ECAT Mathematics Sets Functions and Groups Online Test

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

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

3. Multiplicative inverse of “1” is

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

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

6. (a + bi) – (c + di) =

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

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

9. The set {-1, 1} is

10. The set of complex numbers forms

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

12. The function {(x,y)|y = ½ x²} is

13. 202.04 is an example of

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

15. Additive inverse of – a – b is

16. The conjugate of √5 i is

17. The identity element with respect to subtraction is

18. If A is any set, then

19. i¹⁰¹ =

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

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

22. π/3 is

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

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

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

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

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

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

29. Associative law of multiplication

30. A semi group is monoid if

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

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

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

34. √2 is a number.

35. a > b ⇒ a + c > b + c is known as

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

37. φ set is the __________ of all sets?

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

39. (a¯¹)¯¹ =

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

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

42. QUQ’ =

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

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

45. If A ⊆ B then A U B is

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

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

48. The graph of a linear function represents

49. The multiplicative inverse of 1 – 2i is

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

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

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

53. If z = 1/Z, then

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

55. 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 =

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

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

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

59. The multiplicative inverse of x ≠ 0 is

60. Which of the following is true?

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

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

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

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

65. The square root of 2i – 20i is

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

67. The negation of a given number is a

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

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

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

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

72. The graph of a quadratic function is

73. Multiplicative inverse of 0 is

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

75. √25 is a number

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

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

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

79. A _________ is an ordered collection of objects.

80. A U A’ = ?

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

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

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

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

85. √23 is

86. {x:x ϵ Z⁺ and x <-1} is

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

88. 6 is

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

90. 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.

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

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

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

94. The set A is

95. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

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

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

99. The set (Q, .)

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

101. (A ∩ B)ᶜ =

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

103. The graph of a quadratic function is

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

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

106. If x ϵ R, then x² + x + 1 is

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

108. The set of integer is

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

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

111. zz = ________

112. If A ∩ B = B, then.

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

114. ∀ a, b ϵ ℜ, ab = be is a

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

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

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

118. 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

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

120. If A and B are overlapping sets, then

121. The set (Q, .)

122. √-1b = ?

123. The value of i⁴ᶜ¯¹

124. Decimal part of irrational number is

125. 0 (zero) is

126. The inverse of A → B is

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

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

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

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

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

132. The multiplicative inverse of -3i is

133. The symbol of irrational is

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

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

136. The set of all positive even integers is

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

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

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

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

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

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

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

144. A subset of B x A is called a

145. i³ =

146. 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

147. (7, 9) + (3, -5) =

148. √–81 – √–36 = ?

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

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

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

152. A set containing only one element is called the

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

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

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

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

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

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

159. a > b, b > c ⇒ a > is a

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

161. If Z = (1,2), then Z¯¹ = ?

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

163. In polar form of complex number

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

165. 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

166. Multiplicative inverse of “1” is

167. The set of students of your class is

168. 3/2 is

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

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

171. For any set B, BUB’ is

172. 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 =

173. 1/3 is a decimal.

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

175. √-1 b =

176. a.a¯¹ = a¯¹.a = 1 is a

177. A ⊆ B means

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

179. The square root function is defined by the equation

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

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

182. {x|x ϵ N, x ≤ 10} is the

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

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

185. 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.

186. {x : x ϵ Z⁺ and x < 1} is

187. If – P is true, then p is

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

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

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

191. 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.