Algebraic Expressions and Identities Class 8 MCQ Maths Chapter 9

MCQ on Algebraic Expressions and Identities for Class 8

Class 8 Maths Chapter 9 Algebraic Expressions and Identities MCQ

MCQ of Algebraic Expressions and Identities Class 8

I. Choose the correct answer.

Question 1.
For x = -5, the value of (x + 5)² = ___________ .
A) 100
B) 25
C) 0
D) 55
Answer:
C) 0

Question 2.
Highest coefficient in the expression 4x³ + 10x² – 9x + 6 is ___________ .
A) 4
B) 10
C) -9
D) 6
Answer:
B) 10

Question 3.
P = 4x² – 3x + 5 ; Q = – 3x – 4x² – 5, then p – Q = __________ .
A) 6x
B) 8x² – 6x
C) 8x² + 10
D) -8x² – 10
Answer:
C) 8x² + 10

Question 4.
3PQ, 4lm, – 2PQ, 6lm², 4ln, 4PQ in these like terms are __________ .
A) 3PQ, 4lm
B) 3PQ, – 2PQ
C) 4lm, 6lm², 4ln
D) 3PQ, – 2PQ, 4PQ
Answer:
D) 3PQ, – 2PQ, 4PQ

Question 5.
Which of the following is not a monomial ?
A) -4lm²n
B) 6abcd
C) 405x²y³z²
D) none of the above
Answer:
D) none of the above

Question 6.
Separate like, unlike terms from the following.
-xyz, xy²z², 6x²yz, 4xy²z², x²y²z²
A) (- xyz, x²y²z²), (6x²yz, 4xy²z², x²y²z²)
B) (xy²z², 4xy²z²), (-xyz, 6x²yz, x²y²z²)
C) (x²y²z², xy²z², 4xy²z²), (-xyz, 6x²yz)
D) (-xyz, x²y²z², 6x²yz), (4xy²z², x²y²z²)
Answer:
B) (xy²z², 4xy²z²), (-xyz, 6x²yz, x²y²z²)

Question 7.
Subtract 5x² – 2xy – 8 from 10x² + 4xy – 16
A) 5x² + 6xy + 8
B) 5x² – 6xy – 8
C) 5x² + 6xy – 8
D) -15x² – 6xy + 8
Answer:
C) 5x² + 6xy – 8

Question 8.
If A = – 3x² – 4xy + y², then – 3A = _________ .
A) 9x² + 12xy – 3y²
B) – 9x² – 12xy – 3y²
C) – 9x² + 12xy + 3y²
D) 9x² – 12xy – 3y²
Answer:
A) 9x² + 12xy – 3y²

Question 9.
Adding (l² + m²); – (m² + n²); (- n² + l²) we get _________ .
A) 2l² + 2m² – 2n²
B) 2m² – 2n²
C) l² – 2n²
D) 2l² – 2n²
Answer:
D) 2l² – 2n²

Question 10.
P = (x + a), Q = (x + b), then 2P + 3Q = __________ .
A) 5x + 2a + 3b
B) 5x² + 2ax + 3bx
C) 5x – 3ab + 6ax
D) none
Answer:
A) 5x + 2a + 3b

Question 11.
(p – 3) (z + 4) = __________ .
A) pz + 3z + 4p – 12
B) pz – zp – 12
C) pz + 4p – 3z – 12
D) pz – 4p + 3z + 12
Answer:
C) pz + 4p – 3z – 12

Question 12.
If length of a rectangle Is (4x + 3y) and breadth is (3x – 4y), then its perimeter is __________ .
A) 6x – 8y
B) 14x – 6y
C) 16x + 8y
D) 14x – 2y
Answer:
D) 14x – 2y

Question 13.
Perimeter of a square is (8x – 16y), then the side of it is __________ .
A) 32x – 64y
B) 16x – 32y
C) 4x – 8y
D) 2x – 4y
Answer:
D) 2x – 4y

Question 14.
Length of a rectangle is 3lm, and its area is – 9lm²n, then its breadth is __________ .
A) -27l²m³n
B) -3mn
C) –\(\frac{1}{3}\)lmn
D) 27lm²
Answer:
B) -3mn

Question 15.
PQ, QR, RS are length, breadth and height of a cuboid, then its volume is _________ .
A) P²Q²R²
B) PQ²R²
C) P²Q²R²S
D) PQ²R²S
Answer:
D) PQ²R²S

Question 16.
Product of k, – k, – 2k, 2k, 3k, – 3k is ________ .
A) 10k
B) -12k⁴
C) -36k⁶
D) 36k⁶
Answer:
C) -36k⁶

