Class 8

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 2 Linear Equations in One Variable Ex 2.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.2

Question 1.
If you subtract \(\frac {1}{2}\) from a number and multiply the result by \(\frac {1}{2}\), you get \(\frac {1}{8}\). What is the number?
Solution:
Let the required number be x.
By subtracting \(\frac {1}{2}\) from x, we get x-\(\frac {1}{2}\) and by multiplying this result by \(\frac {1}{2}\),
we get \(\frac {1}{2}\)(x – \(\frac {1}{2}\))
But, the result is \(\frac {1}{8}\)
\(\frac {1}{2}\)(x – \(\frac {1}{2}\)) = \(\frac {1}{8}\)
∴ \(\frac {1}{2}\)(x – \(\frac {1}{2}\)) × 2 = \(\frac {1}{8}\) × 2 (Multiplying both the sides by 2)
∴ x – \(\frac {1}{2}\) = \(\frac {1}{4}\)
∴ x = \(\frac{1}{4}+\frac{1}{2}\) (Transposing –\(\frac {1}{2}\) to RHS)
∴ x = \(\frac{1+2}{4}\) (LCM = 4)
∴ x = \(\frac {3}{4}\)
Thus, the required number = \(\frac {3}{4}\)

Question 2.
The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?
Solution:
Perimeter of the pool = 154 m
Let breadth = x metres
Length is 2 m more than twice its breadth.
Length = 2 (breadth) + 2
= (2x + 2) metres
Perimeter of a rectangle = 2 (length + breadth)
2 (length + breadth) = Perimeter
∴ 2[(2x + 2) + x] = 154
∴ 2 [2x + 2 + x] = 154
∴ 2 (3x + 2) = 154
∴ \(\frac{2(3 x+2)}{2}=\frac{154}{2}\) (Dividing both the sides by 2)
∴ 3x + 2 = 77
∴ 3x = 77 – 2 (Transposing 2 to RHS)
∴ 3x = 75
∴ \(\frac{3 x}{3}=\frac{75}{3}\) (Dividing both the sides by 3) x — 25
Breadth = 25 m
Length = 2x + 2
= 2 (25) + 2
= 50 + 2
= 52 m
Thus, the length of the pool is 52 m and its breadth is 25 m.

Question 3.
The base of an isosceles triangle is \(\frac {4}{3}\) cm. The perimeter of the triangle is 4\(\frac {2}{15}\) cm. What is the length of either of the remaining equal sides?
Solution:
Base of an isosceles triangle = \(\frac {4}{3}\) cm
Let the length of each of the equal sides = x cm
Perimeter of the triangle = \(\frac {4}{3}\) + x + x
= \(\frac {4}{3}\) + 2x
Perimeter of the triangle = 4\(\frac {2}{15}\) cm (Given)
∴ \(\frac {4}{3}\) + 2x = 4\(\frac {2}{15}\)
∴ \(\frac {4}{3}\) + 2x = \(\frac {62}{15}\)
∴ 2x = \(\frac{62}{15}-\frac{4}{3}\)(Transposing to RHS)
∴ 2x = \(\frac{62-20}{15}\) (LCM = 15)
∴ 2x = \(\frac {42}{15}\)
∴ \(\frac{2 x}{2}=\frac{42}{15} \times \frac{1}{2}\) (Dividing both the sides by 2)
∴ x = \(\frac {21}{15}\)
∴ x = \(\frac{7 \times 3}{5 \times 3}\)
∴ x = \(\frac {7}{5}\)
∴ x = 1\(\frac {2}{5}\)
Thus, the required length of either of the remaining equal sides is 1\(\frac {2}{5}\) cm.

Question 4.
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Solution:
Let the smaller number be x
∴ The greater number = x + 15
Their sum is 95.
∴ x + (x + 15) = 95
∴ x + x + 15 = 95
∴ 2x + 15 = 95
∴ 2x = 95 – 15 (Transposing 15 to RHS)
∴ 2x = 80
∴ \(\frac{2 x}{2}=\frac{80}{2}\) (Dividing both the sides by 2)
∴ x = 40
The smaller number = x = 40
The greater number = x + 15 = 40 + 15 = 55
Thus, 40 and 55 are the required numbers.

Question 5.
Two numbers are in the ratio 5 : 3. If they differ by 18, what are the numbers ?
Solution:
Ratio of the two numbers = 5 : 3
Let the two numbers be 5x and 3x.
Difference = 18
∴ 5x – 3x = 18
∴ 2x = 18
∴ \(\frac{2 x}{2}=\frac{18}{2}\) (Dividing both the sides by 2)
∴ x = 9
∴ Greater number = 5x = 5 × 9 = 45
Smaller number = 3x = 3 × 9 = 27
Thus, 45 and 27 are the numbers.

Question 6.
Three consecutive integers add up to 51. What are these integers ?
Solution:
Let the consecutive integers be, x, x + 1 and x + 2.
Their sum is 51.
∴ x + (x + 1) + (x + 2) = 51
∴ x + x + 1 + x + 2 = 51
∴ 3x + 3 = 51
∴ 3x = 51 – 3 (Transposing 3 to RHS)
∴ 3x = 48
∴ \(\frac{3 x}{3}=\frac{48}{3}\) (Dividing both the sides by 3)
∴ x = 16
∴ First number = x = 16
Second number = x + 1 = 16 + 1 = 17
Third number = x + 2 = 16 + 2 = 18
Thus, the required consecutive integers are 16, 17 and 18.

Question 7.
The sum of three consecutive multiples of 8 is 888. Find the multiples.
Solution:
Let the three multiples of 8 be x, x + 8, and x + 8 + 8 = x + 16.
Their sum is 888.
∴ x + (x + 8) + (x + 16) = 888
∴ x + x + 8 + x + 16 = 888
∴ 3x + 24 = 888
∴ 3x = 888 – 24 (Transposing 24 to RHS)
∴ 3x = 864
∴ \(\frac{3 x}{3}=\frac{864}{3}\) (Dividing both the sides by 3)
∴ x = 288
∴ First number = x = 288
∴ Second number = x + 8 = 288 + 8 = 296
Third number = x + 16 = 288 + 16 = 304
Thus, the required three consecutives multiples of 8 are 288, 296 and 304.

Question 8.
Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
Solution:
Let the three consecutive integers be, x, (x + 1) and (x + 2).
According to the condition,
∴ 2 × (x) + 3 × (x + 1) + 4 × (x + 2) = 74
∴ 2x + 3x + 3 + 4x + 8 = 74
∴ 9x + 11 = 74
∴ 9x = 74 – 11 (Transposing 11 to RHS)
∴ 9x = 63
∴ \(\frac{9 x}{9}=\frac{63}{9}\) (Dividing both the sides by 9)
∴ x = 7
∴ First integer = x – 7
Second integer = x + 1 = 7 + 1 = 8
Third integer = x + 2 = 7 + 2 = 9
Thus, the required integers are 7, 8 and 9.

Question 9.
The ages of Rahul and Haroon are in the ratio 5 : 7. Four years later the sum of their ages will be 56 years. What are their present ages?
Solution:
Ages of Rahul and Haroon are in the ratio of 5 : 7.
Let their present ages be 5x and 7x years.
∴ 4 years later,
the age of Rahul will be 5x + 4 years and the age of Haroon will be 7x + 4 years.
According to the condition,
(5x + 4) + (7x + 4) = 56
∴ 5x + 4 + 7x + 4 = 56
∴ 12x + 8 = 56
∴ 12x = 56 – 8 (Transposing 8 to RHS)
∴ 12x = 48
∴ \(\frac{12 x}{12}=\frac{48}{12}\) (dividing both the sides by 12)
∴ x = 4
Present age of Rahul = 5x = 5 × 4
= 20 years
Present age of Haroon = 7x = 7 × 4
= 28 years
Thus, present age of Rahul is 20 years and that of Haroon is 28 years.

Question 10.
The number of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. What is the total class strength?
Solution:
Number of boys : Number of girls = 7 : 5
Let the number of boys be 7x, and the number of girls be 5x.
According to the condition
7x = 5x + 8
∴ 7x – 5x = 8 (Transposing 5x to LHS)
∴ 2x = 8
∴ \(\frac{2 x}{2}=\frac{8}{2}\) (Dividing both the sides by 2)
∴ x = 4
Number of boys = 7x = 7 × 4 = 28
Number of girls = 5x = 5 × 4 = 20
Total class strength = 28 + 20 = 48
Thus, total class strength is 48.

