ECAT Mathematics Sets Functions and Groups Online Test

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

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

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

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

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

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

7. The negation of a given number is a

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

9. √25 is a number

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

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

12. A _________ is an ordered collection of objects.

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

14. The square root function is defined by the equation

15. The graph of a quadratic function is

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

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

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

19. (7, 9) + (3, -5) =

20. 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 =

21. The symbol of irrational is

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

23. {x:x ϵ Z⁺ and x <-1} is

24. A subset of B x A is called a

25. If A is any set, then

26. ∀ a, b ϵ ℜ, ab = be is a

27. π/3 is

28. 3/2 is

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

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

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

32. For any set B, BUB’ is

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

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

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

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

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

38. 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

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

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

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

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

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

44. {x : x ϵ Z⁺ and x < 1} is

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

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

47. The inverse of A → B is

48. A U A’ = ?

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

50. Associative law of multiplication

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

52. (a¯¹)¯¹ =

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

54. If z = 1/Z, then

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

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

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

58. 0 (zero) is

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

60. The conjugate of √5 i is

61. Multiplicative inverse of 0 is

62. √23 is

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

64. (A ∩ B)ᶜ =

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

66. The set of all positive even integers is

67. √2 is a number.

68. The set (Q, .)

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

70. Which of the following is true?

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

72. Multiplicative inverse of “1” is

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

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

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

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

77. 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.

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

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

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

81. Decimal part of irrational number is

82. The set of integer is

83. 6 is

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

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

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

87. In polar form of complex number

88. If x ϵ R, then x² + x + 1 is

89. If – P is true, then p is

90. The function {(x,y)|y = ½ x²} is

91. 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

92. A set containing only one element is called the

93. i¹⁰¹ =

94. QUQ’ =

95. If A ∩ B = B, then.

96. The set (Q, .)

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

98. If Z = (1,2), then Z¯¹ = ?

99. The graph of a quadratic function is

100. The value of i⁴ᶜ¯¹

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

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

103. If A and B are overlapping sets, then

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

105. 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 =

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

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

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

109. The graph of a linear function represents

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

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

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

113. Multiplicative inverse of “1” is

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

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

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

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

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

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

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

121. If A ⊆ B then A U B is

122. Additive inverse of – a – b is

123. The set A is

124. √–81 – √–36 = ?

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

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

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

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

129. The set of complex numbers forms

130. 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.

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

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

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

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

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

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

137. The multiplicative inverse of x ≠ 0 is

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

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

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

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

142. a > b, b > c ⇒ a > is a

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

144. {x|x ϵ N, x ≤ 10} is the

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

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

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

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

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

150. √-1 b =

151. A ⊆ B means

152. The set {-1, 1} is

153. 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.

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

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

156. φ set is the __________ of all sets?

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

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

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

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

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

162. The multiplicative inverse of 1 – 2i is

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

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

165. a.a¯¹ = a¯¹.a = 1 is a

166. A semi group is monoid if

167. 1/3 is a decimal.

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

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

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

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

172. √-1b = ?

173. The square root of 2i – 20i is

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

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

176. i³ =

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

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

179. 202.04 is an example of

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

181. The identity element with respect to subtraction is

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

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

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

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

186. The multiplicative inverse of -3i is

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

188. 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

189. zz = ________

190. (a + bi) – (c + di) =

191. The set of students of your class is