gym membership.
    4. Phloem Parenchyma – Storage specialists (aka the snack drawer of the plant).

    *”Phloem’s job: Move food *anywhere*. Xylem’s job: Move water *up*. Me? I move *on—usually to the next taco stand.”


    Why Should You Care? (SEO Hook)

    “How do trees drink without mouths? Why are dead cells better plumbers than your landlord? What’s the deal with plant snack redistribution? Stick around, and I’ll explain—with 200% more sarcasm than your 10th-grade bio teacher!”

    (Coming soon: Transpiration—Or, Why Plants Sweat More Than You at a Family Reunion. Stay weird, folks!) 🌿💦

    Johnny English’s Guide to Plant Hydration: How Roots Drink Like a Clumsy Spy

    *”Ah, so you want to know how plants drink water, do you? Well, it’s not with tiny teacups, I can tell you that much. No no, plants have a far more… *discreet* system. Much like myself when I’m trying to sneak into a villain’s lair – only slightly more competent!”*


    The Great Root Heist: Operation H2O

    Plants don’t have mouths (shocking, I know), so they’ve developed a brilliantly ridiculous system to steal water right from under the soil’s nose. Here’s how the mission unfolds:

    1. Root Hair Reconnaissance
    • Those tiny root hairs? They’re like my surveillance team – except they actually do their job properly.
    • Each hair is a microscopic undercover agent, increasing the plant’s surface area for maximum water theft.
    • “They’re so thin, they make my disguise mustache look bushy by comparison!”
    1. Osmosis: The Silent Extraction
    • Water moves from the soil (high concentration) into roots (low concentration) through a semipermeable membrane.
    • “It’s like when I sneak into a party – I always move from where there’s lots of people (the buffet) to where there’s fewer people (the secret documents).”
    • No energy required! The water just waltzes in uninvited.
    1. Active Transport: The Covert Mineral Mission
    • For minerals, roots have to actively pull them in against concentration gradients.
    • “This is where they call in Q Branch – special protein pumps that work harder than my stunt double!”
    • Requires ATP energy (the plant version of exploding pens).

    Why This Matters (And Why You Should Care)

    • Plants drink like British spies – silently, efficiently, and with minimal collateral damage (unless you count dry soil).
    • Root hairs are nature’s best secret agents – with better success rates than most of my missions.
    • Osmosis is the ultimate stealth tactic – no energy needed, just pure scientific infiltration.

    “Next time you water your plants, remember: you’re not just gardening, you’re running a hydration heist! Now if you’ll excuse me, I need to go… water my cactus. Or was it feed my goldfish? Blast.”

    SEO Bonus: How do plants drink water? What is root absorption? The secret life of thirsty plants revealed! 🌱💦

    Professor Snape’s Guide to Plant Hydration: Or How I Learned to Stop Worrying and Love Osmosis

    “Ten points from Gryffindor for not knowing how water moves through plants before today. Honestly, even Longbottom’s shrivelfig could grasp this concept. Pay attention, or I’ll have you sorting root hairs for detention.”


    The Dark Arts of Water Movement

    Osmosis isn’t some flashy Patronus charm – it’s the subtle, sinister magic that makes water move through plants while no one’s looking. Much like certain Slytherins sneaking into the kitchens after curfew.

    1. The Root Hair Conspiracy
    • Those pathetic little root hairs are your plant’s first line of defense, stretching into soil like first years reaching for the last treacle tart
    • “50 points from Hufflepuff if you think these are actual hairs. They’re epidermal extensions, you dunderheads!”
    • Their permeable cell walls might as well have “Muggle Welcome” signs for water molecules
    1. The Semi-Permeable Membrane Deception
    • The cell membrane plays gatekeeper like Filch with first-years
    • Allows water in but blocks soil particles – “Not unlike how I allow your feeble attempts at potions but block any actual intelligence from entering your skulls”
    • Works through water concentration gradients – high to low, like House points when Potter’s involved
    1. The Cortical Espionage Network
    • Water infiltrates deeper root tissues through sequential osmosis
    • “Moving cell to cell like students passing notes during my lectures”
    • Eventually reaches xylem vessels – the plant equivalent of Slytherin’s secret passages

    Why This Matters (You Insufferable Dunderheads)

    • Osmosis is the silent assassin of plant hydration – no flashy spells required
    • Root pressure builds like house rivalries – pushing water upward against gravity
    • The xylem is your Dark Mark – once water’s in, there’s no escaping upward movement

    “For tomorrow’s lesson: Transpiration Pull – or how plants manage to lose water more efficiently than you lot lose House points. Bring your wands and what little brainpower you possess.”