Question 11.
Bharat’s father is 26 years younger than Bharat’s grandfather and 29 years older than Bharat. The sum of the ages of all the three is 135 years. What is the age of each one of them ?
Solution:
Let the age of Bharat be x years,
His father’s age = (x + 29) years
His grandfather’s age = x + 29 + 26
= (x + 55) years
Sum of their ages is 135 years.
∴ x + (x + 29) + (x + 55) = 135
∴ x + x + 29 + x + 55 = 135
∴ 3x + 84 = 135
∴ 3x = 135 – 84 (Transposing 84 to RHS)
∴ 3x = 51
∴ \(\frac{3 x}{3}=\frac{51}{3}\) (Dividing both the sides by 3)
∴ x = 17
Bharat’s age = x = 17 years
His father’s age = x + 29
= 17 + 29
= 46 years
His grandfather’s age = x + 55
= 17 + 55
= 72 years
Thus, Bharat’s age is 17 years, his father’s age is 46 years and his grandfather’s age is 72 years.

Question 12.
Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?
Solution:
Let Ravi’s present age be x years.
4 times his present age be 4x years.
15 years from now his age be x + 15 years.
According to the condition, x + 15 = 4x
∴ 4x = x + 15 (Interchanging both the sides)
∴ 4x – x = 15 (Transposing x to LHS)
∴ 3x = 15
∴ \(\frac{3 x}{3}=\frac{15}{3}\) (Dividing both the sides by 3)
∴ x = 5
Thus, Ravi’s present age is 5 years.

Question 13.
A rational number is such that when you multiply it by \(\frac {5}{2}\) an\(\frac {2}{3}\) add g to the product, you get –\(\frac {7}{12}\). What is the number ?
Solution:
Let the required rational number be x.
We get \(\frac{5 x}{2}\) by multiplying x with \(\frac {5}{2}\)
By adding \(\frac {2}{3}\) to it we get \(\frac{5 x}{2}+\frac{2}{3}\)
But, the result is \(\frac {-7}{12}\)
∴ \(\frac{5 x}{2}+\frac{2}{3}=\frac{-7}{12}\)
\(\frac{5 x}{2}=-\frac{7}{12}-\frac{2}{3}\) (Transposing \(\frac {2}{3}\) to RHS)
∴ \(\frac{5 x}{2}=\frac{-7-8}{12}\) (LCM = 12)
∴ \(\frac{5 x}{2}=\frac{-15}{12}\)
∴ \(\frac{5 x}{2} \times \frac{2}{5}=\frac{-15}{12} \times \frac{2}{5}\) (Multiplying both the sides by \(\frac {2}{5}\))
∴ x = –\(\frac {1}{2}\)
Thus, the required rational number is –\(\frac {1}{2}\).

Question 14.
Lakshmi is a cashier in a bank. She has currency notes of denominations ₹ 100, ₹ 50 and ₹ 10, respectively. The ratio of the number of these notes is 2 : 3 : 5. The total cash with Lakshmi is ₹ 4,00,000. How many notes of each denomination does she have?
Solution:
Let the number of
₹ 100 notes be 2x,
₹ 50 notes be 3x,
₹ 10 notes be 5x.
Value of ₹ 100 notes = 2x × 100 = ₹ 200x
Value of ₹ 50 notes = 3x × 50 = ₹ 150x
Value of ₹ 10 notes = 5x × 10 = ₹ 50x
According to the condition, value of
₹ 200x + ₹ 150x + ₹ 50x = ₹ 4,00,000
∴ 200x + 150x + 50x = 4,00,000
∴ 400x = 400000
∴ \(\frac{400 x}{400}=\frac{400000}{400}\)
∴ x = 1000
Number of ₹ 100 notes = 2x
= 2 × 1000
= 2000
Number of ₹ 50 notes = 3x
= 3 × 1000
= 3000
Number of ₹ 10 notes = 5x
= 5 × 1000
– 5000
Thus, Lakshmi has 2000 notes of ₹ 100, 3000 notes of ₹ 50 and 5000 notes of ₹ 10.

Question 15.
I have a total of ₹ 300 in coins of denomination ₹ 1, ₹ 2 and ₹ 5. The number of ₹ 2 coins is 3 times the number of ₹ 5 coins. The total number of coins is 160. How many coins of each denomination are with me?
Solution:
Let the number of ₹ 5 coins be x.
Then, the number of ₹ 2 coins = 3x
Total number of coins = 160
Number of ₹ 1 coins = 160 – 3x – x
= 160 – 4x
Now, value of
₹ 5 coins = ₹ 5 × x = ₹ 5x
₹ 2 coins = ₹ 2 × 3x = ₹ 6x
₹ 1 coins = ₹ 1 × (160 – 4x)
= ₹ (160 – 4x)
According to the condition,
5x + 6x + (160 – 4x) = 300
∴ 5x + 6x + 160 – 4x = 300
∴ 11x – 4x + 160 = 300
∴ 7x + 160 = 300
∴ 7x = 300 – 160 (Transposing 160 to RHS)
7x = 140
∴ \(\frac{7 x}{7}=\frac{140}{7}\) (Dividing both the sides by 7)
∴ x = 20
Number of
₹ 5 coins = x = 20
₹ 2 coins = 3x = 3 × 20 = 60
₹ 1 coins = 160 – 4x
= 160 – 4 × 20
= 160 – 80
= 80
Thus, I have 20 coins of ₹ 5, 60 coins of ₹ 2 and 80 coins of ₹ 1.

Question 16.
The organisers of an essay competition decide that a winner in the competition gets a prize of ₹ 100 and a participant who does not win gets a prize of ₹ 25. The total prize money distributed is ₹ 3000. Find the number of winners, if the total number of participants is 63.
Solution:
Let the number of winners be x
∴ Number of participants who are not winners = (63 – x)
Prize money given to winners = x × ₹ 100 = ₹ 100x
Prize money given to non-winner
participants = ₹ 25 × (63 -x)
= ₹ 25 × 63 – ₹ 25x
= ₹ 1575 – ₹ 25x
According to the condition
100x + 1575 – 25x = 3000
∴ 75x + 1575 = 3000
∴ 75x = 3000 – 1575 (Transposing 1575 to RHS)
∴ 75x = 1425
\(\frac{75 x}{75}=\frac{1425}{75}\) (Dividing both the sides by 75)
∴ x = 19
Thus, the number of winners are 19.

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 2 Linear Equations in One Variable Ex 2.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.1

Solve the following equations.

Question 1.
x – 2 = 7
Solution:
x – 2 = 7
∴ x = 7 + 2 (Transposing – 2 to RHS)
∴ x = 9

Question 2.
y + 3 = 10
Solution:
y + 3 = 10
∴ y = 10 – 3 (Transposing 3 to RHS)
∴ y = 7

Question 3.
6 = z + 2
Solution:
6 = z + 2
∴ z + 2 = 6 (Interchanging both the sides)
∴ z = 6 – 2 (Transposing 2 to RHS)
∴ z = 4.