Question 17.
Value of 3y(2y – 7) – 3(y – 4) – 63 for y = 4 is ___________ .
A) -51
B) 51
C) 48
D) none
Answer:
A) -51

Question 18.
Product of (k¹⁰) (2k²⁵) (3k^p) – 6k⁴⁰, then P = ___________ .
A) 45
B) 40
C) 5
D) 8
Answer:
C) 5

Question 19.
Product of (x – 4) and (2x – 3) is ___________ .
A) 2x² – 11x – 12
B) 2x² – 11x + 12
C) x² – 11x + 12
D) none
Answer:
B) 2x² – 11x + 12

Question 20.
(x + 2y)² = ___________ .
A) x² + 2xy + 4y²
B) x² – 4xy – 4y²
C) x² + 4xy + 4y²
D) 4x² – 4xy + y²
Answer:
C) x² + 4xy + 4y²

Question 21.
An equality is said to be an identity, if it is ___________ .
A) true for all values of variable
B) true for ail negative values of variable
C) true for particular values of variable
D) true for the values 0, and 1
Answer:
A) true for all values of variable

Question 22.
Which of the following is not an identity ?
A) x² = x . x
B) (x + y)² = x² + 2xy + y²
C) (x + y)² = x² + 4xy + y²
D) (x – y)² = x² – 2xy + y²
Answer:
C) (x + y)² = x² + 4xy + y²

Question 23.
(100 + 3)² = 100² + (_____?_____ )+ 3²
A) 2(100)(3)
B) -2(100) (3)
C) 200 × 300
D) -4(100)(3)
Answer:
A) 2(100)(3)

Question 24.
(x + 5) (x -3) = x² + px – 15, then p = _________ .
A) 8
B) (5 – 3)
C) (5 × 3)
D) (- 5 + 3)
Answer:
B) (5 – 3)

Question 25.
(x + 4)(x + p) = x² + qx + 20, then the values of p and q are _________ .
A) 9, 20
B) 4, 5
C) 5, 9
D) 20, 9
Answer:
C) 5, 9

For the following questions in A, R type from 26 to 30. Choose correct answer from following options.
A) Both ‘A’ and ‘R’ are correct and ‘R’ is correct explanation of ‘A’
B) Both ‘A’ and ‘R’ are correct but ‘R’ is not correct explanation of ‘A’.
C) ‘A’ is true but ‘R’ is false.
D) ‘A’ is false but ‘R’ is true.

Question 26.
Assertion (A) : Expression 2x – 3y + 4z is linear expression in 3 variables.
Reason (R) : Order of variables x, y, z in 2x – 3y + 4z is 1.
Answer:
A) Both ‘A’ and ‘R’ are correct and ‘R’ is correct explanation of ‘A’

Question 27.
Assertion (A) : Value of 2x – 5 is 1, when x = 3.
Reason (R) : (a + b)² = a² – 2ab + b²
Answer:
C) ‘A’ is true but ‘R’ is false.

Question 28.
Assertion (A): We can find the value of 9982 using the identity (a – b)² = a² – 2ab + b²
Reason (R) : 998² = (1000 – 2)²
= 1000² – 2(2)(1000) + 4.
Answer:
A) Both ‘A’ and ‘R’ are correct and ‘R’ is correct explanation of ‘A’

Question 29.
Assertion (A) : 2x – 5y² + 3z is a binomial.
Reason (R) : A binomial is an expression having two non-zero terms.
Answer:
D) ‘A’ is false but ‘R’ is true.

Question 30.
Assertion (A) : – 3 is coefficient of the term – 3xy².
Reason (R) : Coefficient is the number which multiplies the algebraic term.
Answer:
A) Both ‘A’ and ‘R’ are correct and ‘R’ is correct explanation of ‘A’

Question 31.
Which of the following expressions is the simplified form of (3x + 4y) (3x – 4y) ?
A) 9x² – 16y²
B) 9x² + 16y²
C) 9x² + 24xy + 16y²
D) 9x² – 24xy + 16y²
Answer:
A) 9x² – 16y²

Question 32.
If we subtract the sum of 2a²b and (-7a²b) from the sum of (-5a²b) and (-2a²b), we get _________ .
A) 2a²b
B) -2a²b
C) -12a²b
D) 12a²b
Answer:
B) -2a²b

Question 33.
A piece of ribbon of length 30 cm was cut into three pieces. The lengths of the three pieces are x cm, 16 cm, x cm as shown below.
im
What is the value of x?
A) 7
B) 8
C) 10
D) 14
Answer:
A) 7

Question 34.
Which of these expressions is a binomial?
A) x²
B) 6xy
C) 6 – x
D) 2x + x
Answer:
C) 6 – x

