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Mathematics Sets Functions and Groups Online Test

Maan AliLast Updated: October 15, 2025

Important Math Sets Functions and Groups Online Mcqs Test

Total Questions:	191
Time Allowed:	60 Minutes
Total Marks:	191
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Mathematics Sets Functions and Groups Practice Test Online With Explanation

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Page 1 of 8

Math

1. a/b = ka/kb , (k ≠ 0) is known as

Golden rule of fraction

Principle for equality of Fractions

Rule of quotient of Fraction

Rule for product of fraction

2. The set {-1, 1} is closed under the binary operation of

Division

Subtraction

Addition

Multiplication

3. P: 4 > 7, q:6 > 11, the conjunction p ʌ q is

True

False

Not valid

Unknown

4. If a set S contains “n” elements then P (S) has ………… number of elements.

2ⁿ

n²

2.n

5. If A = {x/x ϵ R ʌ x² - 16 = 0} then A =

{-4, 4}

-x

Infinite set

6. The property used in – 3 < -2 ⇒ 0 < 1

Commutative property

Additive property of inequality

Additive Identity

Additive inverse

7. A disjunction of two statements p and q is true if

Both p and q are false

Q is false

P is false

One of p and q is true

8. If X = 1/X for X ϵ R then the value of x is

± 1

9. √–81 – √–36 = ?

√15i

√3i

√117i

10. i³ =

-i

-1

11. Power set of empty set has exactly __________ subset.

Zero

Two

One

Three

12. The truth value of the statement [(P → q) ʌ P] → q is false when

P is true, q is true

None of these

P is true, q is false

P is false, q is true

13. Associative law of multiplication

(a + b) c = ac + bc

a(a + c) = ab + ac

ab = ba

a(bc) = (ab) c

14. Multiplicative inverse of “1” is

∞

± 1

15. A declarative statement which may be true or false but not both is called

Proposition

Deduction

Knowledge

Induction

16. Which of the following has the same value as i¹¹³?

-i

-1

17. 0 (zero) is

A rational number

An irrational number

A positive number

A negative integer

18. The square root of 2i – 20i is

(5 – 2i)

±(5 – 2i)

None of these

±(5 + 2i)

19. If Z₁ = 1 + i, Z₂ = 2 + 3i, then |Z₁ – Z₂| = ?

√3

√7

√5

-1-2i

20. (a¯¹)¯¹ =

a¯¹

-a

None of these

21. P: 7 <4. q:6>11, the disjunction p v q is

False

True

Unknown

Not valid

22. The set of integer is

A group w.r.t addition

Finite group

Not a group

A group w.r.t multiplication

23. The multiplicative inverse of 1 – 2i is

– 1/5 + 2/5 i

1/3 i

1/5 + 2/5 i

1/5 – 2/5 i

24. An element ‘b’ of a set B can be written as

b ⊆ B

b < B

B ϵ b

b ϵ B

25. The set {{a, b}} is

Infinite set

None of these

Two points set

Singleton set

Page 2 of 8

26. If A = {1,3,4}, B = {c,a,f} then A ⋂ B = ?

{0}

{1, 2, 3, e, d, f}

{c, a, f}

27. ∀ a, b, c ϵ ℜ, ac = bc ⇒ a = b, c ≠ 0 is a

Cancellations property w.r.t. multiplication

Symmetric property

Reflexive property

Transitive property

28. The graph of the function f(x) is symmetrical about the line x = 2, then

f (x) = f (–x)

f (x + 2) = f (x – 2)

f (x) = – f (– x)

f (2 + x) = f(2 – x)

29. What is the Cartesian product of A = {1, 2} and B = {a, b}?

{(1, a),(2, a),(1, b),(2, b)}

{(1, 1),(2, 2),(a, a),(b, b)}

{(1, 1),(a, a),(2, a),(1, b)}

{(1, a),(1, b),(2, a),(b, b)}

30. If # n = (n – 5)² + 5, then find #3 x #4.

31. P : 4 < 7, q : 7 < 11, the disjunction p v q is

False

Not valid

Unknown

True

32. If z = x-iy/x+iy then |Z| is

-1

33. ∀ a ϵ ℜ ∃ o ϵ ℜ such that a + v = 0 + a = a is property of

Additive Identity

Additive inverse

Commutative law of addition

Associative law of addition

34. In a country, 55% of the male population has houses in cities while 30% have houses both in cities and in villages. Find the percentage of the population that has houses only in villages.