Question 4.
\(\frac {3}{7}\) + x = \(\frac {17}{7}\)
Solution:
\(\frac {3}{7}\) + x = \(\frac {17}{7}\)
∴ x = \(\frac{17}{7}-\frac{3}{7}\) (Transposing \(\frac {3}{7}\) to RHS)
∴ x = \(\frac{17-3}{7}\)
∴ x = \(\frac {14}{7}\)
∴ x = 2

Question 5.
6x = 12
Solution:
6x = 12
∴ \(\frac{6 x}{6}=\frac{12}{6}\) (Dividing both the sides by 6)
∴ x = 2

Question 6.
\(\frac{t}{5}\) = 10
Solution:
\(\frac{t}{5}\) = 10
∴ \(\frac{t}{5}\) × 5 = 10 × 5 (Multiplying both the sides by 5)
∴ t = 50

Question 7.
\(\frac{2 x}{3}\) = 15
Solution:
\(\frac{2 x}{3}\) = 15
∴ \(\frac{2 x}{3} \times \frac{3}{2}=18 \times \frac{3}{2}\) (Multiplying both the sides by \(\frac {3}{2}\))

Question 8.
1.6 = \(\frac{y}{1.5}\)
Solution:
1.6 = \(\frac{y}{1.5}\)
∴ 1.6 × 1.5 = \(\frac{y}{1.5}\) × 1.5 (Multiplying both the sides by 1.5)
∴ 2.4 = y (∵ 1.6 × 1.5 = 2.4)
∴ y = 2.4

Question 9.
7x – 9 = 16
Solution:
7x – 9 = 16
∴ 7x = 16 + 9 (Transposing – 9 to RHS)
∴ 7x = 25
∴ \(\frac{7 x}{7}=\frac{25}{7}\) (Dividing both the sides by 7)
∴ x = \(\frac {25}{7}\)

Question 10.
14y – 8 = 13
Solution:
14y – 8 = 13
∴ 14y = 13 + 8 (Transposing – 8 to RHS)
∴ 14y = 21
∴ \(\frac{14 y}{14}=\frac{21}{14}\) (Dividing both the sides by 14)
∴ y = \(\frac{7 \times 3}{7 \times 2}\)
∴ y = \(\frac {3}{2}\)

Question 11.
17 + 16p = 9
Solution:
17 + 16p = 9
∴ 6p = 9 – 17 (Transposing 17 to RHS)
∴ 6p = -8
∴ \(\frac{6 p}{6}=\frac{-8}{6}\) (Dividing both the sides by 6)
∴ p = \(\frac{-4 \times 2}{3 \times 2}\)
∴ p = –\(\frac {4}{3}\)

Question 12.
\(\frac{x}{3}+1=\frac{7}{15}\)
Solution:
\(\frac{x}{3}+1=\frac{7}{15}\)
∴ \(\frac{x}{3}=\frac{7}{15}-1\) (Transposing 1 to RHS)
∴ \(\frac{7-15}{15}\) (LCM = 15)
∴ \(\frac{x}{3}=\frac{-8}{15}\)
∴ \(\frac{x}{3} \times 3=\frac{-8}{15} \times 3\) (Multiplying both the sides by 3)
∴ x = –\(\frac {8}{5}\)

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 1 Rational Numbers Ex 1.1Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1

1. Represent these numbers on the number line:

Question (i).
\(\frac {7}{4}\)
Solution:
To represent \(\frac {7}{4}\), make 7 markings each of a distance equal to \(\frac {1}{4}\) on the right side of 0. The 7th point represents the rational number \(\frac {7}{4}\).

The point A is \(\frac {7}{4}\).

Question (ii).
\(\frac {-5}{6}\)
Solution:
To represent (\(\frac {-5}{6}\)) on the number line, make 5 markings each of a distance equal to on the left side of 0. The 5th point represents the rational number (\(\frac {-5}{6}\)).

The point B is (\(\frac {-5}{6}\))

2. Represent \(\frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11}\) on the number line.
Solution:
To represent the given rational numbers on a number line, make 11 markings each being equal to distance \(\frac {1}{11}\) on the left of 0.

Here, the point A is (\(\frac {-2}{11}\)).
the point B is (\(\frac {-5}{11}\)).
the point C is (\(\frac {-9}{11}\)).

3. Write five rational numbers which are smaller than 2.
Solution:
There are infinite rational numbers below 2, positive as well as negative.
Five of them are 1, \(\frac {1}{3}\), \(\frac {1}{4}\), 0, – 1.

4. Find ten rational numbers between \(\frac {-2}{5}\) and \(\frac {1}{2}\).
Solution:
First, convert \(\frac {-2}{5}\) and \(\frac {1}{2}\) having the same denominator, such that the difference between the numerators is more than 10.
\(\frac{-2}{5}=\frac{-2}{5} \times \frac{4}{4}=\frac{-8}{20}\);
\(\frac{1}{2}=\frac{1}{2} \times \frac{10}{10}=\frac{10}{20}\)
∴ The ten rational numbers between \(\frac {-8}{20}\) and \(\frac {10}{20}\) are
\(\frac{-7}{20}, \frac{-6}{20}, \frac{-5}{20}, \frac{-4}{20}, \frac{-3}{20}, \ldots, 0, \frac{1}{20}, \ldots, \frac{9}{20} .\)
(There can be many more such rational numbers.)

5. Find five rational numbers between

Question (i).
\(\frac {2}{3}\) and \(\frac {4}{5}\)
Solution:
First, convert \(\frac {2}{3}\) and \(\frac {4}{5}\) having the same denominator, such that the difference between the numerators is more than 5.
\(\frac{2}{3}=\frac{2}{3} \times \frac{20}{20}=\frac{40}{60}\);
\(\frac{4}{5}=\frac{4}{5} \times \frac{12}{12}=\frac{48}{60}\)
∴ The five rational numbers between \(\frac {2}{3}\) and \(\frac {4}{5}\) are \(\frac{42}{60}, \frac{43}{60}, \frac{44}{60}, \frac{45}{60}, \frac{46}{60}\).

Question (ii).
\(\frac {-3}{2}\) and \(\frac {5}{3}\)
Solution:
First, convert \(\frac {-3}{2}\) and \(\frac {5}{3}\) having the same denominator, such that the difference between the numerators is more than 5.
\(\frac{-3}{2}=\frac{-3}{2} \times \frac{3}{3}=\frac{-9}{6}\);
\(\frac{5}{3}=\frac{5}{3} \times \frac{2}{2}=\frac{10}{6}\)
∴ The five rational numbers between \(\frac {-3}{2}\) and \(\frac {5}{3}\) are \(\frac{-8}{6}, \frac{-7}{6}, 0, \frac{7}{6}, \frac{8}{6}\).

Question (iii).
\(\frac {1}{4}\) and \(\frac {1}{2}\)
Solution:
First, convert \(\frac {1}{4}\) and \(\frac {1}{2}\) having the same denominator, such that the difference between the numerators is more than 5.
\(\frac{1}{4}=\frac{1}{4} \times \frac{8}{8}=\frac{8}{32}\);
\(\frac{1}{2}=\frac{1}{2} \times \frac{16}{16}=\frac{16}{32}\)
∴ The five rational numbers between \(\frac {1}{4}\) and \(\frac {1}{2}\) are \(\frac{10}{32}, \frac{11}{32}, \frac{12}{32}, \frac{13}{32}, \frac{14}{32}\).
(There can be many more such rational numbers.)
[Note : You can write rational numbers of your choice.]

6. Write five rational numbers greater than -2.
Solution:
There can be many rational numbers greater than – 2. Five of them are \(\frac{-3}{2}, \frac{-1}{4}, 0, \frac{1}{2}, \frac{1}{5}\).

7. Find ten rational numbers between \(\frac {3}{5}\) and \(\frac {3}{4}\).
Solution:
First, convert \(\frac {3}{5}\) and \(\frac {3}{4}\) having the same denominator, such that the difference between the numerators is more than 10.
\(\frac{3}{5}=\frac{3}{5} \times \frac{20}{20}=\frac{60}{100}\);
\(\frac{3}{4}=\frac{3}{4} \times \frac{25}{25}=\frac{75}{100}\)
∴ The ten rational numbers between \(\frac {3}{5}\) and \(\frac {3}{4}\) are \(\frac{61}{100}, \frac{62}{100}, \frac{63}{100}, \frac{64}{100}, \frac{65}{100}, \frac{66}{100}, \frac{67}{100}, \frac{68}{100},\)\(\frac{69}{100}, \frac{70}{100}\)

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 1 Rational Numbers Ex 1.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1

1. Using appropriate properties find.

Question (i).
\(-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}\)
Solution:
\(-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}\)
= \(-\frac{2}{3} \times \frac{3}{5}-\frac{3}{5} \times \frac{1}{6}+\frac{5}{2}\) (Commutative)
= \(\frac{3}{5} \times\left[-\frac{2}{3}-\frac{1}{6}\right]+\frac{5}{2}\) (Distributive)
= \(\frac{3}{5}\left[\frac{-4-1}{6}\right]+\frac{5}{2}\)
= \(\frac{3}{5}\left[\frac{-5}{6}\right]+\frac{5}{2}\)
= \(\frac{3}{5} \times \frac{-5}{6}+\frac{5}{2}\)
= \(-\frac{1}{2}+\frac{5}{2}\)
= \(\frac{-1+5}{2}\)
= \(\frac {4}{2}\)
= 2

