Mathematics Sets Functions and Groups Online Test

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

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

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

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

5. √23 is

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

7. The multiplicative inverse of x ≠ 0 is

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

9. The value of i⁴ᶜ¯¹

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

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

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

13. 0 (zero) is

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

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

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

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

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

19. Decimal part of irrational number is

20. A set containing only one element is called the

21. The identity element with respect to subtraction is

22. 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.

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

24. zz = ________

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

26. (A ∩ B)ᶜ =

27. a/b = ka/kb , (k ≠ 0) is known as

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

29. If Z = (1,2), then Z¯¹ = ?

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

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

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

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

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

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

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

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

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

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

40. The set of students of your class is

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

42. (a + bi) – (c + di) =

43. 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

44. The function {(x,y)|y = ½ x²} is

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

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

47. 202.04 is an example of

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

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

50. The multiplicative inverse of 1 – 2i is

51. 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.

52. If A ⊆ B then A U B is

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

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

55. If A is any set, then

56. {x:x ϵ Z⁺ and x <-1} is

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

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

59. QUQ’ =

60. The set of all positive even integers is

61. a > b ⇒ a + c > b + c is known as

62. Multiplicative inverse of 0 is

63. The set of complex numbers forms

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

65. The conjugate of √5 i is

66. Multiplicative inverse of “1” is

67. √25 is a number

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

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

70. The set (Q, .)

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

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

73. i¹⁰¹ =

74. If – P is true, then p is

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

76. For any set B, BUB’ is

77. If z = 1/Z, then

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

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

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

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

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

83. 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 =

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

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

86. π/3 is

87. (7, 9) + (3, -5) =

88. 1/3 is a decimal.

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

90. √-1b = ?

91. 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.

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

93. 6 is

94. Multiplicative inverse of “1” is

95. {x : x ϵ Z⁺ and x < 1} is

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

97. A _________ is an ordered collection of objects.

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

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

100. If A and B are overlapping sets, then

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

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

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

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

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

106. The square root of 2i – 20i is

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

108. The set (Q, .)

109. The inverse of A → B is

110. The graph of a quadratic function is

111. 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 =

112. The set A is

113. Associative law of multiplication

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

115. √-1 b =

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

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

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

119. The symbol of irrational is

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

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

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

123. A subset of B x A is called a

124. The set {-1, 1} is

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

126. a.a¯¹ = a¯¹.a = 1 is a

127. If x ϵ R, then x² + x + 1 is

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

129. The square root function is defined by the equation

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

131. A ⊆ B means

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

133. The graph of a quadratic function is

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

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

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

137. In polar form of complex number

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

139. 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

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

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

142. 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

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

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

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

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

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

148. a > b, b > c ⇒ a > is a

149. The negation of a given number is a

150. The set of integer is

151. i³ =

152. If A ∩ B = B, then.

153. 3/2 is

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

155. φ set is the __________ of all sets?

156. A U A’ = ?

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

158. The graph of a linear function represents

159. √2 is a number.

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

161. A semi group is monoid if

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

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

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

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

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

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

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

169. Which of the following is true?

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

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

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

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

174. (a¯¹)¯¹ =

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

176. Additive inverse of – a – b is

177. The multiplicative inverse of -3i is

178. √–81 – √–36 = ?

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

180. ∀ a, b ϵ ℜ, ab = be is a

181. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

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

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

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

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

187. {x|x ϵ N, x ≤ 10} is the

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

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

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

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