35. {x|x = P/q ,q ϵ Z ʌ q ≠ 0} is set of all

Rational numbers

Irrational numbers

Integers

Natural numbers

36. To each element of a group there corresponds …………., Inverse element

Three

One

Two

37. The multiplicative inverse of x such that x = 0 is

1/x

-x

Does not exist

38. Additive inverse of – a – b is

a – b

– a + b

a + b

39. Let A, B, and C be any sets such that A U B = A U C and A ∩ B = A ∩ C then

B = C

A ≠ B

A = B

A ≠ C

40. The function f = {(x,y)|y = mx + c} is

Linear function

Constant function

Quadratic function

Cubic function

41. For any set B, BUB’ is

Is set B

Set B’

Universal Set

42. ∀ a, b, c ϵ ℜ, a + c = b + c = > a = b

Reflexive property

Transitive property

Symmetric property

Cancellations property w.r.t. addition

43. In (x + iy), y is called as

Real part

Imaginary part

None of these

Complex number

44. (a, 0) x (c, 0) =

(ac, 0)

(a, c)

(0, 0)

(0, ac)

45. The graph of a quadratic function is

Hexagon

Circle

Parabola

Ellipse

46. Which of the following is the subset of all sets?

{0}

{φ}

{1, 2, 3}

47. The set of all positive even integers is

Not a group

A group w.r.t. subtraction

A group w.r.t. division

A group w.r.t. multiplication

48. The set {Z\{0}} is group w.r.t

Division

Subtraction

Multiplication

Addition

49. The truth value of the proportion is a + ve number or 2 + 2 = 4 is

True

None of these

False

Contingency

50. a + ib form of -2+3i/-i is:

1 – 2i

– 3 – 2i

1 + 2i

3 – 2i

Page 3 of 8

51. If z₁ = √-36, z₂ = √-25, z₃ = √-16, then what is the sum of z₁, z₂ and z₃?

-15i

15i

-15

52. P : 4 < 7, q : 7 < 11 the conjunction p ʌ q

Not valid

True

Unknown

False

53. Decimal part of irrational number is

Repeating only

Repeating and terminating

Neither repeating nor terminating

Terminating

54. The set {-1, 1} is

Does not form a group

Group under the multiplication

Group under addition

Contains no identity element

55. The value of x, and y, when (x + iy)² = 5 + 4i

X = 2, y = -1

X = 2, y = -i

X = 2, y = 2

X = -2, y = 1

56. The statement that a group can have more than one identity elements” is

Some times true

False

Fallacious

True

57. The set {1, 1 – 1, i, – i}, form a group under

Addition

None of these

Multiplication

Subtraction

58. Let R = {(1, 3), (4, 2)(2, 4),(2,3), (3,1)} be a relation on the set A = {1,2,3,4}. The relation R is

A function

Transitive

Reflexive

Not symmetric

59. The set {x + iy/x, y ϵ Q} forms a group under the binary operation of

Division

Both addition and multiplication

Multiplication

Addition

60. If n(X) = 18, n(X∩Y) = 7, n(X U Y) = 40 then n(Y) =

61. If a > b or a < b than a = b is a

Trichotomy property of inequality

None of these

Additive property

Transitive property

62. If A = {4,3}, then P(A) is

{{3}, {4}, {4,3}}

{φ, {3}, {4}}

{φ, {3,4}}

{φ, {4}, {3}, {4,3}}

63. The set Q = { ½ / a, b ϵ z ʌ b ≠ 0} was named as

Rational Numbers

Complex Numbers

Whole Numbers

Set of whole number

64. A _________ is an ordered collection of objects.

Relation

Function

Set

Proposition

65. QUQ’ =

ℜ

66. Let A, B, and C be any sets such that AUB = AUC and A∩B = A∩C then

A ≠ B

A = B

A ≠ C

B = C

67. If x ϵ R, then x² + x + 1 is

ϵ [3/4, ∞]

