These NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.3 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.3
Question 1.
If m – 2, find the value of:
(i) m – 2
(ii) 3m – 5
(iii) 9 – 5m
(iv) 3m2 – 2m – 7
(v) \(\frac { 5m }{ 2 }\) – 4
Answer:
(i) m- 2 = 2 – 2 (m = = 2)
= 0
(ii) 3m – 5 = 3 (2) – 5 (m = – 2)
= 6 – 5 = 1
(iii) 9 – 5m = 9 – 5(2) (m = = 2)
= 9- 10
= -1
(iv) 3m2 – 2m – 7
= 3 (2)2 – 2(2) – 7
(m = 2)
= 3 (4) – 4 – 7
= 12 – 4 – 7
= 12 – 11
= 1
(v) \(\frac { 5m }{ 2 }\) – 4 = \(\frac{5(2)}{2}\) – 4 (m = 2)
= 5 – 4
= 1
Question 2.
If p = -2, find the value of:
(i) 4p + 7
(ii) – 3p2 + 4p + 7
(iii) – 2p2 – 3p2 + 4p + 7
Answer:
(i) 4p + 7 = 4(-2) + 7
= – 8 + 7 = -1
(ii) -3p2 + 4p + 7
= – 3 (-2)2 + 4(-2) + 7
(when p = -2)
= – 3 (4) + (- 8) + 7
= -12 – 8 + 7
= -20 +7
= -13
(iii) -2p3 – 3p2 + 4p + 7 =
-2 (-2)3 – 3 (-2)2 + 4 (-2) + 7
(when p = -2)
= – 2(- 8) — 3 (4) + (— 8) + 7 = + 16 – 12 – 8 + 7 = 23 – 20 = 3
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
Answer:
(i) 2x – 7 = 2(-1) – 7 (whenx = -1)
= -2 – 7 = -9
(ii) -x + 2 = -(-1) + 2 (When x = -1)
= 1 + 2 = 3
(iii) x2 + 2x + 1 = (-1)2 + 2 (-1) + 1
(When x = – 1)
= 1 – 2 + 1
= 2 – 2 = 0
(iv) 2x2 – x – 2 =2 (-1)2 – (-1) – 2
(When x = -1)
= 2 + 1 – 2
= 3 – 2 = 1
Question 4.
If a = 2, b = – 2, find the value of:
(i) a2 + b2
(ii) a2 + ab + b2
(iii) a2 – b2
Answer:
(i) a2 + b2 = (2)2 + (-2)2
(When a = 2, b = -2)
= 4 + 4 = 8
(ii) a2 + ab + b2
= (2)2 + 2(-2) + (-2)2
(When a = 2, b = – 2)
= 4 – 4 + 4
= 8 – 4 = 4
(iii) a2 – b2 = 22 – (-2)2
(When a = 2, b = -2) = 4-(4) = 4- 4 = 0
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
Answer:
(i) 2a + 2b = 2 (0) + 2(—1)
(When a = 0, b = -1)
= 0 – 2 = -2
(ii) 2a2 + b2 +1
= 2 (0)2 + (-1)2 + 1
(When a = 0, b = -1)
= 0 + (1) + (1)
= 1 + 1 = 2
(iii) 2a2b + 2ab2 + ab
= 2(0)2 (-1) + 2(0) (-1)2 + (0) (-1)
(When a = 0, b = -1)
= 2(0) (-1) + 2(0) (1) + 0
= 0 + 0 + 0
= 0
(iv) a2 + ab + 2 = (0)2 + 0 (-1) + 2
(When a = 0, b = -1)
= 0 – 0 + 2 = 2
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 – l) + 3x+ 11
Answer:
(i) x + 7 + 4 (x -5)
= x + 7 + 4x – 20
= x + 4x + 7 – 20
= 5x – 13 (When x = 2)
= 5 (2) – 13
= 10- 13
= -3
(ii) 3 (x + 2) + 5x – 7 = 3x + 6 + 5x – 7
= 3x + 5x + 6 – 7
= 8x – 1 (When x = 2)
= 16 – 1 = 15
(iii) 6x + 5 (x – 2) = 6x + 5x – 10
= 1 lx – 10 (When x = 2)
= 11 (2) – 10 = 22-
= 12
(iv) 4(2x – 1)+ 3x + 11
= 8x + 3x – 4 + 11
= 8x + 3x + 11 – 4
= 11x + 7 (When x = 2)
h = 11(2) + 7
= 22 + 7 = 29
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
Answer:
(i) 3x-5-x + 9
= 3x-x-5 + 9
= 2x + 4 (When x = 3)
= 2(3)+ 4
= 6 + 4
= 10
(ii) 2-8x + 4x + 4
= -8x + 4x + 4 + 2
= (- 8 + 4) x + 6
= – 4x + 6
(When x = 3)
= – 4(3) + 6
= -12+ 6 =-6
(iii) 3a + 5 – 8a + 1
= 3a – 8a + 5 + 1
= (3 – 8) a + 6
= -5a + 6
(When a = – 1)
= -5 (-1) + 6
= 5 + 6= 11
(iv) 10 – 3b – 4 – 5b = -3b -5b +10-4
= (-3 -5) b + 6 = – 8 b + 6
(When b = – 2) = – 8 (-2) + 6
= 16 + 6 = 22
(v) 2a – 2b – 4 – 5 + a =
2a + a – 2b – 4 -5 = 3a – 2b – 9
(When a = – 1 and b = -2) = 3 (-1) -2 (-2) -9 = -3 + 4 -9 = -12+ 4 =-8
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
Answer:
(i) z3 – 3 [z – 10] = 102 – 3 [10- 10]
(When z = 10)
= 1000 – 3 (0)= 1000
(ii) p2 – 2p – 100
= (-10)2 – 2 (-10) – 100
(When p = -10)
= 100 + 20 – 100
= 120 – 100 = 20
Question 9.
What should be the value of a if the value of 2x2 + x – a equals to 5, when x = 0? Ans: 2x2+ x – a = 5 (Given: x = 0)
2(0)2 + 0 – a = 5
0 + 0 – a = 5
-a =5
a = – 5
The value of a = – 5
Question 10.
Simplify the expression and find its value when a = 5 and b = – 3.
2(a2 + ab) + 3 – ab
Answer:
2(a2 + ab) + 3 – ab
= 2 [52 + 5(-3)] + 3 -(5) (-3)
= 2 [25- 15] +3 + 15
= 2(10) + 18
= 20 + 18 = 38