Mathematics Sets Functions and Groups Online Test

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

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

3. Additive inverse of – a – b is

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

5. Decimal part of irrational number is

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

7. {x:x ϵ Z⁺ and x <-1} is

8. √23 is

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

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

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

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

13. √25 is a number

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

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

16. The inverse of A → B is

17. 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.

18. 6 is

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

20. If A and B are overlapping sets, then

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

22. The value of i⁴ᶜ¯¹

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

24. φ set is the __________ of all sets?

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

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

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

28. The identity element with respect to subtraction is

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

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

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

32. The multiplicative inverse of 1 – 2i is

33. 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 =

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

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

36. 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

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

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

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

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

41. QUQ’ =

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

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

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

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

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

47. (7, 9) + (3, -5) =

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

49. i¹⁰¹ =

50. 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 =

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

52. A U A’ = ?

53. If x ϵ R, then x² + x + 1 is

54. √-1b = ?

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

56. The set (Q, .)

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

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

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

60. The multiplicative inverse of -3i is

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

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

63. The multiplicative inverse of x ≠ 0 is

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

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

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

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

68. If – P is true, then p is

69. The graph of a linear function represents

70. A semi group is monoid if

71. The set of all positive even integers is

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

73. The square root of 2i – 20i is

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

75. The symbol of irrational is

76. The function {(x,y)|y = ½ x²} is

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

78. ∀ a, b ϵ ℜ, ab = be is a

79. (a¯¹)¯¹ =

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

81. The set of complex numbers forms

82. The set of integer is

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

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

85. If A ∩ B = B, then.

86. Multiplicative inverse of 0 is

87. The set A is

88. Multiplicative inverse of “1” is

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

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

91. π/3 is

92. If z = 1/Z, then

93. √–81 – √–36 = ?

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

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

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

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

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

99. The set (Q, .)

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

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

102. A subset of B x A is called a

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

104. Multiplicative inverse of “1” is

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

106. 1/3 is a decimal.

107. Associative law of multiplication

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

109. In polar form of complex number

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

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

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

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

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

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

116. (A ∩ B)ᶜ =

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

118. If Z = (1,2), then Z¯¹ = ?

119. 202.04 is an example of

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

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

122. For any set B, BUB’ is

123. The graph of a quadratic function is

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

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

126. The negation of a given number is a

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

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

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

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

131. 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.

132. The conjugate of √5 i is

133. A ⊆ B means

134. i³ =

135. a > b, b > c ⇒ a > is a

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

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

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

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

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

141. If A is any set, then

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

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

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

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

146. Which of the following is true?

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

148. zz = ________

149. (a + bi) – (c + di) =

150. {x : x ϵ Z⁺ and x < 1} is

151. The graph of a quadratic function is

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

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

154. 3/2 is

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

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

157. The set {-1, 1} is

158. 0 (zero) is

159. √2 is a number.

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

161. 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

162. a.a¯¹ = a¯¹.a = 1 is a

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

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

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

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

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

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

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

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

171. If A ⊆ B then A U B is

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

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

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

175. The set of students of your class is

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

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

178. 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

179. A _________ is an ordered collection of objects.

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

181. 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.

182. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

183. A set containing only one element is called the

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

185. {x|x ϵ N, x ≤ 10} is the

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

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

188. √-1 b =

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

190. The square root function is defined by the equation

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