Positive

(1, ∞)

Negative

68. In polar form of complex number

Q = tan¯¹ (x/y)

Q = tan¯¹ (y/x)

Q = tan¯¹ y

Q = tan¯¹ x

69. Let R = {(3,3), (6,6), (9,9), (12,12), (6,12), (3,9), (3,12), (3,6)} be a relation on the set A = {3,6,9,12}. The relation is

An equivalence relation

Reflexive only

Reflexive and transitive

Reflexive and symmetric only

70. To draw general conclusions form a limited number of observation or experiences is called

Deduction

Proposition

Induction

Knowledge

71. The extraction of cube root of a give number is a

Relation

Binary operation

Relation in some set

Unary operation

72. Which of the following is not monoid w.r.t addition?

73. A function in which the second elements of the order pairs are distinct is called

Onto function

Identity function

Inverse function

One-one function

74. A ⊆ B means

A is a superset of B

A is equal to B

A is equivalent to B

A is a subset of B

75. In (x + iy) x is the known as

Complex number

None of these

Imaginary part of complex number

Real part of complex number

Page 4 of 8

76. Given X, Y are any two sets such that number of elements in X = 28, number of elements in set Y = 28, and number of elements in set X U Y = 54, then number of elements in set x∩Y =

77. For any three sets, xy and Z, x ⋂ (y U z) = ?

x ⋂ (y ⋂ z)

(x U y) ⋂ (x U z)

(x ⋂ y) U (x ⋂ z)

(x U y) ⋂ (x ⋂ z)

78. The set of complex numbers forms

Commutative group w.r.t addition

Commutative group w.r.t multiplication

Non commutative group w.r.t addition

Commutative group w.r.t division

79. The identity element of N, w-r-t + is

None

80. The equation [x + 4] = x has solution

x = 4

x = 2

x = -2

x = -4

81. The multiplicative inverse of – 1 in the set {1-,1} is

±1

-1

82. 3/2 is

A positive integer

Whole number

A rational number

An irrational number

83. The square root function is defined by the equation

Y = ± √x, x < 0

Y = ± √x, x ≥ 0

Y = √x, x < 0

Y = √x, x ≥ 0

84. 1/3 is a decimal.

Non-terminating

Terminating

None of these

Recurring

85. a.a¯¹ = a¯¹.a = 1 is a

Multiplicative identity

Multiplicative inverse

Commutative law of multiplication

Associative law of multiplication

86. The function f {(z,y)ly = ax² + bx + c} is

Quadratic function

Onto function

Constant function

One-one function

87. The set (Z, +) forms a group

Forms a group w.r.t multiplication

Doesn’t form a group

Forms a group w.r.t addition

Non commutative group w.r.t multiplication

88. If z₁ = 2 + 6i and z₂ = 3 + 7i, then which expression defines the product of z₁ and z₂?

-36 + 32i

0, +(-12)i

6+(-11)i

36 + (-32)i

89. Power set of X i.e P(X) ………… under the binary operation of union U

Infinite set although X is infinite

Forms a group

Has no identity element

Does not from a group

90. Multiplicative inverse of 0 is

±1

Does not exist

91. Given X, Y are any two sets such that number of elements in X = 18, number of elements in set Y = 24, and number of elements in set X U Y = 40, then number of elements in set x∩Y =

92. Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball, of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is.