    SEO Spells: How do plants drink water? What is osmosis in plants? The secret potion of plant hydration revealed!

    “This concludes today’s lesson. Blackboard, clean yourself!” ✨🌿

    Tony Stark’s Guide to Diffusion: Or How I Learned to Stop Worrying and Let Molecules Party

    *”Alright, listen up, future scientists—or at least, people who pretend to care about science while waiting for the next *Iron Man* movie. Today’s lesson: Diffusion, the universe’s way of letting molecules do whatever the hell they want. No arc reactors required.”*


    What Is Diffusion? (And Why Should You Care?)

    Diffusion is like that one friend who shows up uninvited to every party and somehow ends up in all your photos. It’s the natural movement of molecules from high concentration (where there’s too many of them, like my ego in a room) to low concentration (where there’s space, like Pepper’s patience with me).

    • No energy? No problem! Unlike my suits, diffusion runs on pure laziness.
    • No membrane? Even better! Osmosis needed a semipermeable barrier—diffusion just needs molecules with a sense of adventure.
    • Happens everywhere—from perfume filling a room (cough too much cologne, Thor) to oxygen slipping into your lungs like a spy in Stark Tower.

    Diffusion in Plants: The Silent Superpower

    Plants don’t have Jarvis to move stuff around, so they rely on diffusion like I rely on coffee. Here’s how they do it:

    1. Gas Exchange (aka Plant Breathing)
    • Leaves take in CO₂ (because plants love carbon more than I love sarcasm).
    • They kick out O₂ (the ultimate “thanks for nothing” to animals).
    • “Stomata are like tiny air vents—except they don’t blast AC like Rhodey in summer.”
    1. Water Loss (aka Plant Sweating)
    • Water vapor escapes through stomata—because even plants need to “glow” sometimes.
    • “Transpiration is just diffusion’s fancy cousin who went to grad school.”
    1. Nutrient Uptake (aka Plant Fast Food)
    • Roots absorb minerals when soil’s got more than the plant—like me stealing fries off Cap’s plate.

    Diffusion vs. Osmosis: The Showdown

    DiffusionOsmosis
    “Free-for-all molecule mosh pit”“VIP water-only club”
    No membrane neededNeeds a semipermeable bouncer
    Works in air, liquid, solids (slowly)Strictly liquid affairs
    “Like me at a party—no rules.”“Like Pepper running SI—structured chaos.”

    Why This Matters (Besides Impressing Pepper)

    • Plants stay alive without paying for Uber Eats (thanks, diffusion!).
    • Your lungs get oxygen without you even trying (unlike my attempts at meditation).
    • Perfume works (science: 1, Bad Cologne Choices: 0).

    “Next time you smell coffee brewing, thank diffusion. Then drink it. Then build something reckless.”

    SEO Hook: How do plants breathe? What is diffusion in biology? The science behind why your room smells like tacos after lunch. ☕🌿

    *”Class dismissed. JARVIS, play *Back in Black.” 🎸

    Captain Jack Sparrow’s Guide to Mineral Absorption: Or How Plants Pillage Nutrients Like a Drunk Pirate

    “Ahoy there, ye scurvy landlubbers! Ever wonder how plants get their grub without raidin’ the local tavern? Well, batten down the hatches, because today we’re talkin’ about mineral absorption—the dirtiest, sneakiest heist in nature. Savvy?”


    The Root’s Treasure Map: Where X Marks the Spot

    Plants don’t have gold coins, but they do have root hairs—nature’s version of a pirate’s spyglass, sniffin’ out booty (a.k.a. minerals) in the soil.

    • Root hairs be stretchin’ farther than my excuses to the Royal Navy.
    • Surface area? More like a pirate’s wanted poster—bigger is better for lootin’.
    • “These tiny hairs ain’t for fashion—they’re for plunderin’ potassium like it’s Spanish gold!”

