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## Wednesday, 24 February 2021

### CBSE Class 8 Maths - MCQ and Online Tests - Unit 9 - Algebraic Expressions and Identities

#### CBSE Class 8 Maths – MCQ and Online Tests –  Unit 9 – Algebraic Expressions and Identities

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#### CBSE Class 8 Maths – MCQ and Online Tests – Unit 9 – Algebraic Expressions and Identities

Question 1.
The number of like terms in
$$\frac{1}{4}$$aВbc, – $$\frac{2}{3}$$bcaВ, $$\frac{2}{5}$$ baВc, – $$\frac{1}{2}$$cbaВ is
(a) 4
(b) 3
(c) 2
(d) 6.

Hint:
All are like terms.

Question 2.
The like terms of the following are
(a) x, 3x
(b) x, 2y
(c) 2y, 6xy
(d) 3x, 2y

Question 3.
The like terms of the following are
(a) 2xВ, 9xВ
(b) yВ, xy
(c) xy, 9aВ
(d) yВ, 9xВ

Question 4.
The coefficient of xВy in 7pqrxВ is
(a) 7pqr
(b) pqr
(c) -7pqr
(d) 7

Question 5.
The coefficient of xy in xy is
(a) 1
(b) -1
(c) 2
(d) 3.

Hint:
xy = 1(xy).

Question 6.
The value of 5x when x = 5 is
(a) 5
(b) 10
(c) 25
(d) -5.

Hint:
Value = 5 з 5 = 25.

Question 7.
The value of xВ – 2x + 1 when x = 1 is
(a) 1
(b) 2
(c) -2
(d) 0.

Hint:
Value = (1)В – 2(1) + 1 = 0.

Question 8.
The value of xВ + yВ when x = 1, y = 2 is
(a) 1
(b)2
(c) 4
(d) 5.

Hint:
Value = (1)В + (2)В = 5.

Question 9.
The value of xВ – 2yx + yВ when x = 1, y = 2 is
(a) 1
(b) -1
(c) 2
(d) -2.

Hint:
Value = (1)В – 2(2)(1) + (2)В = 1.

Question 10.
The value of xВ – xy + yВ when x = 0, y = 1 is
(a) 0
(b) -1
(c) 1
(d) none of these.

Hint:
Value = (0)В – (0)(1) + (1)В = 1.

Question 11.
Which of the following is a monomial ?
(a) 4xВ
(b) a + 6
(c) a + 6 + c
(d) a + b + c + d.

Hint:
4xВ contains only one term.

Question 12.
Which of the following is a binomial ?
(a) 3xy
(b) 4l + 5m
(c) 2x + 3y – 5
(d) 4a – 7ab + 3b + 12.

Hint:
4l + 5m contains two terms.

Question 13.
Which of the following is a trinomial ?
(?) -7z
(b) zВ – 4yВ
(c) xВy – xyВ + yВ
(d) 12a – 9ab + 5b – 3.

Answer: (c) xВy – xyВ + yВ
Hint:
xВy – xyВ + yВ contains three terms.

Question 14.
How many terms are there in the expression 5xyВ ?
(a) 1
(b) 2
(c) 5
(d) 3.

Hint:
Only one term 5xyВ.

Question 15.
How many terms are there in the expression 5 – 3xy ?
(a) 1
(b) 2
(c) 3
(d) 5.

Hint:
5, -3xy.

Question 16.
How many terms are there in the expression 7xВ + 5x – 5 ?
(a) 1
(b) 2
(c) 3
(d) 5.

Hint:
7xВ, 5x, -5.

Question 17.
How many terms are there in the expression 4a – lab + 3b + 12 ?
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
4a, -7ab, 3b, 12.

Question 18.
How many terms are there in the expression 5xy + 9yz + 3zx + 5x – 4y ?
(a) 1
(b) 3
(c) 4
(d) 5.

Hint:
5xy, 9yz, 3zx, 5x, – 4y.

Question 19.
The coefficient in the term 7xy is
(a) 7
(b) 3
(c) 1
(d) 2.

Hint:
Coefficient = 7.

Question 20.
The coefficient in the term -5x is
(a) 5
(b) -5
(c) 1
(d) 2.

Hint:
Coefficient = -5.

Question 21.
The coefficient in the term 20 is
(a) 1
(b) 2
(c) 10
(d) 20.

Hint:
Coefficient = 20.

Question 22.
The coefficient in the term -20 is
(a) -1
(b) -2
(c) -10
(d) -20.