216

120

160

240

93. The multiplicative inverse of x ≠ 0 is

-x

1/x

0.5 x

94. What is the conjugate of -6-i?

-6+i

-6-i

6-i

6+i

95. (7, 9) + (3, -5) =

(10, 4)

(4, 4)

(7, 3)

(9, -5)

96. The inverse of A → B is

A’ → B’

B’ → A’

A → B’

B → A

97. The negation of a given number is a

Relation in some set

Uniary operation

Binary operation

Relation

98. Deductive logic in which every statement is regarded as true or false and there is scope for a third or fourth possibility is called

Deduction

Proposition

Aristotelian logic

Non-Aristotelian logic

99. (a + bi) – (c + di) =

(a – c) + (b – d) i

(a + b) = (c + d)

(a + c) + I (b + d)

(a – c) + (c – d)i

100. If z₁ = √-36, z₂ = √-25, z₃ = √-16, then what is the sum of z₁, z₂ and z₃?

15i

-15

-15i

Page 5 of 8

101. The set {1, -1, I, -i} is group w.r.t

–

102. φ set is the __________ of all sets?

Intersection

Subset

Universal

Union

103. The set (Q, .)

Contains no multiplicative identity

Does not form a group

Contains no additive identity

Forms a group

104. 6 is

An irrational number

A rational number

A prime integer

An odd integer

105. The set of real numbers R is a subset of

The set of inters Z

The set of even integers E

The set of natural Numbers N

The set of complex number C

106. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

Closure property of addition

Additive inverse

Associative property w.r.t. to addition

Commutative property of addition

107. zz = ________

|z|

|z|²

None of these

108. If z = 1/Z, then

None of these

z is real

z is purely imaginary

z is any complex number

109. The set of the first elements of the orders pairs forming a relation is called its:

Range

Relation in A

Relation in B

Domain

110. Geometrically, the modulus of a complex number represents its distance from the

Point (1, 1)

Point (0, 1)

Point (1, 0)

Point (0, 0)

111. √-1 b =

None of these

112. The complement of set A relative to universal set U is the set

A – U

{x / x ϵ A ʌ x ϵ U}

{x / x ∉ A ʌ x ϵ U}

{x / x ϵ A and x ∉ U}

113. √23 is

A factor of 36

A irrational number

A rational number

An even integer

114. 202.04 is an example of

Recurring decimals

Non-recurring decimals

Terminating decimals

None of these

115. Which element is the additive inverse of (a, b) in Complex numbers?

(a, 0)

(a, b)

(0, b)

(-a, -b)

116. ∀ a, b ϵ ℜ, ab = be is a

Closure law of multiplication

Associative law of multiplication

Multiplicative Identity

Commutative law of multiplication

117. The solution set of the equation [3x + 2] = 5 is

{-7/3}

{1, - 7/3}

{1}

118. The conjugate of √5 i is

√5

-√5 i

119. If a function ƒ : A → B is such that Ran ƒ ≠ B then ƒ is a/an?

Surjective

Into function

Onto function

None of these

120. The multiplicative inverse of – 1 in the set {1 –, 1} is

– 1

± 1

121. The set of complex numbers forms a group under the binary operation of

Subtraction

Multiplication

Addition

Division

122. A semi group is monoid if

It has inverse property

It is closed

It has identify

It holds associative property

123. Which of the following is true?

a ϵ {{a}}

{a} ⊆ {{a}}

{1,2} = {2,1}

a ⊆ {a}

124. a > b ⇒ a + c > b + c is known as

Trichotomy property

Multiplicative property

Transitive property

Additive property of inequality

125. Multiplicative inverse of “1” is

{0, 1}

Page 6 of 8

126. The value of i⁴ᶜ¯¹

-1

i²

127. {x : x ϵ Z⁺ and x < 1} is

None of these

Singleton Set

A set with two points

Empty set

128. The number of proper subsets of the set {1, 2, 3} is:

129. P : Islamabad is a capital of Pakistan q : Lahore is not a city of Pakistan. The disjunction p v q is

Unknown

True

Not valid

False

130. The symbol of irrational is

Q’

131. If A is any set, then

A∪A’=φ

A∪A’= U

A∩A’=U

A∩A’=U’

132. The graph of a quadratic function is

Circle

Parabola

Triangle

Straight line

133. {x|x ϵ N, x ≤ 10} is the

Non – descriptive method

Set builder method

Tubular method

Descriptive method

134. If A ⊆ B then A U B is

A ∩ B

A’

