ECAT Mathematics Sets Functions and Groups Online Test

1. √–81 – √–36 = ?

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

3. i¹⁰¹ =

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

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

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

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

8. If Z = (1,2), then Z¯¹ = ?

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

10. 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

11. If A ⊆ B then A U B is

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

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

14. 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 =

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

16. A set containing only one element is called the

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

18. If x ϵ R, then x² + x + 1 is

19. φ set is the __________ of all sets?

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

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

22. In polar form of complex number

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

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

25. a.a¯¹ = a¯¹.a = 1 is a

26. i³ =

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

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

29. √2 is a number.

30. The set of complex numbers forms

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

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

33. If z = 1/Z, then

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

35. Decimal part of irrational number is

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

37. Multiplicative inverse of 0 is

38. 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 =

39. Additive inverse of – a – b is

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

41. For any set B, BUB’ is

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

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

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

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

46. {x : x ϵ Z⁺ and x < 1} is

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

48. {x|x ϵ N, x ≤ 10} is the

49. The set (Q, .)

50. If A and B are overlapping sets, then

51. The identity element with respect to subtraction is

52. 202.04 is an example of

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

54. The function {(x,y)|y = ½ x²} is

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

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

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

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

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

60. √25 is a number

61. (a + bi) – (c + di) =

62. The graph of a quadratic function is

63. The square root function is defined by the equation

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

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

66. Associative law of multiplication

67. {x:x ϵ Z⁺ and x <-1} is

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

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

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

71. The value of i⁴ᶜ¯¹

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

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

74. The multiplicative inverse of 1 – 2i is

75. The square root of 2i – 20i is

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

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

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

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

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

81. 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

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

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

84. The inverse of A → B is

85. The set of all positive even integers is

86. 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.

87. The graph of a linear function represents

88. The set of integer is

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

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

91. 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.

92. 6 is

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

94. Which of the following is true?

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

96. A _________ is an ordered collection of objects.

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

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

99. A ⊆ B means

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

101. 0 (zero) is

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

103. The set of students of your class is

104. The multiplicative inverse of x ≠ 0 is

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

106. A U A’ = ?

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

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

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

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

111. The set A is

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

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

114. π/3 is

115. Multiplicative inverse of “1” is

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

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

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

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

120. The conjugate of √5 i is

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

122. If – P is true, then p is

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

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

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

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

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

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

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

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

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

132. √-1 b =

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

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

135. 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

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

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

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

139. The set (Q, .)

140. (a¯¹)¯¹ =

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

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

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

144. Multiplicative inverse of “1” is

145. The negation of a given number is a

146. If A is any set, then

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

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

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

150. 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.

151. zz = ________

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

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

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

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

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

157. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

158. The symbol of irrational is

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

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

161. (A ∩ B)ᶜ =

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

163. A semi group is monoid if

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

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

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

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

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

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

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

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

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

173. If A ∩ B = B, then.

174. The multiplicative inverse of -3i is

175. √23 is

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

177. The set {-1, 1} is

178. A subset of B x A is called a

179. √-1b = ?

180. QUQ’ =

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

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

183. (7, 9) + (3, -5) =

184. 1/3 is a decimal.

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

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

187. ∀ a, b ϵ ℜ, ab = be is a

188. The graph of a quadratic function is

189. a > b, b > c ⇒ a > is a

190. 3/2 is

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