Mathematics Sets Functions and Groups Online Test

1. Multiplicative inverse of “1” is

2. a > b, b > c ⇒ a > is a

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

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

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

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

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

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

9. 202.04 is an example of

10. Multiplicative inverse of “1” is

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

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

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

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

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

16. 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 =

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

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

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

20. In polar form of complex number

21. a > b ⇒ a + c > b + c is known as

22. The set of students of your class is

23. The graph of a quadratic function is

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

25. 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

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

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

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

29. zz = ________

30. i³ =

31. Associative law of multiplication

32. If – P is true, then p is

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

34. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

35. (a + bi) – (c + di) =

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

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

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

39. If A ∩ B = B, then.

40. The graph of a linear function represents

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

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

43. The inverse of A → B is

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

45. The multiplicative inverse of 1 – 2i is

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

47. The square root function is defined by the equation

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

49. The set of complex numbers forms

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

51. A set containing only one element is called the

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

53. A subset of B x A is called a

54. If A and B are overlapping sets, then

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

56. a.a¯¹ = a¯¹.a = 1 is a

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

58. A ⊆ B means

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

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

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

62. The set (Q, .)

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

64. {x|x ϵ N, x ≤ 10} is the

65. If z = 1/Z, then

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

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

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

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

70. Additive inverse of – a – b is

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

72. 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.

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

74. √-1 b =

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

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

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

78. √23 is

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

80. The set of all positive even integers is

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

82. √2 is a number.

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

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

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

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

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

88. The graph of a quadratic function is

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

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

91. For any set B, BUB’ is

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

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

94. {x : x ϵ Z⁺ and x < 1} is

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

96. 3/2 is

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

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

99. √-1b = ?

100. The set of integer is

101. 6 is

102. The set (Q, .)

103. (7, 9) + (3, -5) =

104. A _________ is an ordered collection of objects.

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

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

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

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

109. A U A’ = ?

110. ∀ a, b ϵ ℜ, ab = be is a

111. √25 is a number

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

113. If A is any set, then

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

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

116. Multiplicative inverse of 0 is

117. 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

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

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

120. The square root of 2i – 20i is

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

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

123. The symbol of irrational is

124. The negation of a given number is a

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

126. √–81 – √–36 = ?

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

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

129. The conjugate of √5 i is

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

131. 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

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

133. A semi group is monoid if

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

135. The set A is

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

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

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

139. {x:x ϵ Z⁺ and x <-1} is

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

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

142. QUQ’ =

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

144. The multiplicative inverse of -3i is

145. If Z = (1,2), then Z¯¹ = ?

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

147. The multiplicative inverse of x ≠ 0 is

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

149. The identity element with respect to subtraction is

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

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

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

153. 0 (zero) is

154. Decimal part of irrational number is

155. If A ⊆ B then A U B is

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

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

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

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

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

161. 1/3 is a decimal.

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

163. The value of i⁴ᶜ¯¹

164. 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 =

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

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

167. The function {(x,y)|y = ½ x²} is

168. (A ∩ B)ᶜ =

169. 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.

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

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

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

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

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. What is the conjugate of -6-i?

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

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

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

179. φ set is the __________ of all sets?

180. If x ϵ R, then x² + x + 1 is

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

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

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

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

185. Which of the following is true?

186. i¹⁰¹ =

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

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

189. π/3 is

190. The set {-1, 1} is

191. (a¯¹)¯¹ =