NCERT Solutions Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.2
Introduction:
NCERT Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.1
NCERT Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.2
Class 7 Maths Algebraic Expression Exercise 10.2 (Page-168)
Q1. If m = 2, find the value of:
(i) m - 2
(ii) 3m - 5
(iii) 9 - 5m
(iv) 3m² - 2m - 7
(v) \(\displaystyle \frac{{5m}}{2}\) - 4
Solution:
(i) putting value of m =2
= 2 - 2
= 0
(ii) putting value of m =2
= 3(2) - 5
= 6 - 5
= 1
(iii) putting value of m =2
= 9 - 5(2)
= 9 - 10
= -1
(iv) putting value of m =2
= 3(2)² - 2(2) - 7
= 3 (4) - 4 - 7
= 12 - 11
= 1
(v) putting value of m =2
= \(\displaystyle \frac{{5(2)}}{2}\) - 4
= \(\displaystyle \frac{{10}}{2}\) - 4
= 5 - 4
= 1
Q2. If p = -2, find the value of :
(i) 4p + 7
(ii) -3p² + 4p + 7
(iii) - 2p³ - 3p² + 4p+ 7
Solution:
(i) putting the value of p = -2
= 4(-2) + 7
= -8 + 7
= -1
(ii) putting the value of p = -2
= -3(-2)² + 4(-2) + 7
= -3( 4) + (-8) + 7
= - 12 - 8 + 7
= - 20 + 7
= - 13
(iii) putting the value of p = -2
= - 2(-2)³ - 3(-2)² + 4(-2) + 7
= -2 (-8) - 3 (4) + (-8) + 7
= 16 - 12 - 8 + 7
= 16 - 20 + 7
= -4 + 7
= 3
Q3. 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:
(i) putting the value of x = -1
= 2(-1) - 7
= -2 - 7
= -9
(ii) putting the value of x = -1
= - (-1) + 2
= 1 + 2
= 3
(iii) putting the value of x = -1
= (-1)² + 2(-1) + 1
= 1 - 2 +1
= -1 +1
= 0
(iv) putting the value of x = -1
= 2(-1)² - (-1) -2
= 2(1) + 1 - 2
= 2 + 1 -2
= 3 - 2
= 1
Q4. If a = 2, b= -2, find the value of:
(i) a² + b²
(ii) a² + ab + b²
(iii) a² - b²
Solution:
(i) Putting value of a = 2 and b= -2
= (2)² + (-2)²
= 4 + 4
= 8
(ii) Putting value of a = 2 and b= -2
= (2)² + (2)(-2) + (-2)²
= 4 + (-4) + 4
= 4 - 4 + 4
= 0 + 4
= 4
(iii) Putting value of a = 2 and b= -2
= (2)² - (-2)²
= 4 - 4
= 0
Q5. 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:
(i) Putting value of a = 0 and b= -1
= 2 (0) + 2(-1)
= 0 - 2
= -2
(ii) Putting value of a = 0 and b= -1
= 2(0)² + (-1)² + 1
= 0 + 1 + 1
= 2
(iii) Putting value of a = 0 and b= -1
= 2(0)²(-1) + 2(0)(-1)² + (0)(-1)
= 2 (0) + 2(0) +(0)
= 0 +0+0
= 0
(iv) Putting value of a = 0 and b= -1
= (0)² + (0)(-1) + 2
= 0 + 0 + 2
= 2
Q6. 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) putting the value of x = 2
= (2)+ 7 + 4(2-5)
= 9 + 8 - 20
= 17 - 20
= -3
(ii)putting the value of x = 2
= 3(2+2) + 5(2) - 7
= 3(4) + 10 - 7
= 12 + 10 - 7
= 22 - 7
= 15
(iii)putting the value of x = 2
= 6(2) + 5(2 - 2)
= 12 + 5(0)
= 12 + 0
= 12
(iv)putting the value of x = 2
= 4( 2x - 1) + 3x + 11
= 8x - 4 + 3x + 11
= 8(2) - 4 + 3(2) + 11
= 16 - 4 + 6 + 11
= 12 + 17
= 29
Q7. 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) Putting value of x= 3
= 3x - 5 - x + 9
= 3x -x -5 + 9
= 2x + 4
= 2(3) + 4
= 6 + 4
= 10
(ii) Putting value of x= 3
= 2 - 8x + 4x + 4
= -4x + 2+ 4
= - 4x + 6
= -4(3) + 6
= - 12 + 6
= - 6
(iii) Putting value of a = -1
= 3a + 5 - 8a + 1
= 3a - 8a +5 + 1
= -5a + 6
= - 5(-1) + 6
= 5 + 6
= 11
(iv) Putting value of b= -2
= 10 - 3b - 4 -5b
= - 3b - 5b -4 + 10
= -8b +6
= - 8 (-2) + 6
= 16 + 6
= 22
(v) Putting value of a = -1, b= -2
= 2a - 2b - 4 -5 + a
= 2a + a -2b -9
= 3a - 2b -9
= 3(-1) -2(-2) -9
=-3 + 4 - 9
= 1 - 9
= -8
Q8. (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) Putting value of z = 10
= z³ - 3(z- 10)
= z³ - 3z - 30
= (10)³ - 3(10) - 10
= 1000 - 30 - 30
= 1000 -0
= 1000
(ii) Putting value of p = -10
= p² -2p -100
= (-10)² - 2(-10) - 100
= 100 + 20 - 100
= 120 - 100
= 20
Q9. What should be the value of a if the value of 2x² + x - a equals to 5, when x = 0 ?
Solution: 2x² + x - a = 5
putting value of x = 0
2(0)² + (0) - a = 5
0 + 0 -a = 5
-a = 5
a = -5
So, the value of x is equals to 5.
Q10. 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 the value of a = 5 and b= -3
= 2 (5)² + (5× -3) + 3
= 2 (25) - 15 + 3
= 50 - 12
= 38