NCERT Solutions for Class 7 Maths Chapter 10 Algebraic Expressions Ex 10.2

NCERT Solutions for Class 7 Maths Chapter 10 Algebraic Expressions Ex 10.2 (Rationalised Contents)

NCERT Solutions for Class 7 Maths Chapter 10 Algebraic Expressions Ex 10.2 are the part of NCERT Solutions for Class 7 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 7 Maths Chapter 10 Algebraic Expressions Ex 10.2.

Ex 10.2 Class 7 Maths Question 1.

If m = 2, find the value of:
(i) m – 2
(ii) 3m – 5
(iii) 9 – 5m
(iv) 3m² – 2m – 7
(v) 5m/2 − 4

Solution:
(i) m – 2
Putting m = 2, we get
m – 2 = 2 – 2 = 0
(ii) 3m – 5
Putting m = 2, we get
3m – 5 = 3 × 2 – 5 = 6 – 5 = 1
(iii) 9 – 5m
Putting m = 2, we get
9 – 5m = 9 – 5 × 2 = 9 – 10 = -1
(iv) 3m² – 2m – 7
Putting m = 2, we get
3m² – 2m – 7 = 3(2)² – 2(2) – 7 = 3 × 4 – 4 – 7
= 12 – 4 – 7 = 12 – 11 = 1
(v) 5m/2 − 4
Putting m = 2, we get
5m/2 – 4 = (5 × 2)/2 – 4 = 5 – 4 = 1

Ex 10.2 Class 7 Maths Question 2.

If p = -2, find the value of:
(i) 4p + 7
(ii) -3p² + 4p + 7
(iii) -2p³ – 3p² + 4p + 7

Solution:
(i) 4p + 7
Putting p = -2, we get
4p + 7 = 4(-2) + 7 = -8 + 7 = -1
(ii) -3p² + 4p + 7
Putting p = -2, we get
-3p² + 4p + 7 = -3(-2)² + 4(-2) + 7
= -3 × 4 – 8 + 7 = -12 – 8 + 7 = -13
(iii) -2p³ – 3p² + 4p + 7
Putting p = -2, we get
-2p³ – 3p² + 4p + 7 = –2(-2)³ – 3(-2)² + 4(-2) + 7
= -2 × (-8) – 3 × 4 – 8 + 7
= 16 – 12 – 8 + 7 = 3

Ex 10.2 Class 7 Maths Question 3.

Find the value of the following expressions, when x = –1:
(i) 2x – 7
(ii) – x + 2
(iii) x²+ 2x + 1
(iv) 2x²– x – 2

Solution:
Putting x = –1 in each expression, we get
(i) 2x – 7 = 2(–1) – 7 = –2 – 7 = –9
(ii) –x + 2 = –(–1) + 2 = 1 + 2 = 3
(iii) x²+ 2x + 1 = (–1)² + 2(–1) + 1 = 1 – 2 + 1 = 0
(iv) 2x²– x – 2 = 2(–1)² – (–1) – 2 = 2 + 1 – 2 = 1

Ex 10.2 Class 7 Maths Question 4.

If a = 2, b = -2, find the value of:
(i) a² + b²
(ii) a² + ab + b²
(iii) a² – b²

Solution:
(i) a² + b²
Putting a = 2 and b = -2, we get
a² + b² = (2)² + (-2)² = 4 + 4 = 8
(ii) a² + ab + b²
Putting a = 2 and b = -2, we get
a² + ab + b² = (2)² + 2(-2) + (-2)² = 4 – 4 + 4 = 4
(iii) a² – b²
Putting a = 2 and b = -2, we get
a² – b² = (2)² – (-2)² = 4 – 4 = 0

Ex 10.2 Class 7 Maths Question 5.

When a = 0, b = -1, find the value of the given expressions:
(i) 2a + 2b
(ii) 2a² + b² + 1
(iii) 2a²b + 2ab² + ab
(iv) a² + ab + 2

Solution:
Putting a = 0, b = -1 in each expression, we get
(i) 2a + 2b = 2(0) + 2(-1) = 0 – 2 = -2
(ii) 2a² + b² + 1 = 2(0)² + (-1)² + 1 = 0 + 1 + 1 = 2
(iii) 2a²b + 2ab² + ab = 2(0)²(-1) + 2(0)(-1)² + (0)(-1)
= 0 + 0 + 0 = 0
(iv) a² + ab + 2 = (0)² + (0)(-1) + 2 = 0 + 0 + 2 = 2

Ex 10.2 Class 7 Maths Question 6.