135. A U A’ = ?

A U φ

A U (A – x)

A ⋂ x

A U (x – A)

136. The identity element with respect to subtraction is

Does not exist

-1

137. A function whose range consists of just on element is called

Onto function

Identify function

One – One function

Constant function

138. Total number of subsets that can be formed out of the set {a, b, c} is

139. a/b/c/d = ad/bc is known as

Golden rule of Fraction

Principle for equality of fraction

Rule for product of fractions

Rule of quotient of fraction

140. If ∀ a, b ϵ ℜ, then a + b ϵ ℜ is a property.

Closure law of addition

Additive Identity

Associative law of addition

Additive inverse

141. i¹⁰¹ =

i²

-i

-1

142. P : Islamabad is a capital of Pakistan
Q : Lahore is not a city of Pakistan, the conjunction p ʌ q is

False

True

Unknown

Not valid

143. To each element of a group there correspond how many inverse element

Two

More than one

At least one

Only one

144. What is the conjugate of – 7 – 2i?

–7 + 2i

√53

7 -2i

7 + 2i

145. If E = {1,2,3,4} and F = {1,2}, then the number of onto functions from E to F is

146. For a ϵ A, b ϵ B, r = {(a, b)} is a

Relation from A to B

Relation in A

Relation from B to A

Relation in B

147. If – P is true, then p is

Equivalent to p

True

Has no information

False

148. The statement that a group can have more than one identity elements” is

True

Ambiguous

False

Some times true

149. In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The student enrolled for English cannot attend any other class, but the students of mathematics and physic can take two courses at a time. Find the number of students who have taken both physics and mathematics.

150. The value of x, and y, when (x + iy)² = 5 + 4i

X = -2, y = 1

X = 2, y = 2

X = 2, y = -i

X = 2, y = 1

Page 7 of 8

151. If p is any proposition and ~ p is its negation then truth table is

p P T F F T

p P T F F F

p P T F T F

p P T F F T

152. The set (Z, +) forms a group

Non commutative group w.r.t multiplication

Doesn’t form a group

Forms a group w.r.t addition

Forms a group w.r.t multiplication

153. The set {{a, b}} is

Infinite set

Empty set

Singleton set

Two point set

154. An element e ϵ A is said to be the identity element with respect to a binary operation * on A if for all a ϵ A

e*a = a*e = e

e*a = a*e ≡ 0

e*a = a*e = 0

e*a = a*e = a

155. The set of the second elements of the ordered pairs forming

Range

Domain

Relation in A

Relation in B

156. The set {1, -1, i, -i}

Does not form a group w.r.t multiplication

Form a group w.r.t addition

Not closed under multiplication

Form a group w.r.t multiplication

157. If A and B are overlapping sets, then

A ⋂ B = φ

A = B

A U B = φ

A ⋂ B ≠ φ

158. The inverse of a binary relation r is a binary relation

{(b,a)|a = b}

{(b,a)|(a,b) r}

{(b,a)|(a,b)ϵ r}

{(b,a)|(b,a)ϵ r}

159. The set (Q, .)

Contains no additive inverse

Does not form a group

Forms a group

Contains no additive identity

160. The set R is …….. w.r.t subtraction

Non commutative group

A group

No conclusion drawn

Not a group

161. The set of students of your class is

Finite set

Infinite set

Empty set

Null set

162. Circumference of any circle/length of its diameter =

163. (a, b) + (-a, -b) =

(-a, -b)

(0, 0)

(a, b)

(1, 1)