Hint:
Coefficient = -20.

Question 23.
The like terms of the following are
(a) ab, 9ba
(b) ab, -5b
(c) -5b, 9ba
(d) ab, -3a

Question 24.
The expression x + 3 is in
(a) one variable
(b) two variables
(c) no variable
(d) none of these.

Hint:
The only variable is x.

Question 25.
The expression 4xy + 7 is in
(a) one variable
(b) two variables
(c) no variable
(d) none of these.

Hint:
There are two variables x and y.

Question 26.
The expression x + y + z is in
(a) one variable
(b) no variable
(c) three variables
(d) two variables.

Hint:
There are three variables x, y and z.

Question 27.
The coefficient of xВy in -15 xВy is
(a) 15
(b) -15
(c) 3
(d) 5.

Question 28.
The product of 4x and 0 is:
(a) 4x
(b) 4
(c) 0
(d) None of the above

Hint:
Anything multiplied by zero is zero.

Question 29.
The volume of a rectangle with length, breadth and height as 5x, 3x2 and 7x4 respectively is:
(a) 105x7
(b) 105x2
(c) 105x4
(d) 105x

Hint:
Volume of rectangle = Length з breadth з height
V = 5x з 3x2 з 7x4
V = 105 x1+2+4
V = 105x7 cubic unit.

Question 30.
In which of the following, the two expressions are like terms ?
(a) 7x and 7y
(b) 7x and 9x
(c) 7x and 7x2
(d) 7x and 7xy

Question 31.
If we subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3, then the answer is:
(a) 8a + 2ab + 2b + 15
(b) 8a + 2ab + 2b – 15
(c) 8a – 2ab + 2b – 15
(d) 8a – 2ab – 2b – 15

Answer: (c) 8a – 2ab + 2b – 15
Hint:
(12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12)
= 12a – 9ab + 5b – 3 – 4a + 7ab – 3b – 12
= (12 – 4)a – (9 – 7)ab + (5 – 3)b – 3 – 12
= 8a – 2ab + 2b – 15

Question 32.
If we multiply 5x and (-4xyz), then we get:
(a) 20x2yz
(b) -20x2yz
(c) x2yz
(d) -2xyz

Hint:
(5x) x (-4xyz)
= 5 з x з (-4) з x з y з z
= -20x1+1yz
= -20x2yz

Question 33.
The coefficient of xy in 6xВyВ is
(a) xy
(b) 2xy
(c) 3xy
(d) 6xy

Hint:
6xВyВ = (6xy)(xy).

Question 34.
The coefficient of xy2z in -7x2y3z is
(a) -7xy
(b) 7xy
(c) -xy
(d) xy.

Hint:
-7xВyГz = (-7xy)(xyВz).

Question 35.
The sum of 7x, 10x and 12x is
(a) 17x
(b) 22x
(c) 19x
(d) 29x.

Hint:
Sum = (7 + 10 + 12) x = 29x.

Question 36.
The sum of 8pq and -17 pq is
(a) pq
(b) 9pq
(c) -9pq
(d) -pq.

Hint:
Sum = {8 + (-17)} pq = -9pq.

Question 37.
The sum of 5xВ, -7xВ, 8xВ, 11xВ and -9xВ is
(a) 2xВ
(b) 4xВ
(c) 6xВ
(d) 8xВ.

Hint:
Sum = {5 + (-7) + 8 + 11 + (-9)} xВ = 8xВ.

Question 38.
The sum of xВ – yВ, yВ – zВ and zВ – xВ is
(a) 0
(b) 3xВ
(c) 3yВ
(d) 3zВ.

Hint:
Sum = (xВ – yВ) + (yВ – zВ) + (zВ – xВ) = 0.

Question 39.
What do you get when you subtract -3xy from 5xy?
(a) 3xy
(b) 5xy
(c) 8xy
(d) xy.

Hint:
5xy – (-3xy) = 5xy + 3xy = 8xy

Question 40.
The result of subtraction of 7x from 0 is
(a) 0
(b) 7x
(c) -7x
(d) x.

Hint:
0 – 7x = -7x.

Question 41.
The result of subtraction of 3x from -4x is
(a) -7x
(b) 7x
(c) x
(d) -x.

Hint:
-4x -3x = -7x.

Question 42.
The product of 4mn and 0 is
(a) 0
(b) 1
(c) mn
(d) 4 mn.

Hint:
(4 mn)(0) = 0.