Simplify the expressions and find the value if x is equal to 2.
(i) x + 7 + 4(x – 5)
(ii) 3(x + 2) + 5x – 7
(iii) 6x + 5(x – 2)
(iv) 4(2x – 1) + 3x + 11

Solution:
(i) x + 7 + 4(x – 5) = x + 7 + 4x – 20 = 5x – 13
Putting x = 2, we get
5x – 13 = 5 × 2 – 13 = 10 – 13 = -3
(ii) 3(x + 2) + 5x – 7 = 3x + 6 + 5x – 7 = 8x – 1
Putting x = 2, we get
8x – 1 = 8 × 2 – 1 = 16 – 1 = 15
(iii) 6x + 5(x – 2) = 6x + 5x – 10 = 11x – 10
Putting x = 2, we get
11x – 10 = 11 × 2 – 10 = 22 – 10 = 12
(iv) 4(2x – 1) + 3x + 11 = 8x – 4 + 3x + 11 = 11x + 7
Putting x = 2, we get
11x + 7 = 11 × 2 + 7 = 22 + 7 = 29

Ex 10.2 Class 7 Maths Question 7.

Simplify these expressions and find their values if x = 3, a = -1, b = -2.
(i) 3x – 5 – x + 9
(ii) 2 – 8x + 4x + 4
(iii) 3a + 5 – 8a + 1
(iv) 10 – 3b – 4 – 5b
(v) 2a – 2b – 4 – 5 + a

Solution:
(i) 3x – 5 – x + 9 = 2x + 4
Putting x = 3, we get
2x + 4 = 2 × 3 + 4 = 6 + 4 = 10
(ii) 2 – 8x + 4x + 4 = -8x + 4x + 2 + 4 = -4x + 6
Putting x = 2, we have
-4x + 6 = -4 × 3 + 6 = -12 + 6 = -6
(iii) 3a + 5 – 8a + 1 = 3a – 8a + 5 + 1 = -5a + 6
Putting a = -1, we get
-5a + 6 = -5(-1) + 6 = 5 + 6 = 11
(iv) 10 – 3b – 4 – 5b = -3b – 5b + 10 – 4 = -8b + 6
Putting b = -2, we get
-8b + 6 = -8(-2) + 6 = 16 + 6 = 22
(v) 2a – 2b – 4 – 5 + a = 2a + a – 2b – 4 – 5 = 3a – 2b – 9
Putting a = -1 and b = -2, we get
3a – 2b – 9 = 3(-1) – 2(-2) – 9
= -3 + 4 – 9 = 1 – 9 = -8

Ex 10.2 Class 7 Maths Question 8.

(i) If z = 10, find the value of z³ – 3(z – 10).
(ii) If p = -10, find the value of p² – 2p – 100.

Solution:
(i) z³ – 3(z – 10) = z³ – 3z + 30
Putting z = 10, we get
z³ – 3z + 30 = (10)³ – 3(10) + 30
= 1000 – 30 + 30 = 1000
(ii) p² – 2p – 100
Putting p = -10, we get
p² – 2p – 100 = (-10)² – 2(-10) – 100
= 100 + 20 – 100 = 20

Ex 10.2 Class 7 Maths Question 9.

What should be the value of a if the value of 2x² + x – a equals to 5, when x = 0?

Solution:
When x = 0, 2x² + x – a = 5
Putting x = 0, we get
2(0)² + (0) – a = 5
0 + 0 – a = 5
-a = 5
Or, a = -5 which is required value of a.

Ex 10.2 Class 7 Maths Question 10.

Simplify the expression and find its value when a = 5 and b = -3.
2(a² + ab) + 3 – ab

Solution:
2(a² + ab) + 3 – ab = 2a² + 2ab + 3 – ab
= 2a² + 2ab – ab + 3
= 2a² + ab + 3
Putting, a = 5 and b = -3, we get
2a² + ab + 3 = 2(5)² + (5)(-3) + 3
= 2 × 25 – 15 + 3
= 50 – 15 + 3
= 53 – 15 = 38
Hence, the required value of the expression is 38.

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