164. The complement of set A relative to universal set U is the set

{x/x ∉ A ʌ ϵ U}

A \ U

{x/x ϵ Aʌ x ϵ U}

{x/x ϵ A and x ∉ U}

165. If Z₁ = 1 + i, Z₂ = 2 + 3i then |Z₂ – Z₁| = ?

–2–i

√7

√3 i

√5

166. A conditional is regarded as false only when the antecedent is true and consequent is

Unknown

True

False

Known

167. If A ∩ B = B, then.

B ⊂ A

A = ø

B = ø

A ⊂ B

168. √25 is a number

Odd

Natural

Irrational

Rational

169. The graph of a linear function represents

Straight line

Parabola

Triangle

Circle

170. The multiplicative inverse of -3i is

1/3 i

- 1/3 i

-3i

171. The polar form of complex number x ≠ I y =

r cos θ + r sin θ

r cos θ + is sin θ

i cos θ + i sin θ

cos θ + r sin θ

172. If the number of elements in a set S are 5. Then the number of elements of the power set P(S) are

173. If a function f: A → B is such that Ran f = B then f is a/an?

None of these

Into function

Onto function

Injective

174. π/3 is

A negate integer

An irrational number

A natural number

A positive integer

175. In set builder notation the set {0, 1, 2, ……….., 100} can be written as

The set of first 100 whole numbers

{x/x ϵ N ʌ x ≤ 100}

{x/x ϵ Z ʌ x ≤ s 100}

{x/x ϵ W ʌ x < 101}

Page 8 of 8

176. The set A is

Proper subset of A

Improper subset of A

Not a superset of A

Not a subset of A

177. The function {(x,y)|y = ½ x²} is

None of these

One – One

Onto

Constant

178. (A ∩ B)ᶜ =

A ∩ B

Aᶜ U Bᶜ

(A U B)ᶜ

179. If A, B, C be three sets such that A U B = A U C and A ∩ B = A ∩ C, then

A = B = C

A = B

B = C

A = C

180. The set {1, 2, 3, 4, ……..} is called

Set of irrational numbers

Set of rational numbers

Set of whole numbers

Set of Natural numbers

181. √2 is a number.

Rational

Even

Irrational

Odd

182. A disjunction of tow statements p and q is true if

Both p and q are false

One of p and q is true

Q is false

P is false

183. a > b, b > c ⇒ a > is a

Trichotomy property

Additive property

Transitive property of inequality

Multiplicative property

184. The set of the first elements of the ordered pairs forming a relation is called its

Function on B

A into B

Domain

Range

185. √-1b = ?

b²

-i b

b i

i√b

186. If Z = (1,2), then Z¯¹ = ?

(0.2, -0.4)

(-0.2, -0.4)

(0.2, 0.4)

(-0.2, 0.4)

187. The number of subsets of a set of 4 elements

188. {x:x ϵ Z⁺ and x <-1} is

A set with three points

Singleton set

A set with two points

Empty set

189. A set containing only one element is called the

Singleton set

Empty set

Solution set

Null set

190. A subset of B x A is called a

Relation from B to A

Relation of A to B

Relation in B

Relation in A

191. A function whose range is just one element is called

Identity function

One-one function

Constant function

Onto function

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Maan AliLast Updated: October 15, 2025

14 Comments

Altaf Hussain says:

October 14, 2022 at 9:07 am

Work hard

Muhammad Ali says:

July 30, 2022 at 1:26 pm

I got full marks
Yes

Aqib says:

July 4, 2022 at 1:08 pm

Plz add the solution of mcqs

Abbas says:

September 25, 2021 at 7:58 pm

System are not working

Abbas says:

September 25, 2021 at 7:56 pm

Test start nahi ho raha

Hamza says:

September 6, 2020 at 5:16 pm

Many of the questions in this are wrong

Masood meddi says:

July 29, 2020 at 11:09 pm

Could you please provide a solution

Asif Iqbal says:

July 16, 2020 at 12:04 pm

I have got 88%

saher says:

July 9, 2020 at 3:09 pm

i just wrong 1 its too easy

M.Arslan says:

December 8, 2018 at 5:05 pm

I got only 6 right

HUSNAIN says:

July 31, 2017 at 12:19 pm

I WANT TO ASKED YOU
IS YOUR ANSWER IS TRUE

Sadia Javed says:

July 13, 2017 at 12:24 pm

Plz add the solutions of the msqs……

umair ahmed says:

March 19, 2017 at 2:01 pm

nice but so easy i got 96%

Syed Rehan says:

July 29, 2016 at 11:11 am

100 %

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Maan Ali

14 Comments

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