Question (ii).
\(\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}\)
Solution:
\(\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}\)
= \(\frac{2}{5} \times\left(\frac{-3}{7}\right)+\frac{1}{14} \times \frac{2}{5}-\frac{1}{6} \times \frac{3}{2}\) (Commutative)
= \(\frac{2}{5} \times\left(\frac{-3}{7}+\frac{1}{14}\right)-\frac{1}{6} \times \frac{3}{2}\) (Distributive)
= \(\frac{2}{5} \times\left[\frac{-6+1}{14}\right]-\frac{1}{4}\)
= \(\frac{2}{5} \times \frac{-5}{14}-\frac{1}{4}\)
= \(-\frac{1}{7}-\frac{1}{4}=\frac{-4-7}{28}\)
= \(\frac{-11}{28}\)

2. Write the additive inverse of each of the following:

Question (i).
\(\frac{2}{8}\)
Solution:
Additive inverse of \(\frac{2}{8}\) = \(\frac{-2}{8}\)

Question (ii).
\(\frac{-5}{9}\)
Solution:
Additive inverse of \(\frac{-5}{9}\) = \(\frac{5}{9}\)

Question (iii).
\(\frac{-6}{-5}\)
Solution:
Additive inverse of \(\frac{-6}{-5}\) means \(\frac{6}{5}\) = \(\frac{-6}{5}\)

Question (iv).
\(\frac{2}{-9}\)
Solution:
Additive inverse of \(\frac{2}{-9}\) = \(\frac{2}{9}\)

Question (v).
\(\frac{19}{-6}\)
Solution:
Additive inverse of \(\frac{19}{-6}\) = \(\frac{19}{6}\)

3. Verify that – (- x) = x for

(i) x = \(\frac {11}{15}\)
Solution:
x = \(\frac {11}{15}\)
∴ (-x) = \(\left(\frac{-11}{15}\right)\)
-(-x) = –\(\left(\frac{-11}{15}\right)\)
= \(\frac {11}{15}\) = x
∴ -(-x) = x

(ii) x = \(\frac {-13}{17}\)
Solution:
x = \(\frac {-13}{17}\)
∴ (-x) = \(\left(\frac{-13}{17}\right)\)
= \(\frac {13}{17}\)
-(-x) = –\(\left(\frac{-13}{17}\right)\)
= \(\frac {-13}{17}\) = x
∴ -(-x) = x

4. Find the multiplicative inverse of the following:

Question (i).
-13
Solution:
Multiplicative inverse of -13 = \(\frac {-1}{13}\)

Question (ii).
\(\frac {-13}{19}\)
Solution:
Multiplicative inverse of \(\frac {-13}{19}\) \(\frac {-19}{13}\)

Question (iii).
\(\frac {1}{5}\)
Solution:
Multiplicative inverse of \(\frac {1}{5}\) = 5

Question (iv).
\(\frac{-5}{8} \times \frac{-3}{7}\)
Solution:
\(\left(\frac{-5}{8}\right) \times\left(\frac{-3}{7}\right)\)
= \(\frac{(-5 \times-3)}{8 \times 7}\)
= \(\frac {15}{56}\)
Multiplicative inverse of \(\frac {15}{56}\) = \(\frac {56}{15}\)

Question (v) .
1 × \(\frac {-2}{5}\)
Solution:
-1 × \(\frac {-2}{5}\) = \(\frac{(-1 \times-2)}{5}\)
= \(\frac {2}{5}\)
Multiplicative inverse of \(\frac {2}{5}\) = \(\frac {5}{2}\)

Question (vi).
-1
Solution:
Multiplicative inverse of -1 = (-1)
(∵ \(\frac{1}{(-1)}\) = (-1))

5. Name the property under multiplication used in each of the following:

Question (i).
\(\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5}\)
Solution:
1 is the multiplicative identity.

Question (ii).
\(-\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}\)
Solution:
Commutative property of multiplication.

Question (iii).
\(\frac{-19}{29} \times \frac{29}{-19}=1\)
Solution:
Existence of multiplicative inverse.

6. Multiply \(\frac {6}{13}\) by the reciprocal of \(\frac {-7}{16}\).
Solution:
Reciprocal of \(\frac{-7}{16}=\frac{-16}{7}\)
∴ \(\frac{6}{13} \times \frac{-16}{7}\)
= \(\frac{6 \times(-16)}{13 \times 7}\)
= \(\frac {-96}{91}\)

7. Tell what property allows you to compute.
\(\frac{1}{3} \times\left(6 \times \frac{4}{3}\right)\) as \(\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}\)
Solution:
In computing
\(\frac{1}{3} \times\left(6 \times \frac{4}{3}\right)\) as \(\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}\)
we use the associativity.

8. Is \(\frac {8}{9}\) the multiplicative inverse of – 1 \(\frac {1}{8}\) ? Why or why not ?
Solution:
\(-1 \frac{1}{8}=\frac{-9}{8}\)
\(\frac{8}{9} \times \frac{-9}{8}\) = (-1)
∴ \(\frac {8}{9}\) is is not the multiplicative inverse of -1 \(\frac {1}{8}\) as product of two multiplicative inverse is always 1.

9. Is 0.3 the multiplicative inverse of 3 \(\frac {1}{3}\) ? Why or why not?
Solution:
0.3 = \(\frac {3}{10}\) and 3 \(\frac {1}{3}\) = \(\frac {10}{3}\)
\(\frac{3}{10} \times \frac{10}{3}\) = 1
∴ the multiplicative inverse of 3 \(\frac {1}{3}\) is 0.3.

10. Write:

Question (i).
The rational number that does not have a reciprocal.
Solution:
The rational number that does not have a reciprocal is 0.

Question (ii).
The rational numbers that are equal to their reciprocals.
Solution:
The rational numbers that are equal to their reciprocals are 1 and (-1).

Question (iii).
The rational number that is equal to its negative.
Solution:
The rational number that is equal to its negative is zero (0).

11. Fill in the blanks:

Question (i).
Zero has ……………. reciprocal.
Solution:
Zero has no reciprocal.

Question (ii).
The numbers ……………. and ……………. are their own reciprocals.
Solution:
The numbers 1 and -1 are their own reciprocals.

Question (iii).
The reciprocal of – 5 is …………….
Solution:
The reciprocal of – 5 is \(\frac {-1}{5}\)

Question (iv).
Reciprocal of \(\frac{1}{x}\), where x ≠ 0 is …………….
Solution:
Reciprocal of \(\frac{1}{x}\), where x ≠ 0 is x

Question (v) .
The product of two rational numbers is always a …………….
Solution:
The product of two rational numbers is always a rational number.

Question (vi).
The reciprocal of a positive rational number is …………….
Solution:
The reciprocal of a positive rational number is positive.

Punjab State Board PSEB 8th Class English Book Solutions English Grammar Translation Exercise Questions and Answers, Notes.

PSEB 8th Class English Grammar Translation

1. अपना बस्ता खोलो। – Open your bag.
2. अपना नाम बताओ। – Tell our name.
3. बातें मत करो। – Dont’t talk.

