ECAT Mathematics Sets Functions and Groups Online Test

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

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

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

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

5. 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

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

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

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

9. The graph of a linear function represents

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

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

12. 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 =

13. A ⊆ B means

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

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

16. A _________ is an ordered collection of objects.

17. If z = 1/Z, then

18. If A and B are overlapping sets, then

19. (a + bi) – (c + di) =

20. A U A’ = ?

21. √25 is a number

22. For any set B, BUB’ is

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

24. In polar form of complex number

25. 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.

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

27. The set of all positive even integers is

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

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

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

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

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

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

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

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

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

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

38. Decimal part of irrational number is

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

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

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

42. The inverse of A → B is

43. The multiplicative inverse of -3i is

44. (a¯¹)¯¹ =

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

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

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

48. If x ϵ R, then x² + x + 1 is

49. 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.

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

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

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

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

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

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

56. The set of complex numbers forms

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

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

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

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

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

62. The negation of a given number is a

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

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

65. 6 is

66. (7, 9) + (3, -5) =

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

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

69. {x|x ϵ N, x ≤ 10} is the

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

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

72. √23 is

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

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

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

76. Multiplicative inverse of “1” is

77. If Z = (1,2), then Z¯¹ = ?

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

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

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

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

82. The set (Q, .)

83. The symbol of irrational is

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

85. 0 (zero) is

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

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

88. If A ∩ B = B, then.

89. 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

90. A subset of B x A is called a

91. a > b, b > c ⇒ a > is a

92. i¹⁰¹ =

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

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

95. Multiplicative inverse of “1” is

96. a/b = ka/kb , (k ≠ 0) is known as

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

98. The set of students of your class is

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

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

101. The multiplicative inverse of 1 – 2i is

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

103. √–81 – √–36 = ?

104. π/3 is

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

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

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

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

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

110. 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

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

112. i³ =

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

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

115. The square root function is defined by the equation

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

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

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

119. The multiplicative inverse of x ≠ 0 is

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

121. √2 is a number.

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

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

124. If A is any set, then

125. φ set is the __________ of all sets?

126. Additive inverse of – a – b is

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

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

129. The set {-1, 1} is

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

131. √-1 b =

132. Associative law of multiplication

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

134. The square root of 2i – 20i is

135. Which of the following is true?

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

137. (A ∩ B)ᶜ =

138. If A ⊆ B then A U B is

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

140. If – P is true, then p is

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

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

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

144. {x : x ϵ Z⁺ and x < 1} is

145. A semi group is monoid if

146. Multiplicative inverse of 0 is

147. {x:x ϵ Z⁺ and x <-1} is

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

149. 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.

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

151. The conjugate of √5 i is

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

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

154. 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 =

155. The graph of a quadratic function is

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

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

158. QUQ’ =

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

160. The value of i⁴ᶜ¯¹

161. The set of integer is

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

163. √-1b = ?

164. ∀ a, b ϵ ℜ, ab = be is a

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

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

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

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

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

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

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

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

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

174. a.a¯¹ = a¯¹.a = 1 is a

175. The set (Q, .)

176. The set A is

177. The function {(x,y)|y = ½ x²} is

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

179. zz = ________

180. The identity element with respect to subtraction is

181. The graph of a quadratic function is

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

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

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

185. A set containing only one element is called the

186. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

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

189. 1/3 is a decimal.

190. 202.04 is an example of

191. 3/2 is