Mathematics Sets Functions and Groups Online Test

1. The graph of a quadratic function is

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

3. The graph of a linear function represents

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

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

6. i³ =

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

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

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

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

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. Multiplicative inverse of “1” is

13. A ⊆ B means

14. The inverse of A → B is

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

16. √25 is a number

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

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

19. Additive inverse of – a – b is

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

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

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

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

24. The multiplicative inverse of 1 – 2i is

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

26. Multiplicative inverse of 0 is

27. √2 is a number.

28. Which of the following is true?

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

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

31. Associative law of multiplication

32. i¹⁰¹ =

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

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

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

36. If – P is true, then p is

37. The multiplicative inverse of -3i is

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

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

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

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

42. The set (Q, .)

43. If z = 1/Z, then

44. a > b, b > c ⇒ a > is a

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

46. The set of all positive even integers is

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

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

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

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

51. If Z = (1,2), then Z¯¹ = ?

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

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

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

55. ∀ a, b ϵ ℜ, ab = be is a

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

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

58. If x ϵ R, then x² + x + 1 is

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

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

61. The symbol of irrational is

62. 1/3 is a decimal.

63. The set of integer is

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

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

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

67. The set {-1, 1} is

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

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

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

71. The identity element with respect to subtraction is

72. 0 (zero) is

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

74. The graph of a quadratic function is

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

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

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

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

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

80. A semi group is monoid if

81. The set of students of your class is

82. The conjugate of √5 i is

83. Multiplicative inverse of “1” is

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

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

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

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

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

89. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

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

92. √23 is

93. The square root of 2i – 20i is

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

95. {x : x ϵ Z⁺ and x < 1} is

96. The negation of a given number is a

97. A set containing only one element is called the

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

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

100. A U A’ = ?

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

102. φ set is the __________ of all sets?

103. 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 =

104. (a + bi) – (c + di) =

105. If A is any set, then

106. The value of i⁴ᶜ¯¹

107. 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.

108. zz = ________

109. √–81 – √–36 = ?

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

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

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

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

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

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

116. (a¯¹)¯¹ =

117. For any set B, BUB’ is

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

119. {x:x ϵ Z⁺ and x <-1} is

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

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

122. In polar form of complex number

123. The multiplicative inverse of x ≠ 0 is

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

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

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

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

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

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

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

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

132. 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.

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

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

135. The square root function is defined by the equation

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

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

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

139. (7, 9) + (3, -5) =

140. If A and B are overlapping sets, then

141. The set (Q, .)

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

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

144. The set of complex numbers forms

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

146. {x|x ϵ N, x ≤ 10} is the

147. 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.

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

149. 3/2 is

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

151. A subset of B x A is called a

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

153. √-1b = ?

154. QUQ’ =

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

156. A _________ is an ordered collection of objects.

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

158. Decimal part of irrational number is

159. 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

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

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

162. 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

163. If A ⊆ B then A U B is

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

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

166. a.a¯¹ = a¯¹.a = 1 is a

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

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

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

170. If A ∩ B = B, then.

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

172. The function {(x,y)|y = ½ x²} is

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

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

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

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

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

178. 6 is

179. π/3 is

180. √-1 b =

181. (A ∩ B)ᶜ =

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

183. The set A is

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

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

186. 202.04 is an example of

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

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

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

190. 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

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