ECAT Mathematics Sets Functions and Groups Online Test

1. The identity element with respect to subtraction is

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

3. The graph of a linear function represents

4. Which of the following is true?

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

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

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

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

9. π/3 is

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

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

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

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

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

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

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

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

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

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

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

21. 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

22. QUQ’ =

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

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

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

26. 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 =

27. If Z = (1,2), then Z¯¹ = ?

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

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

30. The multiplicative inverse of x ≠ 0 is

31. If – P is true, then p is

32. i¹⁰¹ =

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

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

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

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

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

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

39. 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

40. The graph of a quadratic function is

41. The function {(x,y)|y = ½ x²} is

42. A ⊆ B means

43. (7, 9) + (3, -5) =

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

45. ∀ a, b ϵ ℜ, ab = be is a

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

47. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

49. The negation of a given number is a

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

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

52. zz = ________

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

54. 1/3 is a decimal.

55. A subset of B x A is called a

56. The value of i⁴ᶜ¯¹

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

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

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

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

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

62. A U A’ = ?

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

64. The graph of a quadratic function is

65. In polar form of complex number

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

67. φ set is the __________ of all sets?

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

69. The set of complex numbers forms

70. If x ϵ R, then x² + x + 1 is

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

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

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

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

75. Decimal part of irrational number is

76. The inverse of A → B is

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

78. The square root of 2i – 20i is

79. (A ∩ B)ᶜ =

80. Multiplicative inverse of “1” is

81. a.a¯¹ = a¯¹.a = 1 is a

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

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

84. √25 is a number

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

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

87. The set of integer is

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

89. For any set B, BUB’ is

90. The set (Q, .)

91. √2 is a number.

92. The multiplicative inverse of 1 – 2i is

93. (a¯¹)¯¹ =

94. A _________ is an ordered collection of objects.

95. The set {-1, 1} is

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

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

98. a > b, b > c ⇒ a > is a

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

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

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

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

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

104. If A is any set, then

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

106. The square root function is defined by the equation

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

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

109. If A and B are overlapping sets, then

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

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

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

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

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

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

116. If A ⊆ B then A U B is

117. Additive inverse of – a – b is

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

119. Multiplicative inverse of 0 is

120. 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.

121. {x|x ϵ N, x ≤ 10} is the

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

123. The set of all positive even integers is

124. 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.

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

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

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

128. If z = 1/Z, then

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

130. √–81 – √–36 = ?

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

132. √-1 b =

133. Multiplicative inverse of “1” is

134. If A ∩ B = B, then.

135. 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 =

136. √23 is

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

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

139. {x:x ϵ Z⁺ and x <-1} is

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

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

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

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

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

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

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. The set (Z, +) forms a group

148. The multiplicative inverse of -3i is

149. The set of students of your class is

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

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

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

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

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

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

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

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

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

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

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

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

162. i³ =

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

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

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

166. The symbol of irrational is

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

168. Associative law of multiplication

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

170. A set containing only one element is called the

171. (a + bi) – (c + di) =

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. 6 is

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

175. 3/2 is

176. The set (Q, .)

177. 202.04 is an example of

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

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

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

181. {x : x ϵ Z⁺ and x < 1} is

182. The set A is

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

184. √-1b = ?

185. 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.

186. 0 (zero) is

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

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

189. The conjugate of √5 i is

190. A semi group is monoid if

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