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.
Answer
Answer: (a) 4
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
Answer
Answer: (a) x, 3x
Question 3.
The like terms of the following are
(a) 2xВ, 9xВ
(b) yВ, xy
(c) xy, 9aВ
(d) yВ, 9xВ
Answer
Answer: (a) 2xВ, 9xВ
Question 4.
The coefficient of xВy in 7pqrxВ is
(a) 7pqr
(b) pqr
(c) -7pqr
(d) 7
Answer
Answer: (a) 7pqr
Question 5.
The coefficient of xy in xy is
(a) 1
(b) -1
(c) 2
(d) 3.
Answer
Answer: (a) 1
Hint:
xy = 1(xy).
Question 6.
The value of 5x when x = 5 is
(a) 5
(b) 10
(c) 25
(d) -5.
Answer
Answer: (c) 25
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.
Answer
Answer: (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.
Answer
Answer: (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.
Answer
Answer: (a) 1
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.
Answer
Answer: (c) 1
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.
Answer
Answer: (a) 4xВ
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.
Answer
Answer: (b) 4l + 5m
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
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.
Answer
Answer: (a) 1
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.
Answer
Answer: (b) 2
Hint:
5, -3xy.
Question 16.
How many terms are there in the expression 7xВ + 5x – 5 ?
(a) 1
(b) 2
(c) 3
(d) 5.
Answer
Answer: (c) 3
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.
Answer
Answer: (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.
Answer
Answer: (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.
Answer
Answer: (a) 7
Hint:
Coefficient = 7.
Question 20.
The coefficient in the term -5x is
(a) 5
(b) -5
(c) 1
(d) 2.
Answer
Answer: (b) -5
Hint:
Coefficient = -5.
Question 21.
The coefficient in the term 20 is
(a) 1
(b) 2
(c) 10
(d) 20.
Answer
Answer: (d) 20
Hint:
Coefficient = 20.
Question 22.
The coefficient in the term -20 is
(a) -1
(b) -2
(c) -10
(d) -20.
Answer
Answer: (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
Answer
Answer: (a) ab, 9ba
Question 24.
The expression x + 3 is in
(a) one variable
(b) two variables
(c) no variable
(d) none of these.
Answer
Answer: (a) one variable
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.
Answer
Answer: (b) two variables
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.
Answer
Answer: (c) three 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.
Answer
Answer: (b) -15
Question 28.
The product of 4x and 0 is:
(a) 4x
(b) 4
(c) 0
(d) None of the above
Answer
Answer: (c) 0
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
Answer
Answer: (a) 105x7
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
Answer
Answer: (b) 7x and 9x
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
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
Answer
Answer: (b) -20x2yz
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
Answer
Answer: (d) 6xy
Hint:
6xВyВ = (6xy)(xy).
Question 34.
The coefficient of xy2z in -7x2y3z is
(a) -7xy
(b) 7xy
(c) -xy
(d) xy.
Answer
Answer: (a) -7xy
Hint:
-7xВyГz = (-7xy)(xyВz).
Question 35.
The sum of 7x, 10x and 12x is
(a) 17x
(b) 22x
(c) 19x
(d) 29x.
Answer
Answer: (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.
Answer
Answer: (c) -9pq
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.
Answer
Answer: (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.
Answer
Answer: (a) 0
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.
Answer
Answer: (c) 8xy
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.
Answer
Answer: (c) -7x
Hint:
0 – 7x = -7x.
Question 41.
The result of subtraction of 3x from -4x is
(a) -7x
(b) 7x
(c) x
(d) -x.
Answer
Answer: (a) -7x
Hint:
-4x -3x = -7x.
Question 42.
The product of 4mn and 0 is
(a) 0
(b) 1
(c) mn
(d) 4 mn.
Answer
Answer: (a) 0
Hint:
(4 mn)(0) = 0.
Question 43.
The product of 5x and 2y is
(a) xy
(b) 2xy
(c) 5ay
(d) 10ay.
Answer
Answer: (d) 10ay
Hint:
(5x)(2y) = 10xy.
Question 44.
The product of 7x and -12x is
(a) 84xВ
(b) -84xВ
(c) xВ
(d) -xВ.
Answer
Answer: (b) -84xВ
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
Answer
Answer: (c) 36yГ
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.
Answer
Answer: (a) 6lГmГ
Hint:
Area = (2lВm)(3lmВ) = 6lГmГ.
Question 47.
The volume of a cube of side 2a is
(a) 4aВ
(b) 2a
(c) 8aГ
(d) 8.
Answer
Answer: (c) 8aГ
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.
Answer
Answer: (a) abc
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
Answer
Answer: (a) x9
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.
Answer
Answer: (a) 0
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
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
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
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
Answer
Answer: (a) Monomial
Hint:
2x is a monomial
Question 55.
5x + 6y is a:
(a) A. Monomial
(b) Binomial
(c) Trinomial
(d) None of the above
Answer
Answer: (b) Binomial
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
Answer
Answer: (c) Trinomial
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
Answer
Answer: (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
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.
Answer
Answer: (a) 3
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.
Answer
Answer: (a) 6
Hint:
All are like terms.
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