Question 35.
Which of these is SAME as (x – \(\frac{1}{4}\)) (x – \(\frac{3}{4}\))
A) x² – x + \(\frac{3}{16}\)
B) x² + x – \(\frac{3}{16}\)
C) x² – \(\frac{x}{2}\) + \(\frac{3}{16}\)
D) x² + \(\frac{3 x}{16}\) + 1
Answer:
A) x² – x + \(\frac{3}{16}\)

Question 36.
(2x² + 3xy – 3y²) – (x² – y²) =
A) x² – 2y²
B) 3xy – 2y²
C) x² + 3xy – 2y²
D) x² + 3xy – 4y²
Answer:
C) x² + 3xy – 2y²

Question 37.
If the mean of (x – 4) observations is (x² + 4x + 16), then what is the sum of observations ?
A) (x² + 16)
B) (x² – 16)
C) (x³ + 64)
D) (x³ – 64)
Answer:
A) (x² + 16)

Question 38.
If the product of (x + 4) and (x + p) is x² + kx + 28, then the values of p and k are
A) p = 7 and k = 11
B) p = 11 and k = 7
C) p = 7 and k = 4
D) p = 11 and k = 4
Answer:
D) p = 11 and k = 4

Question 39.
What is the coefficient of “y” in the expression \(\frac{-3 x y}{z}\) ?
A) \(\frac{-3 x}{z}\)
B) \(\frac{3 x}{z}\)
C) \(\frac{-x}{z}\)
D) \(\frac{-3}{z}\)
Answer:
A) \(\frac{-3 x}{z}\)

Question 40.
What is the result of multiplying (2a + 3b) by (a – b) ?
A) 2a² – 3b²
B) 2a² + 3b²
C) 2a² – ab – 3b²
D) 2a² + ab – 3b²
Answer:
D) 2a² + ab – 3b²

Question 41.
Varsha travelled with constant speed for (x + 5) hours, covering a total distance represented by the expression (x² + 7x + 10) km. How far does she travel in
lhour?
A) (x + 2) km
B) (x + 5) km
C) (x + 9) km
D) (2x + 10) km
Answer:
A) (x + 2) km

II. Fill in the blanks.

1. (\(\frac{x}{2}\) + \(\frac{3 y}{8}\)) (\(\frac{x}{2}\) + \(\frac{3 y}{8}\)) can be computed easily using the identity _________ .
Answer:
\(\frac{x^2}{4}\) + \(\frac{3 x y}{8}\) + \(\frac{9 y^2}{64}\) (a + b)² = a² + 2ab + b²

2. (x + 4) (x – 7) = x² – px + q, then the values of p, q are _________ .
Answer:
p = 3, q = -28

3. expand (\(\frac{3 \mathrm{~m}}{2}\) – \(\frac{4 n}{3}\))² = ________ .
Answer:
\(\frac{9 m^2}{4}\) – 4mn + \(\frac{16 \mathrm{n}^2}{9}\)

4. (7a + mb) (7a – mb) = 49a² – 64b², then (m) = _________
Answer:
m = 8

5. (a² – b²) (a² + b²) = _________ .
Answer:
a⁴ – b⁴

6. (a³ – b³)² = _________ .
Answer:
a⁶ – 2a³b³ + b⁶

7. (a + b + c) (a + b – c) = _________ .
Answer:
(a + b)² – c² = a² + 2ab + b² – c² + 2ab

8. 3x(4xy + 5yz + 6zx) = _________ .
Answer:
12x²y + 15xyz = 18zx²

9. 3x(5y + z) – 4y(5y + z) can be written in product form as _________ .
Answer:
(3x – 4y) (5y + z)

10. Subtract 4p²q – 3pq + 5pq² from – 5pq² + 3pq – 4p²q, we get _________ .
Answer:
-8p²q + 6pq – 10pq²

III. Match the following.

Question 1.

A	B
1) 2x(- 3y + 4z) =	a) (100 + 1)2 = 1002 + 2(1)(100) + 12
2) (4x – 5y) (4x + 5y) =	b) x2 + x(a + b) + ab
3) (101)2 =	c) 15 – x – 2x2
4) (x + a) (x + b) =	d) – 6xy + 8xz
5) (5 – 2x) (3 + x) =	e) 16x2 – 25y2

Answer:
(1, d) (2, e) (3, a) (4, b) (5, c)

A	B
1) 2x(- 3y + 4z) =	d) – 6xy + 8xz
2) (4x – 5y) (4x + 5y) =	e) 16x2 – 25y2
3) (101)2 =	a) (100 + 1)2 = 1002 + 2(1)(100) + 12
4) (x + a) (x + b) =	b) x2 + x(a + b) + ab
5) (5 – 2x) (3 + x) =	c) 15 – x – 2x2

Class 8 Maths MCQ