Mathematics Sets Functions and Groups Online Test

1. √–81 – √–36 = ?

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

3. Multiplicative inverse of “1” is

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

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

6. The value of i⁴ᶜ¯¹

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

8. 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 =

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

10. 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.

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

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

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

14. (a + bi) – (c + di) =

15. If A ⊆ B then A U B is

16. The set A is

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

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

19. ∀ a, b ϵ ℜ, ab = be is a

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

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

22. zz = ________

23. 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

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

25. If A and B are overlapping sets, then

26. The multiplicative inverse of 1 – 2i is

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

28. The graph of a quadratic function is

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

30. The set of all positive even integers is

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

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

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

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

35. 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.

36. A _________ is an ordered collection of objects.

37. If x ϵ R, then x² + x + 1 is

38. 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 =

39. The square root of 2i – 20i is

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

41. φ set is the __________ of all sets?

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

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

44. 3/2 is

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

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

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

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

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

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

51. A ⊆ B means

52. 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.

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

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

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

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

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

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

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

60. a/b = ka/kb , (k ≠ 0) is known as

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

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

63. a.a¯¹ = a¯¹.a = 1 is a

64. {x|x ϵ N, x ≤ 10} is the

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

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

67. √-1 b =

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

69. a > b ⇒ a + c > b + c is known as

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

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

72. The multiplicative inverse of x ≠ 0 is

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

74. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

76. The set (Q, .)

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

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

79. √-1b = ?

80. The negation of a given number is a

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

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

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

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

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

86. The symbol of irrational is

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

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

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

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

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

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

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

94. √2 is a number.

95. 202.04 is an example of

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

97. 0 (zero) is

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

100. The function {(x,y)|y = ½ x²} is

101. The conjugate of √5 i is

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

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

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

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

106. If – P is true, then p is

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

108. a > b, b > c ⇒ a > is a

109. (A ∩ B)ᶜ =

110. The identity element with respect to subtraction is

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

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

113. 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

114. The graph of a linear function represents

115. For any set B, BUB’ is

116. Which of the following is true?

117. The square root function is defined by the equation

118. Associative law of multiplication

119. The set of students of your class is

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

121. {x : x ϵ Z⁺ and x < 1} is

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

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

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

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

126. The set (Q, .)

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

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

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

130. The set of integer is

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

132. QUQ’ =

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

134. Additive inverse of – a – b is

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

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

137. If Z = (1,2), then Z¯¹ = ?

138. {x:x ϵ Z⁺ and x <-1} is

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

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

141. (7, 9) + (3, -5) =

142. The multiplicative inverse of -3i is

143. √25 is a number

144. 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

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

146. The inverse of A → B is

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

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

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

150. i¹⁰¹ =

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

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

153. A semi group is monoid if

154. The set {-1, 1} is

155. A U A’ = ?

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

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

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

159. If A is any set, then

160. The graph of a quadratic function is

161. Multiplicative inverse of “1” is

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

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

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

165. Decimal part of irrational number is

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

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

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

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

170. (a¯¹)¯¹ =

171. 6 is

172. Multiplicative inverse of 0 is

173. A subset of B x A is called a

174. If z = 1/Z, then

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

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

177. The set of complex numbers forms

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

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

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

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

182. 1/3 is a decimal.

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

184. If A ∩ B = B, then.

185. i³ =

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

187. √23 is

188. A set containing only one element is called the

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

190. In polar form of complex number

191. π/3 is