Mathematics Sets Functions and Groups Online Test

1. ∀ a, b ϵ ℜ, ab = be is a

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

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

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

5. The inverse of A → B is

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

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

8. √23 is

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

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

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

12. (7, 9) + (3, -5) =

13. 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.

14. Associative law of multiplication

15. The multiplicative inverse of -3i is

16. For any set B, BUB’ is

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

18. 1/3 is a decimal.

19. The set (Q, .)

20. The set of integer is

21. If A is any set, then

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

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

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

25. The symbol of irrational is

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

27. 0 (zero) is

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

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

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

31. 202.04 is an example of

32. (A ∩ B)ᶜ =

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

34. 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

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

36. Multiplicative inverse of 0 is

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

38. The set of all positive even integers is

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

40. A set containing only one element is called the

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

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

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

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

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

46. The set {-1, 1} is

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

48. If Z = (1,2), then Z¯¹ = ?

49. Additive inverse of – a – b is

50. 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

51. √25 is a number

52. The square root function is defined by the equation

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

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

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

56. a.a¯¹ = a¯¹.a = 1 is a

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

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

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

60. The function {(x,y)|y = ½ x²} is

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

62. Decimal part of irrational number is

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

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

65. Multiplicative inverse of “1” is

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

67. A U A’ = ?

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

69. If x ϵ R, then x² + x + 1 is

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

71. (a¯¹)¯¹ =

72. 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 =

73. If z = 1/Z, then

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

75. The set A is

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

77. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

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

80. The set of students of your class is

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

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

83. i³ =

84. {x:x ϵ Z⁺ and x <-1} is

85. √-1b = ?

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

87. The set (Q, .)

88. a > b, b > c ⇒ a > is a

89. If A ∩ B = B, then.

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

91. The graph of a quadratic function is

92. If A ⊆ B then A U B is

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

94. a/b = ka/kb , (k ≠ 0) is known as

95. 6 is

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

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

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

99. The conjugate of √5 i is

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

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

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

103. {x : x ϵ Z⁺ and x < 1} is

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

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

106. The negation of a given number is a

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

108. √–81 – √–36 = ?

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

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

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

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

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

114. QUQ’ =

115. The square root of 2i – 20i is

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

117. {x|x ϵ N, x ≤ 10} is the

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

119. The multiplicative inverse of x ≠ 0 is

120. i¹⁰¹ =

121. A ⊆ B means

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

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

124. 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.

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

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

127. If A and B are overlapping sets, then

128. The value of i⁴ᶜ¯¹

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

130. 3/2 is

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

132. The set of complex numbers forms

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

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

135. The graph of a quadratic function is

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

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

138. φ set is the __________ of all sets?

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

140. The multiplicative inverse of 1 – 2i is

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

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

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

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

145. (a + bi) – (c + di) =

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

147. zz = ________

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

149. π/3 is

150. Multiplicative inverse of “1” is

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

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

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

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

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

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

157. A _________ is an ordered collection of objects.

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

159. 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 =

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

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

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

163. 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.

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

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

166. If – P is true, then p is

167. Which of the following is true?

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

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

170. A semi group is monoid if

171. The identity element with respect to subtraction is

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

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

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

175. √2 is a number.

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

177. √-1 b =

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

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

180. The graph of a linear function represents

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

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

183. 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

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

185. A subset of B x A is called a

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

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

188. In polar form of complex number

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

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

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