4. बुरी संगत से बचो। – Avoid bad company.
5. बड़ों का कहना मानो। – Obey your elders.
6. कूड़ा मत बिखराओ। – Don’t spread the litter.
7. अपने हाथ ऊपर उठाओ। – Hands up.
8. कभी झूठ मत बोलो। – Never tell a lie.
9. अपना काम पूरा करो। – Complete your work.
10. अपनी त्रुटियों को सुधारो। – Mend/Correct your mistakes.
11. मैं थका हुआ हूँ। – I am tired.
12. वह मूर्ख नहीं है। – He is not foolish.
13. मेरे माता-पिता जी शिक्षक हैं। – My parents are teachers.
14. हम भारतीय हैं। – We are Indians.
15. उसकी बहन बहुत बुद्धिमान है। – His/Her sister is very wise.
16. मुझे आप पर गर्व है। – I am proud of you.
17. पानी साफ है। – Water is clean.
18. वह बहुत स्वार्थी है। – He is very selfish.
19. घास हरी-भरी है। – Grass is green.
20. मैं आज स्वस्थ महसूस नहीं कर रहा हूँ। – I am not feeling well today.
21. मैं रोज़ स्कूल जाता हूँ। – I go to school daily.
22. मेरे माता जी स्वादिष्ट भोजन बनाते हैं। – My mother cooks tasty food.
23. सभी ने पाठ याद कर लिया है। – All have learnt their lesson.
24. मैंने अपना जन्मदिन मनाया। – I celebrated my birthday.
25. मेरे पिता जी बाज़ार जाएंगे। – My father will go to the market.
26. भगवान मेरी मदद करेगा। – God will help me.
27. वह तेज़ दौड़ रहा है। – He is running fast.
28. चपरासी घंटी नहीं बजा रहा है। – The peon is not ringing the bell.
29. छात्र पढ़ रहे होंगे। – The students will be studying.
30. किसान आराम नहीं कर रहे होंगे। – The farmers will not be taking rest.
31. सुशील ने अपना काम कर लिया है। – Susheel has done his work.
32. मेरे शिक्षक ने कापी चैक कर ली है। – The teacher has checked my notebook.
33. लड़कों ने कुर्सी नहीं तोड़ी है। – The boys have not broken the chair.
34. मुझे एक नौकरी मिल गई है। – I have got a job.
35. किसी ने मुझे बुलाया है। – Someone has called me.
36. मोहन ने एक गीत गाया है। – Mohan has sung a song.
37. लड़कियां कक्षा में चली गई हैं। – The girls have gone into the class.

38. पुलिस ने चोर को नहीं पकड़ा है। – The police have not caught the thief.
39. वह इस वर्ष पास नहीं हुआ है। – He has not passed this year.
40. मेरे चाचा जी ने मुझे तोहफे में घड़ी दी। – My uncle gave me a watch as a gift.
41. उसने सच नहीं बोला। – He did not speak the truth.
42. मुझे उस दिन बुखार था। – I was ill that day.
43. हमने डॉक्टर को बुला लिया था। – We had called in the doctor.
44. बूढ़े व्यक्ति ने घर बनाया। – The old man built a house.
45. हम बहुत मज़ा कर चुके थे। – We had a lot of fun.
46. सुधा ने खेल खेला था। – Sudha had played a game.
47. मेरी सहेली ने मेरी मदद की थी। – My friend had helped me.
48. बिल्ली ने दूध नहीं पिया। – The cat had not drunk milk.
49. सोनू ने आपको धक्का नहीं दिया था। – Sonu had not pushed you.
50. दादी ने अच्छी कहानी सुनाई। – The grandmother had told a good story.
51. आप कहाँ रहते हो? – Where do you live?
52. आपने झूठ क्यों बोला? – Why did you tell a lie?
53. आपने अपनी छुट्टी कहां बिताई? – Where did you pass your holiday.
54. कक्षा में कौन था? – Who was in the class?
55. आपका घनिष्ठ मित्र कौन है? – Who is your fast friend?
56. अध्यापिका ने क्या पढ़ाया? – What did the teacher teach?
57. उसने उत्तर क्यों नहीं दिया? – Why did he/she not reply?
58. आप कहाँ जा रहे हो? – Where are you going?
59. आप शोर क्यों मचा रहे हैं? – Why are you making a noise?
60. आप कब आ रहे हो? – When are you coming?
61. आप पुस्तक कब पढ़ रहे थे? – When were you reading the book?
62. आप कल क्या कर रहे थे? – What were you doing yesterday?
63. आप काम कब करोगे? – When will you do the work?
64. वह सवाल कैसे हल करेगी? – How will she solve the sum?
65. अब आप कहां जाओगे? – Where will you go now?
66. वह पार्टी पर क्यों नहीं आएगी? – Why will she not attend the party?
67. क्या आपने उत्तर लिख लिया है? – Have you written the answer?
68. क्या उसने पाठ याद कर लिया है? – Has he learnt the lesson?
69. उसने अपना घर क्यों बेच दिया? – Why did he sell his house?

70. क्या उन्होंने मैच जीत लिया था? – Had they won the match?
71. वह परीक्षा में किस तरह पास हो गया? – How did he pass the test?
72. क्या मैं अन्दर आ सकता हूँ? – May I come in?
73. क्या मैं बाहर जा सकता है। – May I go out?
74. क्या वह तैर सकती है? – Can she swim?
75. क्या मैं अब जा सकता हूँ? – May I go now?
76. अपने हाथ हमें भोजन से पहले धोने चाहिए। – We should wash our hands before meal.
77. मुझे अब सोना चाहिए। – I should go to bed now.
78. परिश्रम करो नहीं तो आप फेल हो जाओगे। – Work hard otherswise you will fail.
79. कृपया करके पृष्ठ पलटो। – Please turn the page.
80. शाबाश! आपने बहुत बढ़िया किया। – Well done!

Punjab State Board PSEB 8th Class English Book Solutions English Grammar Formation of Adverb Exercise Questions and Answers, Notes.

PSEB 8th Class English Grammar Formation of Adverb

Word – Adverb
Able – ably
Abrupt – Abruptly
Accident – Accidently
Active – Actively
Actual – Actually
Anger – Angrily
Annual – Annually
Awful – Awfully
Bad – Badly
Basic – Basically
Busy – Busily
Brief – Briefly
Bold – Boldly
Clear – Clearly
Close – Closly
Calm – Calmly
Certain – Certainly
Comfort – Comfortably

Dear – Dearly
Dead – Deadly
Easy – Easily
Different – Differently
Equal – Equally
Fair – Fairly
Entire – Entirely
Quiet – Quietly
Real – Reality
Rude – Rudely
Safe – Safely
Warm – Warmly
Virtual – Virtually
right – Tighdy
Tender – Tenderly
Wild – Wildly

Punjab State Board PSEB 8th Class English Book Solutions English Grammar Subject-Verb Agreement Exercise Questions and Answers, Notes.

PSEB 8th Class English Grammar Subject-Verb Agreement

Subject Verb Agreement

अंग्रेजी भाषा को शुद्ध लिखने के लिए वाक्य में Subject (कर्ता) का Verb (क्रिया) के साथ ठीक ताल-मेल होना अनिवार्य है। कहने का अभिप्राय यह है कि Verb वाक्य के Subject के वचन (Number) तथा पुरुष (Person) के अनुसार होना चाहिए; जैसे,
Ram goes.
Ram and Sham go.
They go.
She goes.
The boys are going
A boy is going.
They were going.
He/She was going.
Subject तथा Verb के उपयुक्त तालमेल के लिए अग्रलिखित नियमों का अध्ययन करें:

(1) यदि दो या दो से अधिक एकवचन Subjects को and से जोड़ा जाए तो प्रायः उनके साथ बहुवचन Verb का प्रयोग होता है; जैसे,
Mohan and Ram are friends.
Mohan, Sham and Ram play together.
He and his brother have done the work.
Sham and Gopal were there in the meeting.
He and his friend do not work together.

(2) यदि दो एकवचन संज्ञाएं (Nouns) किसी एक व्यक्ति या किसी एक चीज़ का बोध कराती हों तो ऐसी एकवचन संज्ञाओं (Nouns) के साथ एकवचन Verb का प्रयोग होता है; जैसे,-
My brother and helper has arrived.
The leader and speaker is sitting on the stage.
A great Gandhian and leader is dead.

नोट-
(i) यदि एक ही व्यक्ति का बोध कराना हो तो Article का प्रयोग दोनों संज्ञाओं अथवा विशेषणों में से पहली संज्ञा या विशेषण के साथ ही किया जाता है। ऊपर के वाक्य (2) में केवल leader से पहले
The और वाक्य (3) में Gandhian से पहले A का प्रयोग किया गया है।

(ii) यदि वाक्य दो संज्ञाओं से दो अलग व्यक्तियों का बोध कराता हो तो दोनों संज्ञाओं के साथ उचित Article का प्रयोग किया जाता है। ऐसे वाक्य में बहुवचन क्रिया का प्रयोग होता है।
The leader and the speaker are sitting on the stage.

