Mathematics Sets Functions and Groups Online Test

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

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

3. Associative law of multiplication

4. A U A’ = ?

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

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

7. a > b ⇒ a + c > b + c is known as

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

9. 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.

10. ∀ a, b ϵ ℜ, ab = be is a

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

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

13. The inverse of A → B is

14. If Z = (1,2), then Z¯¹ = ?

15. The set (Q, .)

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

17. The function {(x,y)|y = ½ x²} is

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

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

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

21. √23 is

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

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

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

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

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

27. The symbol of irrational is

28. 1/3 is a decimal.

29. The multiplicative inverse of -3i is

30. If z = 1/Z, then

31. The set of integer is

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

33. The graph of a quadratic function is

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

35. Decimal part of irrational number is

36. A ⊆ B means

37. QUQ’ =

38. If A ⊆ B then A U B is

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

40. The square root function is defined by the equation

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

42. The identity element with respect to subtraction is

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

44. 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 =

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

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

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

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

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

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

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

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

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

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

55. The square root of 2i – 20i is

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

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

58. zz = ________

59. π/3 is

60. {x : x ϵ Z⁺ and x < 1} is

61. Which of the following is true?

62. The graph of a quadratic function is

63. The set of students of your class is

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

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

66. The set of all positive even integers is

67. If A ∩ B = B, then.

68. The graph of a linear function represents

69. For any set B, BUB’ is

70. In polar form of complex number

71. a > b, b > c ⇒ a > is a

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

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

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

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

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

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

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

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

80. If x ϵ R, then x² + x + 1 is

81. A _________ is an ordered collection of objects.

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

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

84. A set containing only one element is called the

85. If – P is true, then p is

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

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

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

89. The set (Q, .)

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

91. Additive inverse of – a – b is

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

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

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

95. Multiplicative inverse of “1” is

96. The set A is

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

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

99. 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

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

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

102. The multiplicative inverse of x ≠ 0 is

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

104. 0 (zero) is

105. a.a¯¹ = a¯¹.a = 1 is a

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

107. √2 is a number.

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

109. √–81 – √–36 = ?

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

111. The multiplicative inverse of 1 – 2i is

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

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

114. φ set is the __________ of all sets?

115. 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

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

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

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

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

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

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

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

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

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

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

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

127. Multiplicative inverse of “1” is

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

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

130. (7, 9) + (3, -5) =

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

132. (a + bi) – (c + di) =

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

134. i³ =

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

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

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

138. {x:x ϵ Z⁺ and x <-1} is

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

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

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

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

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

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

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

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

147. i¹⁰¹ =

148. 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.

149. 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.

150. √-1b = ?

151. The set of complex numbers forms

152. (A ∩ B)ᶜ =

153. The negation of a given number is a

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

155. {x|x ϵ N, x ≤ 10} is the

156. 3/2 is

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

158. √-1 b =

159. 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 =

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

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

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

163. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

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

166. 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

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

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

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

170. The set {-1, 1} is

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

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

173. √25 is a number

174. If A and B are overlapping sets, then

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

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

177. If A is any set, then

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

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

180. The conjugate of √5 i is

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

182. (a¯¹)¯¹ =

183. A semi group is monoid if

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

185. 6 is

186. 202.04 is an example of

187. The value of i⁴ᶜ¯¹

188. Multiplicative inverse of 0 is

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

190. A subset of B x A is called a

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