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ECAT Mathematics Sets Functions and Groups Online Test

Maan AliLast Updated: April 18, 2025

Mathematics Sets Functions and Groups MCQS Online Test

ECAT Math Sets Functions and Groups Chapter Online 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 MCQS Online Test

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Page 1 of 8

Math

1. If x ϵ R, then x² + x + 1 is

ϵ [3/4, ∞]

(1, ∞)

Negative

Positive

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

Does not exist

1/x

-x

3. 1/3 is a decimal.

Non-terminating

Recurring

Terminating

None of these

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

{0}

{φ}

{1, 2, 3}

5. √–81 – √–36 = ?

√15i

√3i

√117i

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

Range

Domain

Relation in A

Relation in B

7. Additive inverse of – a – b is

– a + b

a + b

a – b

8. If A and B are overlapping sets, then

A ⋂ B = φ

A U B = φ

A = B

A ⋂ B ≠ φ

9. √-1 b =

None of these

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

A ≠ B

B = C

A = B

A ≠ C

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

(0, 0)

(0, ac)

(a, c)

(ac, 0)

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

Point (1, 0)

Point (1, 1)

Point (0, 1)

Point (0, 0)

13. {x|x ϵ N, x ≤ 10} is the

Descriptive method

Set builder method

Tubular method

Non – descriptive method

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

Division

Subtraction

Multiplication

Addition

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

Onto function

Identity function

Inverse function

One-one function

16. For any set B, BUB’ is

Is set B

Universal Set

Set B’

17. i¹⁰¹ =

-i

-1

i²

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

(0, 0)

(-a, -b)

(a, b)

(1, 1)

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

{c, a, f}

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

{0}

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

21. The set of complex numbers forms

Commutative group w.r.t multiplication

Non commutative group w.r.t addition

Commutative group w.r.t division

Commutative group w.r.t addition

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

Subtraction

Division

Addition

Multiplication

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

Addition

Subtraction

None of these

Multiplication

24. The set of all positive even integers is

A group w.r.t. multiplication

Not a group

A group w.r.t. subtraction

A group w.r.t. division

25. 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

Reflexive

Transitive

Not symmetric

Page 2 of 8

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

Additive inverse

Associative law of addition

Additive Identity

Closure law of addition

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

√53

–7 + 2i

7 + 2i

7 -2i

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

Empty set

Two point set

Singleton set

Infinite set

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

Rational Numbers

Set of whole number

Complex Numbers

Whole Numbers

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

P is true, q is true

P is true, q is false

None of these

P is false, q is true

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

Set of Natural numbers

Set of rational numbers

Set of irrational numbers

Set of whole numbers

32. √2 is a number.

Rational

Even

Odd

Irrational

33. The function {(x,y)|y = ½ x²} is

One – One

None of these

Constant

Onto

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

(a, 0)

(0, b)

(a, b)

(-a, -b)

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

-1

±1

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

x ⋂ (y ⋂ z)

(x ⋂ y) U (x ⋂ z)

(x U y) ⋂ (x U z)

(x U y) ⋂ (x ⋂ z)

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

Onto function

Identity function

Constant function

One-one function

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

Irrational numbers

Integers

Natural numbers

Rational numbers

39. The set A is

Proper subset of A

Not a superset of A

Not a subset of A

Improper subset of A

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

True

Some times true

False

Fallacious

41. The multiplicative inverse of -3i is

1/3 i

- 1/3 i

-3i

42. 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

240

120

160

43. The set (Q, .)

Contains no additive identity

Does not form a group

Forms a group

Contains no multiplicative identity

44. 6 is

An odd integer

An irrational number

A rational number

A prime integer

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

Additive inverse

Commutative law of addition

Additive Identity

Associative law of addition

46. A subset of B x A is called a

Relation in A

Relation from B to A

Relation of A to B

Relation in B

47. 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 =

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

√3 i

√5

–2–i

√7

49. The inverse of A → B is

A’ → B’

A → B’

B → A

B’ → A’

50. i³ =

-1

-i

Page 3 of 8

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

Only one

At least one

Two

More than one

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

{x/x ϵ A and x ∉ U}

A \ U

{x/x ϵ Aʌ x ϵ U}

{x/x ∉ A ʌ ϵ U}

53. A set containing only one element is called the

Empty set

Singleton set

Solution set

Null set

54. 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 = a

e*a = a*e = e

e*a = a*e = 0

e*a = a*e ≡ 0

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

± 1

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

b ⊆ B

B ϵ b

b ϵ B

b < B

57. The square root of 2i – 20i is

±(5 – 2i)

None of these

(5 – 2i)

±(5 + 2i)

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

Not valid

False

Unknown

True

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

-6+i

6+i

6-i

-6-i

60. zz = ________

|z|²

|z|

None of these

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

Onto function

Surjective

Into function

None of these

62. 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}

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

True

Not valid

Unknown

False

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

X = 2, y = 2

X = -2, y = 1

X = 2, y = -i

X = 2, y = -1

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

True

Not valid

False

Unknown

66. A U A’ = ?

A U (x – A)

A U (A – x)

A ⋂ x

A U φ

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

1 – 2i

3 – 2i

1 + 2i

– 3 – 2i

68. Multiplicative inverse of “1” is

{0, 1}

69. 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.