(3) यदि दो Subjects मिलकर किसी एक ही विचार (one idea) को व्यक्त करते हों तो एकवचन क्रिया (Verb in Singular) का प्रयोग होता है; जैसे,-
Fish and meat is the food of the Bengalis.
Slow and steady wins the race.
Twenty kilometres is not a long distance.
The horse and the carriage has arrived.
Early to bed and early to rise makes a man healthy, wealthy and wise.

(4) यदि एकवचन कर्ता (Subject) से पूर्व each अथवा every का प्रयोग किया जाए तो एकवचन क्रिया (Verb in Singular) का प्रयोग होता है; जैसे,-
Every boy and girl was well dressed.
Every man, woman and child was present.
Each day and each hour takes its account.

(5) यदि दो या दो से अधिक एकवचन Subjects को or, nor, either…….. or, neither………..nor से जोड़ा जाए तो एकवचन क्रिया का प्रयोग होता है; जैसे,
Work or play has no difference for me.
Either Mohan or Sohan has broken the slate.
Neither he nor I was present.
Neither food nor water was available there.

(6) जब or तथा nor से जोड़े गए Subjects का वचन भिन्न-भिन्न हो तो बहुवचन क्रिया का प्रयोग किया जाता है तथा बहुवचन Subject को क्रिया के साथ रखा जाता है; जैसे,
Sham or his brothers have broken the slate.
Neither the monitor nor the students were present.
Neither the speaker nor the listeners were serious.
Either the man or his sons have gone wrong.

(7) जब विभिन्न कर्ता (Subjects) or अथवा nor से जुड़े हुए हों, तो क्रिया (Verb) अपने निकटतम् Subject के Person (पुरुष) से मेल खाती है; जैसे,
Either he or I have to go to Delhi.
Neither you nor he is to blame.
Either your father or you are paying for it.

(8) जब Subjects के वचन अथवा पुरुष (Person) में अन्तर हो और वे and से जुड़े हों तो क्रिया (Verb) बहुवचन में प्रयोग होती है; जैसे,
He and I are good friends.
My father and I have jointly done this.
You and he are always together.
You and I are always in time.

(9) समूहवाचक संज्ञा (Collective Noun) के साथ पूरे समूह का भाव व्यक्त करने के लिए एकवचन क्रिया (Verb in Singular) का प्रयोग होता है। परन्तु यदि समूह के व्यक्तियों (individuals) का बोध कराना हो तो बहुवचन क्रिया (Verb in Plural) का प्रयोग होता है; जैसे,
The Committee has chosen its Chairman.
The fleet has set sail.
The Council is one in its opinion for the choice of Chairman.
The Council (councillors) are not one in their opinion for the choice of Chairman.
There is a large number of boys in the class.
A number of players were playing foul.
The police were called out.

(10) कुछ संज्ञाएं देखने में बहुवचन लगती हैं, परन्तु वे अर्थ की दृष्टि से एकवचन होती हैं। ऐसी संज्ञाओं के साथ एकवचन क्रिया (Verb) लगती है; जैसे,
The news is good.
Physics is an easy subject.
The wages of sin is death.
Politics is a dirty game.

(11) कुछ संज्ञाएं देखने में एकवचन लगती हैं परन्तु अर्थ में बहुवचन होती हैं। ऐसी संज्ञाओं के साथ बहुवचन क्रिया (Verb in Plural) का प्रयोग होता है; जैसे,
The gentry were invited to the party.
These poultry are mine.
The cattle are grazing in the field.
People are shouting for nothing.

(12) क्रिया का मेल हमेशा वास्तविक Subject के साथ ही कराना चाहिये। यह जरूरी नहीं है कि क्रिया का निकटतम Subject ही वास्तविक हो। इसलिए वास्तविक Subject को ध्यान में रखना आवश्यक है; जैसे,
Each of the players was rewarded.
Neither of the women was tall.
Each one of plots is for sale.
The quality of these machines is good.
One of the boys was my friend.

(13) यदि Subject में दो Nouns या Pronouns ‘with’ या ‘as well as’ के साथ जुड़े हों, तो क्रिया उनमें से चहले Noun या Pronoun से मेल खती हहै; जैसे
Ram, with all the members of his family, was present.
He, as well as his friends, is present.
Mohan, and not his friend, has done this.
I, as well as he, have worked hard.

(14) जब किसी क्रिया का Subject कोई Relative Pronoun हो, तो क्रिया Relative Pronoun से ठीक पहले वाले Subject के अनुसार लगती है; जैसे
I, who am your guide, shall stand by you.
You, who are my guide, are expected to stand by me.
He is among the persons who are against me.

Exercises (Solved)

I. Say whether the Verbs in the following sentences are Transitive or Intransitive. If the Verb is Transitive name the Object.
(T = Transitive, I = Intransitive, O = Object)

1. He killed a snake.
2. The fire burns brightly.
3. Birds fly in the air.
4. I drink tea five times a day.
5. A blind man cannot see.
6. He came here last night.
7. She has lost her books.
8. He walked twenty miles.
9. A woman came to buy tea.
10. You should teach him a lesson.
Hints :
1. T, O = a snake
2. In.
3. In.
4. T, O = tea
5. In.
6. In.
7. T, O = her books
8. In.
9. T, O = tea.
10. T, O = him, a lesson.

II. Pick out the Auxiliary Verbs in the following sentences:

1. I am writing a novel.
2. He has done wrong.
3. He did not come in time.
4. He is treated badly.
5. I had heard of this before.
6. I shall leave for Mumbai tomorrow.
7. The boy said that he might have done so.
8. He must have gone home.
9. Did he ask you to write to him?
10. I can fly an aeroplane.
Hints:
1. am
2. has
3. did
4. is
5. had
6. shall
7. might have
8. must have
9. Did
10. can.

III. Put the correct Verb in the blanks:

(a) 1. The tallest of these boys ……….. next door to me. (live, lives)
2. All the players in my team ……….. done well. (has, have)
3. The cost of all types of pens ………… gone up. (has, have)
4. The toys that were bought by my son ………… really useful. (are, is)
5. He ……….. regularly. (work, works)
Hints:
1. lives
2. have
3. has
4. are
5. works.

(b) 1. Slow and steady ………. the race. (win, wins)
2. Bread and butter ………. what they want. (is, are)
3. Time and tide ………… for none. (wait, waits)
4. Oil and water ……….. mix. (does not, do not)
5. Tobacco and alcohol ………. injurious to health. (is, are)
Hints:
1. wins
2. is
3. wait
4. do not
5. are.

(c) 1. Neither the captain nor the soldiers ………. been arrested. (has, have)
2. Neither he nor his servants ………… honest. (was, were)
3. Either Rajinder or his parents ……….. responsible for this. (was, were)
4. Neither the Principal nor the lecturers ………………. present at the meeting. (was, were)
5. He or his friends ……….. to blame. (was, were)
Hints:
1. have
2. were
3. were
4. were
5. were.

(e) 1. You, as well as he ……….. innocent. (is, are)
2. Not only the workman but the supervisor also …………………. been dismissed. (has, have)
3. He, as well as you, ………… innocent. (is, are)
4. The workmen, with their leader, ………… been arrested. (have, has)
5. The gallery, with its beautiful pictures, ………… a great attraction. (is, are)
Hints:
1. are
2. have
3. is
4. have
5. is.

(g) 1. None but the brave ………… the fair. (deserve, deserves)
2. Each day and each hour ………… its own importance. (has, have)
3. None of the ships ………… rescued from the storm. (was, were)
4. One of my friends ……….. the owner of this factory. (is, are)
5. Either of these two proposals ……….. acceptable to me. (is, are)
Hints:
1. deserve
2. has
3. was
4. is
5. is.

(h) 1. The United States ……….. a prosperous country. (is, are)
2. The news of the flood ……….. caused great anxiety. (has, have)
3. The Arabian Nights ………. interesting stories. (contain, contains)
4. Good crockery ………. expensive. (is, are)
5. The West Indies ………. a land of great cricketers. (is, are)

Punjab State Board PSEB 8th Class English Book Solutions English Vocabulary Antonyms Exercise Questions and Answers, Notes.

