Mathematics Sets Functions and Groups Online Test

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

2. A U A’ = ?

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

4. 1/3 is a decimal.

5. The identity element with respect to subtraction is

6. A set containing only one element is called the

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

8. 0 (zero) is

9. φ set is the __________ of all sets?

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

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

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

13. The set of complex numbers forms

14. a/b = ka/kb , (k ≠ 0) is known as

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

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

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

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

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

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

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

22. The graph of a quadratic function is

23. √-1b = ?

24. {x:x ϵ Z⁺ and x <-1} is

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

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

27. The graph of a quadratic function is

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

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

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

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

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

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

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

35. The negation of a given number is a

36. π/3 is

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

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

39. A subset of B x A is called a

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

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

42. Associative law of multiplication

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

44. If A and B are overlapping sets, then

45. If A ∩ B = B, then.

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

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

48. 3/2 is

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

50. A semi group is monoid if

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

52. √25 is a number

53. a.a¯¹ = a¯¹.a = 1 is a

54. In polar form of complex number

55. A _________ is an ordered collection of objects.

56. The square root of 2i – 20i is

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

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

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

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

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

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

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

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

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

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

67. 202.04 is an example of

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

69. If Z = (1,2), then Z¯¹ = ?

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

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

72. √–81 – √–36 = ?

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

74. QUQ’ =

75. The inverse of A → B is

76. {x : x ϵ Z⁺ and x < 1} is

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

78. 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

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

80. a > b, b > c ⇒ a > is a

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

82. If A ⊆ B then A U B is

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

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

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

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

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

88. A ⊆ B means

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

90. Multiplicative inverse of “1” is

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

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

93. 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

94. The set (Q, .)

95. √23 is

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

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

98. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

99. The value of i⁴ᶜ¯¹

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

101. The graph of a linear function represents

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

103. The set {-1, 1} is

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

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

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

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

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

109. The symbol of irrational is

110. The set (Q, .)

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

112. The multiplicative inverse of 1 – 2i is

113. If A is any set, then

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

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

116. (7, 9) + (3, -5) =

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

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

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

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

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

122. Decimal part of irrational number is

123. (a¯¹)¯¹ =

124. The conjugate of √5 i is

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

126. If x ϵ R, then x² + x + 1 is

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

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

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

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

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

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

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

134. 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.

135. The multiplicative inverse of -3i is

136. If z = 1/Z, then

137. Multiplicative inverse of “1” is

138. The set of students of your class is

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

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

141. 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 =

142. 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.

143. 6 is

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

145. zz = ________

146. {x|x ϵ N, x ≤ 10} is the

147. (a + bi) – (c + di) =

148. For any set B, BUB’ is

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

150. √-1 b =

151. The set of integer is

152. ∀ a, b ϵ ℜ, ab = be is a

153. i³ =

154. The function {(x,y)|y = ½ x²} is

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

156. If – P is true, then p is

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

158. 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.

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

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

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

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

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

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

165. Additive inverse of – a – b is

166. (A ∩ B)ᶜ =

167. √2 is a number.

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

169. The set A is

170. The square root function is defined by the equation

171. 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 =

172. Which of the following is true?

173. The multiplicative inverse of x ≠ 0 is

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

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

176. Multiplicative inverse of 0 is

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

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

179. i¹⁰¹ =

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

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

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

183. The set of all positive even integers is

184. 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

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

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

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

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

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

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

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