    Active Transport: The Midnight Raid

    Now, minerals don’t just waltz into roots like a drunkard into a brothel. Oh no—this be a high-stakes operation requiring energy (and maybe a bit o’ rum).

    1. Against the Current
    • Minerals often be more concentrated inside roots than in the soil (like how I’m more concentrated on rum than common sense).
    • So roots use active transport—a fancy term for “stealin’ what don’t want to be stole.”
    1. Protein Pumps: The Crew’s Muscle
    • Special proteins in root cells pump minerals inward, like my crew hauling barrels of grog.
    • Costs ATP energy—“the plant’s version of payin’ the crew (or at least promisin’ to).”
    1. No Passive Pirate Here!
    • Unlike water (which just wanders in via osmosis), minerals need a fight.
    • “Think of it like stealin’ from the East India Company—ye gotta WORK for it!”

    Why This Matters (Or Why Ye Should Care)

    • No minerals? The plant be lookin’ as sick as Davey Jones without his moisturizer.
    • Active transport be the difference between a thriving plant and one that’s walkin’ the plank.
    • “It’s not just dirt—it’s a treasure chest o’ nitrogen, phosphorus, and potassium (NPK, the pirate’s ABCs).”

    The Pirate’s Cheat Sheet: How Roots Loot Minerals

    StepWhat HappensPirate Translation
    1. Scout the SoilRoot hairs search for minerals“Send out the crew to spot Spanish galleons!”
    2. Hoist the Sails (ATP)Energy fuels mineral pumps“No rum, no loot—simple as that.”
    3. Plunder & StowMinerals stored in plant cells“Hide the gold where the Navy won’t find it!”

    Final Broadside: SEO Gold

    “How do plants eat? What’s active transport in roots? The secret life of nutrient-pillaging plants—revealed! (No parrots were harmed in the making of this lesson.)”

    Next Lesson: Transpiration—or Why Plants Sweat More Than a Pirate in Wool Trousers.

    “Now, if ye excuse me, I’ve got a date with a bottle o’ rum and some suspiciously fertile soil. Drink up, me hearties!” ☠️🌿

    Professor Dumbledore’s Guide to Plant Hydrology: Or How Roots Perform Magic Without Wands

    “Ah, students! Today we shall discuss a most fascinating bit of herbology – how plants manage to drink without lips, chew without teeth, and transport their supper without so much as a single house elf to help. Ten points to whichever house can tell me why root hairs are more useful than a first-year’s attempt at Wingardium Leviosa!”


    The Root Hair Conspiracy

    Our story begins with those unassuming little root hairs – nature’s equivalent of the Weasley twins’ Extendable Ears, stretching into the soil to eavesdrop on water and mineral gossip:

    1. Osmosis Operation
    • Water enters roots like students sneaking into the kitchens – moving from where there’s lots (soil) to where there’s little (roots)
    • “Much easier than getting past that blasted Snitch of a fruit painting, I must say”
    • No magic required – just good old concentration gradients doing Dobby’s work
    1. Mineral Mayhem
    • While water waltzes in freely, minerals need more… persuasion
    • Active transport works harder than Hermione during exams, using ATP (the plant version of Pepper Imps) to force nutrients inside
    • “Think of it as the Slytherin common room – some substances need special passwords to enter”

    Xylem: The Hogwarts Express of Plants

    Once inside, our liquid heroes board the most peculiar train:

    • Xylem vessels – hollow tubes deader than History of Magic lectures
    • Root pressure pushes water upward like first years rushing to the Great Hall
    • Transpiration pull sucks water skyward more effectively than a Dementor’s kiss

    “Remarkable, really – no steam engine, no conductor, just physics working harder than Professor Snape on a detention spree”


    Why This Matters (My Dear Wizarding Friends)

    • Without this system, plants would be as limp as Neville’s first attempt at herbology
    • The entire wizarding world’s potion ingredients depend on this silent magic
    • “Even mandrakes need their morning drink, though mercifully with less screaming”

    SEO Spell: How do plants drink? Magical water transport in nature revealed! What roots and wands have in common

    “Now, if you’ll excuse me, I must attend to my lemon drops and that rather curious Whomping Willow. Class dismissed!”