PSEB 8th Class English Vocabulary Antonyms

An Antonym is a word which is opposite (विपरितर्थक) in meaning to another words as:

Word – Antonym
ago – now
gentle – harsh
earn – waste
narrow – broad
holy – dirty
suffer – enjoy

big – small
obedient – disobedian
fail – pass
outside – inside
at last – in the beginning
useful – useless
came – wild
found – lost
back – front
none – all
waste – use
lazy – active
borrow – Jend
sunsel – sunrise
flat – round
modern – ancient
freedom – slavery
clear – unclear
peace – wat
rough – smooth
fresh – staff
profit – loss
unwise – wise
select – reject
pleasure – pain
minor – major
spoil – mend
patient – impatient
pure – impure
defeat – victory
action – inaction
gain – loss
sow – reap
agree – disagree
think – thin
enemy – friend
right – left
openly – secretly
heru – villain
real – false
fit – unfit
remove – cover
war – peace
beggar – king
ugly – beautiful
happily – sadly
gather – scatter
dropped – collecte
answer – question
helieve – disbelieve
absent – present
necessary – unnecessory
older – younger
death – birth
appear – disappear
able – unable
powerful – weak
fool – wise
unhappy – happy
trust – mistrust
fine – ugle
many – few
true – untrue

stand – sit
silent – noisy
difficult – easy
punish – reward
trouble – comfort
began – stopped
before – after
enter – exist
punishment – reward
pleased – displeased
dead – alive
remove – fix
whole – some
pet – wild
top – bottom
kindly – unkindly
glad – sad
joy – sorrow
far – near
less – more
bless – curse
quick – slew
divide – multiply
praise – condemn
reply – question
truth – lie
correct – incorrect
always – forever
clever – foolish
hard – soft
mountain – valley
loving – hateful
refuse – accept
young – old
warm – cool
short – long
good – bad
laugh – weep
cleverest – dullest
night – day
long – short
easily – late
morning – evening
join – leave
before – after
light – heavy
either – neither
famous – notorious
nor – or
slow – fast
like – dislike
small – big
started – reached
beautiful – ugly
happy – sad
thick – thin
give – take
victory – defeat
dark – light
winner – loser
ancient – modern
light – dark
last – first
honour – shame

come – go
below – above
forgive – punish
stupid – wise
honest – dishonest
free – slave
loud – low
soft – hard
alone – together
tiny – big
wide – narrow
gait – small
sharp – blunt

Punjab State Board PSEB 8th Class English Book Solutions English Grammar Formation of Nouns Exercise Questions and Answers, Notes.

PSEB 8th Class English Grammar Formation of Nouns

Formation of Nouns from Adjectives

Adjectives – Nouns
Able – ability
Capable – capability
Abandant – abundance
Cheap – cheapness
Accurate – accuracy
Certain – certainly
Active – activity
Chaste – chastity
Adequate – adequacy

Compulsory – compulsion
Brave – bravery
Cowardly – cowardice
Bread – breadth
Curious – curiosity
Brief – brevity
Dear – dearth
Busy – business
Deep – depth
Calm – calmness
Dense – density
Casual – casualty
Equal – equality
False – falsehood
Perfect – perfection
Fast – fastness
Pious – piety
Fertile – fertility
Poor – poverty
Financial – finance
Popular – popularity
Free – freedom
Private – privacy
Frequent – frequency
Proud – pride
Frank – frankness
Proper – propriety
Gay – gaiety
Public – publicity
Generous – generosity
Pure – purity
Grand – grandour
Quick – quickness
Great – greatness
Real – reality
Happy – happiness
Red – redness
Hard – hardship
Rival – rivalry
High – height
Rich – richness
Holy – holiness
Round – roundness
Honest – honesty
Royal – royalty
Hot – heat
Safe – safety
Human – humanity
Scarce – scarcity
Humble – humility
Secret – secrecy
Inferior – inferiorty
Short – shortage
Innocent – innocence
Solid – solidity
Intense – intensity
Solitary – solitude
Just – justice
Special – speciality
Little – littleness
Strong – strength
Local – locality
Splendid – splendour
Long – length
Stupid – stupidity
Mean – meanness
Supreme – supremacy
Merry – merriment
Sweet – sweetness
Moist – moisture
True – truth
Magnificant – magnificent
Uniform – uniformity
Mortal – mortality
Vacant – vacancy
Necessary – necessity
Vain – vanity
New – newness
Weak – weakness
Noble – nobility
Wide – width
One – oneness
Wise – wisdom
Obedient – obedience
Young – youth

Foundation of Nouns from Verbs

Verbs – Nouns
Abound – abundance
Arrive – arrival
Accomplish – accomplishment
Bear – birth
Acknowledge – acknowledgement
Betray – betrayal
Acquaint – acquaintance
Bind – bond
Acquire – acquisition
Bite – bite
Admit – admission
Bless – blessing
Advise – advice
Break – breakage
Amuse – amusement
Amuse – amusement
Approve – approval
Believe – belief
Carry – carriage
Practise – practice
Choose – choice
Pretend – pretence
Consume – consumption
Proceed – procedure
Contain – contents
proceed – process
Decide – decision
Protect – protection
Deny – denial
Prove – proof
Depart – departure
Provide – provision
Dig – ditch
Purify – purification
Do – deed
Pursue – pursuit
Drink – draught
Quote – quotation
Envelop – envelope
Receive – receipt
Exceed – excess
Reduce – reduction

Exist – existence
Relieve – relief
Expect – expectation
Refer – reference
Except – exception
Refine – refinement
Float – fleet
Reveal – revelation
Flow – flood
Refuse – refusal
Fly – flight
Refresh – refreshment
Free – freedom
Reform – reformation
Furnish – furniture
See – sight
Give – gift
Sit – seat
Go – gait
Serve – service
Grieve – grief
Slay – slaughter
Grow – growth
Sow – seed
Elate – hatred
Speak – speech
Heal – health
Steal – stealth
Judge – judgement, justice
Strike – stroke
Succeed – success, succession
Know – knowledge
Laugh – laughter
Secure – security
Learn – learning
Tell – tale
Lend – loan
Trace – track
Live – life
Try – trial
Manage – management
Think – thought
Mean – meaning
Thieve – theft
Marry – marriage
Urge – urgency
Move – motion, movement
Vacate – vacancy, vacation
Obey – obedience
Vary – variety
Object – objection
Weave – web
Occupy – occupation
Write – writ, writing
Offend – offence
Oppose – opposition
Weigh – weight
Perform – performance
Wed – weeding
Please – pleasure
Withdraw – withdrawal

Formation of Abstract Nouns

Words – Abstract Noun
Act – action
Agent – agency
Boy – boyhood
Man – manhood
Bond – bondage
owner – ownership
Beggar – beggary
Patriot – patriotism
Child – childhood
Priest – priesthood
Coward – cowardice
Servant – service
Creature – creation
Speaker – speech
Friend – friendship
Slave – slavery
Hero – herosim
Thief – theft
Infant – infancy
Woman – womanhood
King – kingship
Widow – widowhood
Mother – motherhood
Young – youth

Punjab State Board PSEB 8th Class English Book Solutions English Grammar Adjective and Degree Exercise Questions and Answers, Notes.

PSEB 8th Class English Grammar Adjective and Degree

An Adjective is a word which qualifies or adds something to the meaning of a Noun or a Pronoun.

जो शब्द किसी Noun अथवा Pronoun की विशेषता प्रकट करता है उसे Adjective (विशेषण) कहते हैं। Adjective प्रायः Noun के साथ प्रयोग होता है। यह या तो किसी व्यक्ति, पशु अथवा स्थान का वर्णन करता है या किसी संख्या अथवा मात्रा का बोध कराता है; जैसे-

1. Many years ago there was a miser. (संख्या)
2. He never ate good food. (गुण)
3. He spent little money. (मात्रा)

इन वाक्यों में Many, good तथा little शब्द क्रमशः संख्या, गुण एवं मात्रा का बोध कराते हैं। अतः ये शब्द Adjectives हैं।
Adjective मुख्यतः 9 प्रकार के होते हैं-
1. Adjectives of Quality-जो विशेषण किसी व्यक्ति अथवा वस्तु के गुण या प्रकार का बोध कराते हैं, उन्हें Adjectives of Quality (गुणवाचक विशेषण) कहते हैं ; जैसे-good, fresh; bad आदि।

2. Proper Adjectives_Proper Nouns से बनने वाले विशेषण Proper Adjectives (व्यक्तिवाचक विशेषण) कहलाते हैं; जैसे-Indian, Chinese.

