Mathematics Sets Functions and Groups Online Test

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

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

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

4. The set of students of your class is

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

6. 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.

7. The conjugate of √5 i is

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

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

10. The graph of a quadratic function is

11. The multiplicative inverse of x ≠ 0 is

12. If z = 1/Z, then

13. √25 is a number

14. √–81 – √–36 = ?

15. √2 is a number.

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

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

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

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

20. √23 is

21. A set containing only one element is called the

22. If A ⊆ B then A U B is

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

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

25. A subset of B x A is called a

26. √-1b = ?

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

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

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

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

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

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

33. a > b ⇒ a + c > b + c is known as

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

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

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

37. The graph of a quadratic function is

38. If Z = (1,2), then Z¯¹ = ?

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

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

41. {x : x ϵ Z⁺ and x < 1} is

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

43. The inverse of A → B is

44. Additive inverse of – a – b is

45. The set (Q, .)

46. Which of the following is true?

47. The set of complex numbers forms

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

49. {x|x ϵ N, x ≤ 10} is the

50. The square root function is defined by the equation

51. Associative law of multiplication

52. Decimal part of irrational number is

53. 202.04 is an example of

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

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

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

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

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

59. A U A’ = ?

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

61. 1/3 is a decimal.

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

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

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

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

66. The set of all positive even integers is

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

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

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

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

71. If – P is true, then p is

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

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

74. (A ∩ B)ᶜ =

75. Multiplicative inverse of 0 is

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

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

78. √-1 b =

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

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

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

82. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

83. φ set is the __________ of all sets?

84. i³ =

85. {x:x ϵ Z⁺ and x <-1} is

86. zz = ________

87. 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.

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

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

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

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

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

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

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

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

96. If x ϵ R, then x² + x + 1 is

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

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

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

100. The symbol of irrational is

101. For any set B, BUB’ is

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

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

104. a.a¯¹ = a¯¹.a = 1 is a

105. In polar form of complex number

106. The function {(x,y)|y = ½ x²} is

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

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

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

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

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

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

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

114. If A ∩ B = B, then.

115. 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

116. A semi group is monoid if

117. 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 =

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

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

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

121. (a¯¹)¯¹ =

122. The square root of 2i – 20i is

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

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

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

126. The set (Q, .)

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

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

129. 0 (zero) is

130. 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 =

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

132. The set {-1, 1} is

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

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

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

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

137. 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

138. a > b, b > c ⇒ a > is a

139. A _________ is an ordered collection of objects.

140. Multiplicative inverse of “1” is

141. ∀ a, b ϵ ℜ, ab = be is a

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

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

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

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

146. The multiplicative inverse of 1 – 2i is

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

148. The negation of a given number is a

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

150. The set A is

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

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

153. The multiplicative inverse of -3i is

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

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

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

157. If A and B are overlapping sets, then

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

159. 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

160. 6 is

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

162. Multiplicative inverse of “1” is

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

164. The graph of a linear function represents

165. (7, 9) + (3, -5) =

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

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

168. A ⊆ B means

169. i¹⁰¹ =

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

171. If A is any set, then

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

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

174. (a + bi) – (c + di) =

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

176. π/3 is

177. The identity element with respect to subtraction is

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

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

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

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

182. The value of i⁴ᶜ¯¹

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

184. 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.

185. 3/2 is

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

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

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

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

190. QUQ’ =

191. The set of integer is