    Bonus House Points Question:
    Which plant transport system would make the best Horcrux?
    (A) Xylem – already full of dead stuff (B) Phloem – constantly moving like a certain Dark Lord (C) Root hairs – Voldemort would never suspect them

    Johnny English’s Guide to Plant Hydration: Or How to Not Kill Your Office Fern (Again)

    “Ah, water. The stuff that falls from the sky, fills your shoes when you step in a puddle, and apparently keeps plants alive—who knew? Let me, Johnny English, international man of mystery and accidental plant murderer, explain why your leafy friends are more high-maintenance than a secret agent’s earpiece.”


    1. Transportation: The Plant’s Underground Subway

    Water in plants is like MI6’s intel network—always moving, always critical, and occasionally leaking where it shouldn’t.

    • Root Pressure: The plant’s version of a “pushy colleague” shoving water upward.
    • “Imagine me trying to force my way into a secure facility—except the roots actually succeed.”
    • Ascent of Sap: Fancy term for water’s elevator ride from roots to leaves.
    • “No buttons, no ‘going down’—just pure botanical defiance of gravity. Take that, Newton!”

    Why it matters: Without this, plants would be as limp as my disguise mustache in the rain.


    2. Food Production: Photosynthesis or Starvation

    Plants use water to cook their food, which is more than I can say for myself (cough burnt toast cough).

    • Recipe for Disaster (or Photosynthesis):
    • 1 part water (stolen from soil)
    • 1 part sunlight (free, unlike my agency’s budget)
    • 1 part carbon dioxide (exhaled by humans who forget to water plants)
    • “Mix violently in chloroplasts—voilà! Salad.”

    Why it matters: No water = no photosynthesis = your fern becomes a crispy, brown “art installation.”


    3. Cooling Effect: Plant Sweat is Fashionable

    Plants don’t have armpits (thank goodness), but they do sweat through their leaves like a nervous recruit on their first mission.

    • Transpiration: Water evaporates from leaves, cooling the plant.
    • “It’s like me after running from a henchman—except plants don’t complain about dry-cleaning bills.”
    • Bonus: This sweat-fest also creates cloud cover.
    • “Move over, weather apps—plants invented humidity.”

    Why it matters: Without it, plants would overheat faster than my gadget-laden Aston Martin.


    In Summary (For Those Who Stopped Paying Attention)

    FunctionWhat It DoesJohnny English Equivalent
    TransportationMoves water/mineralsMe escaping through air vents
    Food ProductionMakes plant foodMy attempt at microwaving tea
    Cooling EffectPrevents leaf meltdownMe fanning myself with classified files

    SEO Goldmine:
    “Why do plants drink? How water secretly runs the botanical world. Keep your ferns alive (unlike my last mission).”

    “Now, if you’ll excuse me, I need to go water my cactus. Or is it a rubber plant? Blast.” 🌵💦

    P.S. If your plant dies, just tell people it’s “undercover.” Works for me.

    Deadpool’s Guide to Plant Sweat: Or Why Your Fern is More Dramatic Than My Love Life

    “Okay, listen up chlorophyll-chugging chuckleheads! Today we’re talking about transpiration—which is just a fancy way of saying plants sweat like Ryan Reynolds in a sauna suit. And just like me after taco night, they lose way more water than they probably should. Let’s break it down with maximum sarcasm and minimum scientific dignity!”


    What the Hell is Transpiration?

    Imagine you’re a plant. You drink a gallon of water, but only need a sip. What do you do with the rest? You sweat it out like a nervous stand-up comedian on open mic night.

    • Stomata Drama: Tiny leaf pores (stomata) open up like my mouth during an inappropriate joke, letting water vapor escape.
    • Gravity? Pfft. Plants spit in the face of physics, pushing water vapor upward like my middle finger to common sense.
    • *”It’s not evaporation—it’s *botanical sass.”

    The Sucky Science of Transpirational Pull

    1. Leaves Lose Water → Creates a vacuum in the xylem (like my soul after the Green Lantern reviews).
    2. Roots Panic → Suck up more water like me chugging margaritas on a Tuesday.
    3. Cycle Continues → Water zooms up the plant like my ADHD during a weapons catalog binge.

