ECAT Mathematics Sets Functions and Groups Online Test

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

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

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

4. The function {(x,y)|y = ½ x²} is

5. A _________ is an ordered collection of objects.

6. The set A is

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

8. {x : x ϵ Z⁺ and x < 1} is

9. √–81 – √–36 = ?

10. (a + bi) – (c + di) =

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

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

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

14. √2 is a number.

15. Multiplicative inverse of “1” is

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

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

18. A semi group is monoid if

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

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

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

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

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

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

25. i³ =

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

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

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

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

30. Multiplicative inverse of 0 is

31. The square root function is defined by the equation

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

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

34. The multiplicative inverse of -3i is

35. In polar form of complex number

36. The set {-1, 1} is

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

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

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

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

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

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

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

44. 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

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

46. √23 is

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

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

49. a.a¯¹ = a¯¹.a = 1 is a

50. a > b, b > c ⇒ a > is a

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

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

53. A U A’ = ?

54. 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.

55. The value of i⁴ᶜ¯¹

56. ∀ a, b ϵ ℜ, ab = be is a

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

58. The identity element with respect to subtraction is

59. √-1 b =

60. 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 =

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

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

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

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

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

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

67. The graph of a linear function represents

68. 202.04 is an example of

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

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

71. a/b = ka/kb , (k ≠ 0) is known as

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

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

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

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

76. i¹⁰¹ =

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

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

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

80. The multiplicative inverse of x ≠ 0 is

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

82. 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

83. 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

84. If A is any set, then

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

86. The graph of a quadratic function is

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

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

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

90. If Z = (1,2), then Z¯¹ = ?

91. Multiplicative inverse of “1” is

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

93. If A ⊆ B then A U B is

94. A ⊆ B means

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

96. √25 is a number

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

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

99. zz = ________

100. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

101. The square root of 2i – 20i is

102. A set containing only one element is called the

103. The set (Q, .)

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

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

106. 1/3 is a decimal.

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

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

109. φ set is the __________ of all sets?

110. The set (Q, .)

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

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

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

114. (A ∩ B)ᶜ =

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

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

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

118. If A and B are overlapping sets, then

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

120. The set of integer is

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

122. The graph of a quadratic function is

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

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

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

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

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

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

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

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

131. Which of the following is true?

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

133. {x:x ϵ Z⁺ and x <-1} is

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

135. √-1b = ?

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

137. The conjugate of √5 i is

138. If – P is true, then p is

139. 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 =

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

141. If z = 1/Z, then

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

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

144. A subset of B x A is called a

145. {x|x ϵ N, x ≤ 10} is the

146. The symbol of irrational is

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

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

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

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

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

152. QUQ’ =

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

154. Associative law of multiplication

155. π/3 is

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

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

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

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

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

161. The set of students of your class is

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

163. 6 is

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

165. The set of complex numbers forms

166. 3/2 is

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

168. The negation of a given number is a

169. Decimal part of irrational number is

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

171. Additive inverse of – a – b is

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

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

174. 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.

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

176. The multiplicative inverse of 1 – 2i is

177. If x ϵ R, then x² + x + 1 is

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

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

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

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

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

183. If A ∩ B = B, then.

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

185. The inverse of A → B is

186. (a¯¹)¯¹ =

187. 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.

188. 0 (zero) is

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

190. For any set B, BUB’ is

191. The set of all positive even integers is