3. Adjectives of Quantity-जो विशेषण किसी वस्तु की मात्रा का बोध कराते हैं उन्हें Adjectives of Quantity (परिमाणवाचक विशेषण) कहते हैं। इस प्रकार के Adjective प्रायः कितने (How much) शब्द का उत्तर देते हैं; जैसे-some, no, great.

4. Adjectives of Number-जो विशेषण संख्या अथवा क्रम का बोध कराते हैं, उन्हें Adjectives of Number (संख्यावाचक विशेषण) कहते हैं; जैसे-two, all आदि।

5. Distributive Adjectives-जो विशेषण किसी विशेष वर्ग के व्यक्ति अथवा वस्तु को अलग-अलग प्रकट करें, उन्हें Distributive Adjectives (विभाजन विशेषण) कहते हैं; जैसे-each, either, every आदि।

6. Demonstrative Adjectives-जो विशेषण सम्बन्धित व्यक्ति अथवा वस्तु की ओर संकेत करते हैं, उन्हें Demonstrative Adjectives (संकेतवाचक विशेषण) कहते हैं; जैसे-this, that आदि।

7. Interrogative Adjectives -जो विशेषण प्रश्न पूछने के लिए प्रयोग किया जाता है, उसे Interrogative Adjective (प्रश्नवाचक विशेषण) कहते हैं; जैसे-which, what, whose आदि।

8. Possessive Adjectives- किसी वस्तु या व्यक्ति पर अधिकार व्यक्त करने वाले विशेषण को Possessive Adjectives (सम्बन्धवाचक विशेषण) कहा जाता है; जैसे, My book, Your brother, आदि।

9. Emphasizing Adjectives- जो शब्द Possessive Adjectives पर बल देने के लिए प्रयोग किए जाते __ . हैं, वे Emphasizing Adjectives (निजवाचक विशेषण) कहलाते हैं। इसके लिए प्रायः own शब्द प्रयोग किया जाता है; जैसे,
I became my own servant.

A- Degrees of Adjectives

There are three degrees of comparison:

1. Positive Degree.
2. Comparative Degree.
3. Superlative Degree.

B-Degrees के प्रयोग के नियम

1. Adjective (विशेषण) की पहली Degree (Positive) का प्रयोग उस समय होता है जब कोई तुलना न करनी हो या तुलना की दोनों वस्तुएं (Noun या Pronoun) एक जैसी हों। इसमें as’ का प्रयोग होता है, जैसे-

• Ram is a good boy.
• He is as strong as I.
• This book is as good as Ram’s.

2. दूसरी Degree (Comparative) का प्रयोग उस समय होता है जब दो वस्तुओं या दो व्यक्तियों की तुलना करनी हो। इसमें than’ का प्रयोग होता है; जैसे-

• He is more intelligent than his brother.
• Ram is more intelligent of the two brothers.
• This is better of the two pens.

3. तीसरी Degree (Superlative) का प्रयोग उस समय होता है जब कोई व्यक्ति या वस्तु अन्य सभी व्यक्तियों या वस्तुओं की तुलना में अच्छी हो। इसका प्रयोग एक वस्तु की दो से अधिक वस्तुओं के साथ तुलना करने में होता है; जैसे,-

• She is the most beautiful of all the sisters.
• Ram is the eldest of the four brothers.

C–Use of Some Adjectives

(Note : Adjectives are given in italics.)
1. Your elder brother will captain our team.
2. Our school is older than yours.
3. He is older than I.
4. Who is the eldest member in the family ?
5. It is the oldest temple of the area.
6. My bat is superior to yours.
7. This wood is inferior to that.
8. Is John junior to Gopal ?
9. Ishwar is senior to me.
10. There is little milk in the jug.
11. I have a little money in my pocket.
12. The little money I saved is spent.
13. He makes few mistakes.
14. He makes a few mistakes.
15. The few boys who were present in the morning have run away.
16. He has some books on American literature.
17. I have some friends here in this town.
18. Do you have any books on grammar ?
19. Have you any money?
20. I have not received any help from him.
21. I reached the school later than Shyam.
22. What is the latest score ?
23. The latest issue of this magazine is awaited.
24. Mohan narrated two tales but I found the latter more interesting.
25. The last train leaves at 11-50 at night.
26. The last batsman played extremely well.
27. We have much amount to spend on clothing.
28. Many students in our class have won prizes.

Exercises (Solved)

I. Write out the story, putting one of the adjectives from the list in each blank:
Long delightful high sour ripe warm hungry

It was a ………….. day. A fox had just entered a garden. Among the many……….. things in the garden was a vine laden with bunches of grapes. One of them was a ……..3…….. bunch which hung invitingly over the fox’s head. The very sight of it made the fox feel ……..4……… He leapt up at the grapes several times. But they were too ……..5……. for him to reach. After a ……..6…… time he decided to give up trying. He went away declaring that the grapes were ……..7…….. This is the origin of the expression ‘sour grapes’.
Hints:
1. warm
2. delightful
3. ripe
4. hungry
5. high
6. long
7. sour.

II. Fill in the blanks with the comparative or superlative degree of the adjectives given in the brackets:

1. The Taj is ……………… than any other building. (beautiful)
2. This is the ……………… book I have ever read. (good)
3. The climate of Shimla is ………………. than that of Delhi. (good)
4. Mohan is the …………….. boy in his class. (tall)
5. Hardwar is one of the ……………… places for the Hindus. (holy)
6. Ram is …………… than his sister. (intelligent)
7. Mumbai is ……………… than any other city in Maharashtra. (large)
8. This dress is ………………. than that. (costly)
9. Radha has …………….. sense than her sister. (much)
10. My table is the ……………… of all. (big)
Hints:
1. more beautiful
2. best
3. better
4. tallest
5. holiest
6. more intelligent
7. larger
8. costlier
9. more
10. biggest.

III. Put the correct word in the blank spaces:

(a) 1. He came …………….. than Sham. (later, latter)
2. The ……………… train leaves the station at 11 p.m. (last, later)
3. What is the …………….. news ? (latest, last)
4. I met Shila and Rita yesterday. The former promised to come to the party but the ………………… gave a flat refusal. (later, latter)
5. Ram is ………………… than Hari. (elder, older)
6. He is the ……………. member of the family. (eldest, oldest)
7. The ……………… brother controls the entire business. (older, elder)
8. Delhi is ………………… from Ludhiana than Ambala. (further, farther)
9. You are not going to get any ……………… help from us. (further, farther)
10. History is ……………….. difficult than Mathematics. (less, fewer)
11. ……………… boys attended the meeting this time. (less, fewer)
12. These chairs cost sixty rupees ……….. (every, each)
13. ……………….. man loves him. (every, each)
14. His days are numbered; he has ……………… hope to survive. (little, a little)
15. …………….. effort on your part will help me a lot. (little, a little)
Hints :
1. later
2. last
3. latest
4. latter
5. older
6. eldest
7. elder
8. farther
9. further
10. less
11. Fewer
12. each
13. Every
14. little
15. a little.

IV. Correct the following sentences:

1. The poors always deserve mercy.
2. The three friends helped each other.
3. Shakespeare is greater than any dramatist.
4. There were no less than fifty persons present.
5. Every of the two friends is ill.
6. Iron is more useful than any metal.
7. My hat is more superior than yours.
8. The three brothers understand each other well.
9. He is a best boy in the class.
10. The higher you go the coolest it is.
Hints:
1. The poor always deserve mercy.
2. The three friends helped one another.
3. Shakespeare is greater than any other dramatist.
4. There were no fewer than fifty persons present.
5. Each of the two friends is ill.
6. Iron is more useful than any. other metal.
7. My hat is superior to yours.
8. The three brothers understand one another well.
9. He is the best boy in the class.
10. The higher you go, the cooler it is.