    *”This is why trees don’t need pumps—they’ve got *natural drama* to move fluids.”*


    When Plants Get Thirsty: The Wilting Shame

    If a plant loses more water than it drinks (aka “Saturday night decisions”):

    • Leaves droop like my will to live in a PG-13 movie.
    • Stems sag like my gym membership after January.
    • *”Congratulations, you’ve just invented plant *hangover mode.”

    Why Should You Care? (Besides Not Killing Your Ficus)

    • Cooling Effect: Plants sweat so you don’t have to (looking at you, cactus lovers).
    • Water Cycle MVP: Transpiration is why rain exists. You’re welcome, humanity.
    • Botanical Peer Pressure: More transpiration = more water sucked from roots = nature’s version of “chug, chug, chug!”

    SEO Hook:
    “Why do plants sweat? The NSFW truth about transpiration! How leaves pull water like a Vegas bachelorette party.”


    Deadpool’s Pro Tips

    ☠️ Mist your plants (they’re into that).
    ☠️ Wilting? Water them, you monster.
    ☠️ Stomata sounds like a rejected Star Wars villain. Use that.

    *”Now go hydrate something. And by ‘something,’ I mean *yourself. Priorities, people.” 🌿💦

    P.S. If your plant dies, just say it’s “method acting” as a dried herb. Works for me.

    Professor Snape’s Guide to Plant Perspiration: Or Why Your Herbology Grade Hangs by a Thread

    “Ten points from Gryffindor for not knowing why your pathetic potted plants are gasping for air. Honestly, even a flobberworm could grasp this. Pay attention, or I’ll have you bottling bubotuber pus for a month.”


    The Dark Arts of Leaf Sweat (a.k.a. Transpiration)

    Plants don’t have the decency to sweat like normal creatures—no, they must do it dramatically, through tiny pores called stomata. And just like Potter’s excuses, the rate depends on several irritatingly variable factors.


    Factors Affecting Transpiration (Or How to Annoy Your Professor)

    1. Sunlight: The Stomata’s Alarm Clock
    • Stomata open during the day like first years gawking at a golden snitch.
    • “Close at night? How…predictable.* Unlike Mr. Potter’s detentions.”*
    • More light = more transpiration, much like how more Potter = more migraine potions for me.
    1. Temperature: The Great Sauna Conspiracy
    • Hotter days make plants lose water faster than I lose patience with incompetence.
    • “30°C? That’s a Tuesday in my dungeons. The leaves, however, act like melted chocolate frogs.”
    • Cold days slow transpiration to a crawl—like Filch without his cat.
    1. Humidity: The Air’s Tea Party
    • Humid air is already stuffed with moisture, like Hagrid’s pockets with illegal creatures.
    • “Why should leaves bother evaporating when the air’s as saturated as Slughorn at a free buffet?”
    • Low humidity = leaves sweat like Neville in a practical exam.
    1. Wind: The Invisible Bully
    • Wind whisks away moist air like Peeves stealing homework.
    • “A breezy day? Perfect for transpiration. A hurricane? Even better—free defoliation!”
    • Still air lets water cling like a Hufflepuff to their last scrap of dignity.

    Why This Matters (You Dunderheads)

    • Overheat a plant? It wilts faster than Lockhart’s career.
    • No wind? Stagnation occurs, much like the Slytherin common room’s conversation topics.
    • “Humidity is the difference between a thriving greenhouse and a moldy cauldron cupboard.”

    SEO Spell:
    “Why do plants hate humidity? How wind makes leaves sweat. The dark secrets of stomata revealed!”


    Snape’s Final Verdict

    FactorEffectHogwarts Equivalent
    SunlightStomata open = more sweatFirst years spotting a dragon
    HeatWater flees like a cursed objectMy patience with Potter
    HumiditySlows transpirationA prefect’s curfew lecture
    WindEvaporates water fasterPeeves with a stolen wand

    “Class dismissed. Longbottom, for Merlin’s sake, stop drowning that geranium.”