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

Rule of quotient of fraction

Principle for equality of fraction

Golden rule of Fraction

Rule for product of fractions

71. a/b = ka/kb , (k ≠ 0) is known as

Rule for product of fraction

Principle for equality of Fractions

Golden rule of fraction

Rule of quotient of Fraction

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

Injective

Onto function

None of these

Into function

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

Contingency

True

False

None of these

74. (A ∩ B)ᶜ =

Aᶜ U Bᶜ

A ∩ B

(A U B)ᶜ

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

The set of even integers E

The set of inters Z

The set of natural Numbers N

The set of complex number C

Page 4 of 8

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

{-4, 4}

Infinite set

-x

77. Which of the following is true?

{1,2} = {2,1}

a ⊆ {a}

a ϵ {{a}}

{a} ⊆ {{a}}

78. ∀ a, b ϵ ℜ, ab = be is a

Associative law of multiplication

Closure law of multiplication

Commutative law of multiplication

Multiplicative Identity

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

B = C

A ≠ B

A = B

A ≠ C

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

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

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

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

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

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

82. The identity element with respect to subtraction is

-1

Does not exist

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

-1

84. 0 (zero) is

An irrational number

A positive number

A negative integer

A rational number

85. The multiplicative inverse of x ≠ 0 is

-x

0.5 x

1/x

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

15i

-15i

-15

87. The set of students of your class is

Infinite set

Finite set

Null set

Empty set

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

Knowledge

Proposition

Induction

Deduction

89. QUQ’ =

ℜ

90. A ⊆ B means

A is equal to B

A is equivalent to B

A is a superset of B

A is a subset of B

91. The value of i⁴ᶜ¯¹

-1

i²

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

None

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

Forms a group w.r.t addition

Doesn’t form a group

Non commutative group w.r.t multiplication

Forms a group w.r.t multiplication

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

Transitive property

Trichotomy property of inequality

Additive property

None of these

95. (a + bi) – (c + di) =

(a – c) + (b – d) i

(a – c) + (c – d)i

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

(a + b) = (c + d)

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

{φ, {4}, {3}, {4,3}}

{φ, {3,4}}

{φ, {3}, {4}}

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

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

Not a group

A group

Non commutative group

No conclusion drawn

98. Multiplicative inverse of “1” is

± 1

∞

99. Decimal part of irrational number is

Repeating only

Repeating and terminating

Neither repeating nor terminating

Terminating

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

Page 5 of 8

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

-15

-15i

15i

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

–

103. φ set is the __________ of all sets?

Intersection

Universal

Union

Subset

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

True

False

Known

Unknown

105. 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 =

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

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

f (x) = f (–x)

f (x) = – f (– x)

f (x + 2) = f (x – 2)

f (2 + x) = f(2 – x)

108. In polar form of complex number

Q = tan¯¹ x

Q = tan¯¹ y

Q = tan¯¹ (y/x)

Q = tan¯¹ (x/y)

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

Both p and q are false

P is false

Q is false

One of p and q is true

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

Division

Addition

Multiplication

Both addition and multiplication

111. √-1b = ?

b²

-i b

i√b

b i

112. (7, 9) + (3, -5) =

(7, 3)

(9, -5)

(10, 4)

(4, 4)

113. The graph of a quadratic function is

Ellipse

Parabola

Circle

Hexagon

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

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

x = -4

x = -2

x = 4

x = 2

116. The set {-1, 1} is

Group under the multiplication

Contains no identity element

Group under addition

Does not form a group

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

Symmetric property

Transitive property

Cancellations property w.r.t. addition

Reflexive property

118. A _________ is an ordered collection of objects.

Set

Function

Proposition

Relation

119. If A ∩ B = B, then.

B = ø

A ⊂ B

B ⊂ A

A = ø

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

Forms a group w.r.t addition

Non commutative group w.r.t multiplication

Forms a group w.r.t multiplication

Doesn’t form a group

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

cos θ + r sin θ

r cos θ + r sin θ

r cos θ + is sin θ

i cos θ + i sin θ

122. The set (Q, .)

Contains no additive identity

Does not form a group

Contains no additive inverse

Forms a group

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

Range

Relation in A

Relation in B

Domain

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

Linear function

Constant function

Cubic function

Quadratic function

125. If Z = (1,2), then Z¯¹ = ?

(0.2, -0.4)

(0.2, 0.4)

(-0.2, 0.4)

(-0.2, -0.4)

