Mathematics Sets Functions and Groups Online Test

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

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

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

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

5. 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 =

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

7. 6 is

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

9. 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.

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

11. 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 =

12. 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

13. In polar form of complex number

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

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

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

17. The graph of a quadratic function is

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

19. The square root function is defined by the equation

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

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

22. 1/3 is a decimal.

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

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

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

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

27. The square root of 2i – 20i is

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

29. The set (Q, .)

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

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

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

33. √23 is

34. If A and B are overlapping sets, then

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

36. The value of i⁴ᶜ¯¹

37. Additive inverse of – a – b is

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

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

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

41. A _________ is an ordered collection of objects.

42. The graph of a linear function represents

43. Multiplicative inverse of 0 is

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

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

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

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

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

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

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

51. The multiplicative inverse of 1 – 2i is

52. The identity element with respect to subtraction is

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

54. a/b = ka/kb , (k ≠ 0) is known as

55. Decimal part of irrational number is

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

57. (a¯¹)¯¹ =

58. The conjugate of √5 i is

59. The set (Q, .)

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

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

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

63. The inverse of A → B is

64. √-1b = ?

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

66. √2 is a number.

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

68. φ set is the __________ of all sets?

69. The set of all positive even integers is

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

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

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

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

74. i³ =

75. a.a¯¹ = a¯¹.a = 1 is a

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

77. 202.04 is an example of

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

79. {x|x ϵ N, x ≤ 10} is the

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

81. 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

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

83. If A is any set, then

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

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

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

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

88. The symbol of irrational is

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

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

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

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

93. √25 is a number

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

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

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

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

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

99. zz = ________

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

101. A set containing only one element is called the

102. The multiplicative inverse of -3i is

103. The negation of a given number is a

104. A subset of B x A is called a

105. Multiplicative inverse of “1” is

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

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

108. The graph of a quadratic function is

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

110. √-1 b =

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

112. {x : x ϵ Z⁺ and x < 1} is

113. If A ∩ B = B, then.

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

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

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

117. The set {-1, 1} is

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

119. √–81 – √–36 = ?

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

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

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

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

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

125. 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.

126. A U A’ = ?

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

128. The function {(x,y)|y = ½ x²} is

129. 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.

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

131. The set of complex numbers forms

132. 0 (zero) is

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

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

135. a > b, b > c ⇒ a > is a

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

137. Which of the following is true?

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

139. If Z = (1,2), then Z¯¹ = ?

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

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

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

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

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

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

146. If – P is true, then p is

147. 3/2 is

148. A ⊆ B means

149. The multiplicative inverse of x ≠ 0 is

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

151. The set A is

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

153. The set of integer is

154. (a + bi) – (c + di) =

155. If z = 1/Z, then

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

157. For any set B, BUB’ is

158. 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

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

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

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

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

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

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

165. (7, 9) + (3, -5) =

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

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

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

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

170. QUQ’ =

171. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

172. ∀ a, b ϵ ℜ, ab = be is a

173. Associative law of multiplication

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

175. Multiplicative inverse of “1” is

176. A semi group is monoid if

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

178. i¹⁰¹ =

179. If x ϵ R, then x² + x + 1 is

180. If A ⊆ B then A U B is

181. {x:x ϵ Z⁺ and x <-1} is

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

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

184. (A ∩ B)ᶜ =

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

186. π/3 is

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

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

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

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

191. The set of students of your class is