    P.S. Fail to understand this, and I’ll assign you to re-pot mandrakes. Without earmuffs.

    Captain Barbossa’s Guide to Plant Plunderin’: Or Why Yer Leafy Scallywags Be Sweatin’ Gold

    “Arrr, gather ‘round ye bilge rats! Today we be discussin’ the fine art of transpiration—where plants lose water faster than a pirate loses teeth. And translocation, where they move their loot like a proper fleet o’ buccaneers. Savvy?”


    Why Transpiration Be Worth Its Weight in Rum

    1. Coolin’ Effect: Nature’s Sea Breeze
    • When water evaporates from leaves, it cools the plant like a splash o’ seawater on a scorchin’ deck.
    • “Without it, yer plant would be hotter than Jack Sparrow in a wool coat at high noon!”
    • Lesson: Sweaty leaves = happy leaves. Just don’t call it sweat—call it “botanical elegance.”
    1. Transportin’ Water & Minerals: The Root’s Treasure Hunt
    • Transpiration pulls water up from the roots like a crew hoistin’ anchor.
    • “No transpiration? Then the water be as stagnant as a pond full o’ land-lubbers!”
    • Keeps the cell sap strong—like grog, but less likely to make ye sing sea shanties.

    Translocation: The Plant’s Hidden Smugglin’ Operation

    While xylem’s busy hauling water up, the phloem be runnin’ a two-way snack trade like a proper black-market dealer:

    • Sieve Tubes: Stacked like barrels o’ stolen sugar, movin’ food up AND down the plant.
    • “Unlike me dignity, which only goes down.”
    • Why it matters: Without it, the roots would starve, and the fruit wouldn’t get sweet enough to ferment into decent grog.

    Barbossa’s Cheat Sheet: Plant Plunderin’ 101

    What HappensPirate Translation
    Transpiration cools leaves“Like a sea breeze for landlubber plants!”
    Pulls up water/minerals“Hoist the mainsail, lads—we’re drinkin’ from the soil!”
    Phloem moves food“Two-way snack trade, no customs!”

    SEO Hook:
    “Why do plants sweat? How leaves pirate water and sugar! The secret life of thirsty greenery—revealed!”


    Final Broadside

    “So next time ye see a plant, remember: it’s a sneaky, sweaty, snack-smugglin’ machine. Just like me first mate—except with better roots. Now, if ye excuse me, I’ve got a date with a bottle o’ rum and a wilting petunia.” ☠️🌿

    P.S. Fail to water yer plants, and they’ll walk the plank faster than a cowardly cabin boy.

    Search Results for:

    Master Determiners

    Determiners are a fundamental part of English grammar, especially for Class 8 ICSE students diving into the nuances of language structure. These small but mighty words introduce nouns or noun phrases, specifying their reference, quantity, or distribution. Whether you’re preparing for exams or aiming to strengthen your grammar foundation, this comprehensive guide to determiners, based on Chapter 1 of Viva Publication’s Class 8 ICSE English Grammar, will help you master the topic with ease.

    What Are Determiners?

    Definition and Role

    A determiner is a word placed at the beginning of a noun or noun phrase to indicate what it refers to. Think of determiners as pointers that clarify whether you’re talking about a specific or general item, a singular or plural noun, or a certain quantity.

    Examples:

    • Khushi got several job offers after she became a CA. (Determiner: several, before job offers)
    • Deciduous trees shed their leaves every autumn. (Determiners: their and every, before leaves and autumn)

    Types of Determiners

    Determiners come in various types, each serving a unique function. Let’s break them down.

    Articles

    Articles (a, an, the) specify whether a noun is general or specific.

    • A, An: Used before singular countable nouns.
      • There used to be a cinema hall here.
      • We had an emergency situation yesterday.
    • The: Refers to specific things.
      • The old man who lives upstairs is from Russia.
      • The car that was stolen last week has been found.

    Demonstratives

    Demonstratives (this, that, these, those) point to specific nouns based on proximity or number.

    • Are you going there this Friday?
    • Those buildings were built recently.

    Possessives

    Possessive determiners (my, your, his, her, its, our, their) indicate ownership.

    • My school is close to our house.
    • Their wedding is on 29 May.

