ECAT Mathematics Sets Functions and Groups Online Test

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

2. 3/2 is

3. (A ∩ B)ᶜ =

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

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

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

7. a > b, b > c ⇒ a > is a

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

9. √23 is

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

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

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

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

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

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

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

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

18. 1/3 is a decimal.

19. 202.04 is an example of

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

21. A set containing only one element is called the

22. Decimal part of irrational number is

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

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

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

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

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

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

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

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

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

32. A U A’ = ?

33. (7, 9) + (3, -5) =

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

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

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

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

38. i¹⁰¹ =

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

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

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

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

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

44. The set A is

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

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

47. The value of i⁴ᶜ¯¹

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

49. If – P is true, then p is

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

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

52. 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

53. 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 =

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

55. If z = 1/Z, then

56. {x : x ϵ Z⁺ and x < 1} is

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

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

59. 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

60. The identity element with respect to subtraction is

61. The multiplicative inverse of 1 – 2i is

62. Multiplicative inverse of “1” is

63. If A ∩ B = B, then.

64. If A and B are overlapping sets, then

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

66. In polar form of complex number

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

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

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

70. The set of complex numbers forms

71. a.a¯¹ = a¯¹.a = 1 is a

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

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

74. If Z = (1,2), then Z¯¹ = ?

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

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

77. The set {-1, 1} is

78. √-1 b =

79. (a + bi) – (c + di) =

80. π/3 is

81. √2 is a number.

82. 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

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

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

85. QUQ’ =

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

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

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

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

90. If A is any set, then

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

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

93. 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.

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

95. ∀ a, b ϵ ℜ, ab = be is a

96. √-1b = ?

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

98. 0 (zero) is

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

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

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

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

103. 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 =

104. 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.

105. The square root function is defined by the equation

106. a/b = ka/kb , (k ≠ 0) is known as

107. A ⊆ B means

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

109. Which of the following is true?

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

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

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

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

114. i³ =

115. Multiplicative inverse of 0 is

116. {x|x ϵ N, x ≤ 10} is the

117. Multiplicative inverse of “1” is

118. (a¯¹)¯¹ =

119. {x:x ϵ Z⁺ and x <-1} is

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

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

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

123. The conjugate of √5 i is

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

125. The negation of a given number is a

126. The set (Q, .)

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

128. If A ⊆ B then A U B is

129. A _________ is an ordered collection of objects.

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

131. The function {(x,y)|y = ½ x²} is

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

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

134. The set (Q, .)

135. 6 is

136. √25 is a number

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

138. The graph of a linear function represents

139. The multiplicative inverse of -3i is

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

141. For any set B, BUB’ is

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

143. The graph of a quadratic function is

144. Associative law of multiplication

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

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

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

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

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

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

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

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

153. The set of integer is

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

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

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

157. The graph of a quadratic function is

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

159. The square root of 2i – 20i is

160. The inverse of A → B is

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

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

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

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

165. The set of students of your class is

166. 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.

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

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

169. √–81 – √–36 = ?

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

171. The set of all positive even integers is

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

173. If x ϵ R, then x² + x + 1 is

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

175. Additive inverse of – a – b is

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

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

178. A subset of B x A is called a

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

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

181. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

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

184. The symbol of irrational is

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

186. A semi group is monoid if

187. zz = ________

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

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

190. φ set is the __________ of all sets?

191. The multiplicative inverse of x ≠ 0 is