Question 43.
The product of 5x and 2y is
(a) xy
(b) 2xy
(c) 5ay
(d) 10ay.

Hint:
(5x)(2y) = 10xy.

Question 44.
The product of 7x and -12x is
(a) 84xВ
(b) -84xВ
(c) xВ
(d) -xВ.

Hint:
(7x) (-12x) = – 84xВ.

Question 45.
The area of a rectangle whose length and breadth are 9y and 4yВ respectively is
(a) 4yГ
(b) 9yГ
(c) 36yГ
(d) 13yГ

Hint:
Area = (9y)(4yВ) = 36yГ.

Question 46.
The area of a rectangle with length 2lВm and breadth 3lmВ is
(a) 6lГmГ
(b) lГmГ
(c) 2lГmГ
(d) 4lГmГ.

Hint:
Area = (2lВm)(3lmВ) = 6lГmГ.

Question 47.
The volume of a cube of side 2a is
(a) 4aВ
(b) 2a
(c) 8aГ
(d) 8.

Hint:
Volume = 2a з 2a з 2a = 8aГ.

Question 48.
The volume of a cuboid of dimensions a, b, c is
(a) abc
(b) aВbВcВ
(c) aГbГcГ
(d) none of these.

Hint:
Volume = a з b з c = abc.

Question 49.
The product of xВ, – xГ, – x4 is
(a) x9
(b) x5
(c) x7
(d) x6

Hint:
Product = (xВ) (-xГ)(-x4) = x9.

Question 50.
(x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x) is equal to
(a) 0
(b) xВ + yВ + zВ
(c) xy + yz + zx
(d) x + y + z.

Hint:
(x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x) = xВ – yВ + yВ – zВ + zВ – xВ = 0.

Question 51.
(a + b)В is equal to
(a) aВ + bВ – 2ab
(b) aВ + bВ + 2ab
(c) aВ + bВ
(d) 2ab.

Answer: (b) aВ + bВ + 2ab
Hint:
(a + b)В = aВ + bВ + 2 ab.

Question 52.
(a – b)В is equal to
(a) aВ + bВ – 2ab
(b) aВ + bВ + 2ab
(c) aВ + bВ
(d) 2ab.

Answer: (a) aВ + bВ – 2ab
Hint:
(a – b)В = aВ + bВ – 2ab.

Question 53.
aВ – bВ is equal to
(a) 2ab
(b) -2ab
(c) (a + b) (a – b)
(d) ab

Answer: (c) (a + b) (a – b)
Hint:
aВ – bВ = (a + b) (a – b).

Question 54.
An algebraic expression that contains only one term is called:
(a) Monomial
(b) Binomial
(c) Trinomial
(d) None of the above

Hint:
2x is a monomial

Question 55.
5x + 6y is a:
(a) A. Monomial
(b) Binomial
(c) Trinomial
(d) None of the above

Hint:
The expression containing two terms is called binomial.

Question 56.
The algebraic expression 3x + 2y + 6 is
(a) monomial
(b) Binomial
(c) Trinomial
(d) None of the above

Hint:
The algebraic expression containing three terms is called a trinomial. Here, 3x, 2y and 6 are three terms.

Question 57.
A polynomial contains _______ number of terms:
(a) One
(b) Two
(c) Three
(d) Any

Hint:
A polynomial can contain any number of terms, one or more than one.

Question 58.
If we add, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and -3xz + 5x – 2xy, then the answer is:
(a) 5xy + 9yz + 3zx + 5x – 4y
(b) 5xy – 9yz + 3zx – 5x – 4y
(c) 5xy + 10yz + 3zx + 15x – 4y
(d) 5xy + 10yz + 3zx + 5x – 6y

Answer: (a) 5xy + 9yz + 3zx + 5x – 4y
Hint:
Given, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and -3xz + 5x – 2xy.
If we add the three expressions, then we need to combine the like terms together.
(7xy – 2xy)+(5yz + 4yz) – 3zx + 9zx – 3xz – 4y + 5x
5y + 9yz + 3zx + 5x – 4y

Question 59.
The number of like terms in 9xГ, 16xВy, -8xГ, 12xyВ, 6xГ is
(a) 3
(b) 2
(c) 4
(d) 5.

Hint:
9xГ, -8xГ, 6xГ.

Question 60.
The number of like terms in
abc, -abc, -bca, acb, bac, $$\frac{1}{2}$$cab is
(a) 6
(b) 4
(c) 3
(d) 2.