    Practice Exercise : Fill in the Blanks

    Complete these sentences with suitable determiners :

    1. We were meeting after ___ gap of three years. (Answer: a)
    2. ___ news of ___ robbery spread like wildfire. (Answer: The, the)
    3. Ernest Hemingway was ___ American writer. (Answer: an)
    4. Where did you keep ___ flowers? (Answer: the)
    5. My parents are celebrating ___ thirty-fifth anniversary ___ year. (Answer: their, this)

    Quantifiers

    Quantifiers indicate the quantity or amount of a noun, used with countable or uncountable nouns.

    • Countable Nouns: many, a few, few, several
      • Many ideas were discussed in the meeting.
    • Uncountable Nouns: much, a little, little
      • I need a little oil for cooking.
    • Both: all, some, most, enough, no, any, a lot of
      • All the children enjoyed some ice cream.

    Language Tip

    Use many a with singular nouns: Many a tourist visits this place.

    Practice Exercise :

    Choose the correct quantifier :

    1. Not ___ time is left for the flight. (many/much; Answer: much)
    2. Can I have ___ sugar, please? (little/a little; Answer: a little)
    3. ___ people seem to have patience nowadays. (few/a few; Answer: few)

    Determiners of Number

    Numbers act as determiners when placed before nouns.

    • Cardinal Numbers (two, five, seventy): Indicate quantity.
      • India won by seventy runs.
    • Ordinal Numbers (first, third): Show sequence.
      • The third seat in the first row is mine.

    Distributive Determiners

    Distributive determiners (either, neither, each, every) describe how items are distributed.

    • Either: One of two options.
      • Either day – Monday or Tuesday – works for me.
    • Neither: None of two options.
      • Neither candidate cleared the interview.
    • Each/Every: Refer to individual or collective group members.
      • Each team member was rewarded.
      • Every citizen should vote.

    Language Tip :

    Use neither of with plural nouns/pronouns: Neither of the dresses fits me.

    Practice Exercise : Distributive and Interrogative Determiners

    Fill in the blanks :

    1. No parking is allowed on ___ side of the road. (Answer: either)
    2. ___ time do we have to come tomorrow? (Answer: What)
    3. ___ child is special. (Answer: Every)

    Interrogative Determiners

    Interrogative determiners (what, which, whose) introduce questions.

    • What (things): What plans do you have?
    • Which (limited choices): Which book is your favorite?
    • Whose (possession): Whose phone is under the stool?

    Position of Determiners

    Determiners appear in a specific order within a noun phrase: Predeterminers → Central Determiners → Postdeterminers.

    Predeterminers

    These specify quantity and come first.

    • Multipliers : twice, ten times
      • They charged twice its price.
    • Fractions : half, one-third
      • Half the cake was eaten.
    • Words like all, both :
      • All my friends are invited.

    Central Determiners

    These include articles, possessives, and demonstratives.

    • She drinks half a glass of milk.
    • All their time was spent studying.

    Postdeterminers

    These include numbers and quantifiers.

    • Cardinal/Ordinal Numbers: The first five students were rewarded.
    • Quantifiers: Half the little food was shared.

    Language Tip :

    Adjectives follow all determiners: All the six delicious dishes.

    Practice Exercise : Arrange Determiners

    Rewrite with correct determiner order :

    1. (the, all) people lived peacefully. (Answer: All the people lived peacefully.)
    2. (little, his, all) money was used up. (Answer: All his little money was used up.)
    3. (five, the, all) rounds were cleared. (Answer: All the five rounds were cleared.)

    Fun Grammar Activities

    Spot the Wrong Determiners

    Work in pairs to identify incorrect determiners in given phrases. Circle the errors within 10 minutes for points!

    Know Your Determiners

    In groups of four, pick a card naming a determiner type (e.g., possessive, quantifier). Each member gives a unique example and sentence. Score points for creativity and accuracy!

    Conclusion

    Determiners are small words with a big impact, helping you specify and clarify nouns in sentences. By understanding articles, demonstratives, possessives, quantifiers, and more, Class 8 ICSE students can elevate their grammar skills. Practice with the exercises provided, and you’ll be ready to ace your English exams !