Page 6 of 8

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

Identify function

One – One function

Onto function

Constant function

127. √25 is a number

Natural

Odd

Irrational

Rational

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

– 1

± 1

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

Q is false

Both p and q are false

One of p and q is true

P is false

130. 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

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

False

True

Unknown

Not valid

132. π/3 is

A natural number

A negate integer

A positive integer

An irrational number

133. 202.04 is an example of

Non-recurring decimals

None of these

Recurring decimals

Terminating decimals

134. √23 is

A factor of 36

A irrational number

An even integer

A rational number

135. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

Commutative property of addition

Closure property of addition

Additive inverse

Associative property w.r.t. to addition

136. The graph of a quadratic function is

Parabola

Circle

Triangle

Straight line

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

Commutative property

Additive inverse

Additive Identity

Additive property of inequality

138. Associative law of multiplication

(a + b) c = ac + bc

ab = ba

a(a + c) = ab + ac

a(bc) = (ab) c

139. If A is any set, then

A∩A’=U’

A∪A’=φ

A∩A’=U

A∪A’= U

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

-i

-1

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

Relation in some set

Relation

Unary operation

Binary operation

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

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

{(b,a)|a = b}

{(b,a)|(a,b)ϵ r}

{(b,a)|(b,a)ϵ r}

143. {x : x ϵ Z⁺ and x < 1} is

None of these

A set with two points

Singleton Set

Empty set

144. 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

Non-Aristotelian logic

Proposition

Aristotelian logic

145. 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.

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

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

0, +(-12)i

36 + (-32)i

6+(-11)i

-36 + 32i

148. 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

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

2.n

2ⁿ

n²

150. The set of integer is

A group w.r.t multiplication

Finite group

Not a group

A group w.r.t addition

Page 7 of 8

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

A into B

Domain

Range

Function on B

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

√5

-1-2i

√3

√7

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

Deduction

Induction

Proposition

Knowledge

154. The conjugate of √5 i is

-√5 i

√5

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

Infinite set

Two points set

Singleton set

None of these

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

Complex number

Imaginary part of complex number

Real part of complex number

None of these

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

True

Unknown

Not valid

False

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

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

Has no identity element

Does not from a group

Infinite set although X is infinite

Forms a group

160. The multiplicative inverse of 1 – 2i is

1/3 i

1/5 + 2/5 i

– 1/5 + 2/5 i

1/5 – 2/5 i

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

True

False

Some times true

Ambiguous

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

Additive property of inequality

Trichotomy property

Multiplicative property

Transitive property

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

One-one function

Onto function

Quadratic function

Constant function

164. If – P is true, then p is

True

False

Has no information

Equivalent to p

165. 3/2 is

Whole number

A positive integer

A rational number

An irrational number

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

Relation from B to A

Relation from A to B

Relation in B

Relation in A

167. If A ⊆ B then A U B is

A ∩ B

A’

168. (a¯¹)¯¹ =

None of these

a¯¹

-a

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

Transitive property

Symmetric property

Reflexive property

Cancellations property w.r.t. multiplication

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

171. a > b, b > c ⇒ a > is a

Additive property

Transitive property of inequality

Trichotomy property

Multiplicative property

172. The graph of a linear function represents

Straight line

Parabola

Triangle

Circle

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

X = 2, y = -i

X = 2, y = 1

X = 2, y = 2

X = -2, y = 1

174. {x:x ϵ Z⁺ and x <-1} is

Singleton set

A set with two points

A set with three points

Empty set

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

Two

Three

One

Page 8 of 8

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

p P T F F F

p P T F F T

p P T F T F

p P T F F T

177. If z = 1/Z, then

z is purely imaginary

None of these

z is any complex number

z is real

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

One

Zero

Three

Two

179. a.a¯¹ = a¯¹.a = 1 is a

Commutative law of multiplication

Multiplicative identity

Multiplicative inverse

Associative law of multiplication

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

Complex number

None of these

Real part

Imaginary part

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

Unknown

True

Not valid

False

182. 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

Reflexive only

Reflexive and symmetric only

An equivalence relation

Reflexive and transitive

183. The negation of a given number is a

Relation in some set

Relation

Uniary operation

Binary operation

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

185. Multiplicative inverse of 0 is

Does not exist

±1

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

{x/x ϵ Z ʌ x ≤ s 100}

{x/x ϵ W ʌ x < 101}

The set of first 100 whole numbers

{x/x ϵ N ʌ x ≤ 100}

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

Not closed under multiplication

Does not form a group w.r.t multiplication

Form a group w.r.t addition

Form a group w.r.t multiplication

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

Multiplication

Division

Subtraction

Addition

189. The symbol of irrational is

Q’

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

{1, - 7/3}

{1}

{-7/3}

191. A semi group is monoid if

It is closed

It has inverse property

It holds associative property

It has identify

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Maan AliLast Updated: April 18, 2025

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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 %

ECAT Mathematics Sets Functions and Groups Online Test

Mathematics Sets Functions and Groups MCQS Online Test

ECAT Math Sets Functions and Groups Chapter Online Test

Mathematics Sets Functions and Groups MCQS Online Test

Math

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Maan Ali

14 Comments

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