    Ready to test your skills? Try the exercises above or revisit the examples to solidify your understanding of determiners. Happy learning!

    Search Results for:

    Introduction to Rational Numbers

    Standard Form of a Rational Number

    Properties and Operations of Rational Numbers

    Equivalent Rational Numbers

    Comparison of Rational Numbers

    Addition of Rational Numbers

    Subtraction of Rational Numbers

    Multiplication of Rational Numbers

    Division of Rational Numbers

    Absolute Value of Rational Numbers

    Summary

    Search Results for:

    Understanding Numbers Like a Pro! 🔢✨

    1. Natural Numbers

    • What? Counting numbers starting from 1.
    • Examples: 1, 2, 3, 4, … (like counting apples! 🍎🍏🍎)

    Joke: Why did 7 eat 9? Because you’re supposed to eat 3 square meals a day! 😋


    2. Whole Numbers

    • What? Natural numbers + zero.
    • Examples: 0, 1, 2, 3, … (Imagine a basket with 0 to infinite apples! 🧺)

    Fun Fact: Zero (0) is the hero that means “nothing” but is super important! 🦸


    3. Integers

    • What? Whole numbers + their negative twins.
    • Examples: …, -3, -2, -1, 0, 1, 2, 3, … (Like temperatures above/below zero! ❄️🔥)

    Punchline: Negative numbers are like “opposite day” in math! 🔄


    Key Takeaways

    1. Natural: 1, 2, 3, … (counting).
    2. Whole: 0, 1, 2, 3, … (natural + zero).
    3. Integers: …, -2, -1, 0, 1, 2, … (whole + negatives).
    4. Rationals: Any p/q (fractions, integers, certain decimals).

    Final Joke:
    Why was the math book sad?
    Because it had too many problems! 😂

    Try This! Is -5 a rational number? (Hint: Yes! Write it as -5/1 ) 🎯

    Fun with Rational Numbers! 🎲✨

    Key Takeaways

    1. Equivalent Fractions: Multiply/divide top & bottom by the same number.
    2. Simplification: Divide to make fractions smaller and neater.
    3. Equality Test: Cross-multiply to check if fractions are equal.

    Joke:
    Why was the math book happy?
    Because it finally reduced its stress! 😂

    Rational Numbers Explained like Easy – Cheezy ! 😄

    What is a Rational Number?

    A rational number is like a friendly fraction— it’s any number you can write as ‘a’ divided by ‘b’, where:

    • a and b are integers (positive or negative whole numbers).
    • b ≠ 0 (because dividing by zero is as weird as a ghost denominator 👻).

    Joke Time! 🤣

    • Why was the fraction scared of negative numbers?
      Because it didn’t want to be reduced to nothing!

    Standard Form – The “Neat & Tidy” Fraction

    A fraction is in standard form if:

    1. No common factors (like twins who refuse to share clothes 👕).
    2. Denominator is positive (because negativity doesn’t simplify life!).

    Fun Facts & Mind-Blowing Math! 🤯

    Final Thought: Math isn’t just numbers—it’s stories, jokes, and puzzles waiting to be solved! Keep laughing while learning! 🚀

    Would you like to try another example? Let’s turn math into a comedy show! 🎭

    Comparing Rational Numbers & Number Line Fun! 📊➗

    1. How to Compare Fractions? (Like Sorting Candy! 🍬)

    Step 1: Make all denominators positive (no negativity allowed!).
    Step 2: Find the LCM (Least Common Multiple) of denominators.
    Step 3: Convert all fractions to have the same denominator (LCM).
    Step 4: Now, just compare the numerators!

    2. Plotting Rational Numbers on a Number Line (Like a Treasure Map! 🗺️)

    Rule: Every fraction has a unique spot on the number line.

    Exercise 1A

    Operations on Rational Numbers Addition & Subtraction

    Exercise 1B

    Operations on Rational Numbers – Multiplication and Division

    Exercise 1C

    Finding a Rational Number Between Two Given Rational Numbers

    Method of Finding a Rational Number Between Two Given Rational Numbers

    Method of Finding a Large Number of Rational Numbers Between Two Given Rational Numbers

    Exercise 1D

    THINGS TO REMEMBER

    Exercise 1E

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