Mathematics Sets Functions and Groups Online Test

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

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

3. √2 is a number.

4. {x : x ϵ Z⁺ and x < 1} is

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

6. In polar form of complex number

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

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

9. Additive inverse of – a – b is

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

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

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

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

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

15. (a + bi) – (c + di) =

16. 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

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

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

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

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

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

22. A ⊆ B means

23. A subset of B x A is called a

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

25. If Z = (1,2), then Z¯¹ = ?

26. √–81 – √–36 = ?

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

28. Multiplicative inverse of “1” is

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

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

31. {x|x ϵ N, x ≤ 10} is the

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

33. Decimal part of irrational number is

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

35. The multiplicative inverse of 1 – 2i is

36. A _________ is an ordered collection of objects.

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

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

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

40. QUQ’ =

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

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

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

44. √25 is a number

45. a > b, b > c ⇒ a > is a

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

47. The graph of a quadratic function is

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

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

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

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

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

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

54. φ set is the __________ of all sets?

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

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

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

58. Multiplicative inverse of “1” is

59. If z = 1/Z, then

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

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

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

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

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

65. The identity element with respect to subtraction is

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

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

68. If – P is true, then p is

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

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

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

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

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

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

75. 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.

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

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

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

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

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

81. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

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

83. Multiplicative inverse of 0 is

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

85. i¹⁰¹ =

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

87. The inverse of A → B is

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

89. The graph of a linear function represents

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

91. The square root of 2i – 20i is

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

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

94. Associative law of multiplication

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

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

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

98. The symbol of irrational is

99. a > b ⇒ a + c > b + c is known as

100. i³ =

101. The set of all positive even integers is

102. 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

103. 202.04 is an example of

104. 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.

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

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

107. 3/2 is

108. 1/3 is a decimal.

109. 6 is

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

111. A set containing only one element is called the

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

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

114. The square root function is defined by the equation

115. The value of i⁴ᶜ¯¹

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

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

118. The set of complex numbers forms

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

120. π/3 is

121. (a¯¹)¯¹ =

122. A U A’ = ?

123. 0 (zero) is

124. If x ϵ R, then x² + x + 1 is

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

126. If A ⊆ B then A U B is

127. 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.

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

129. {x:x ϵ Z⁺ and x <-1} is

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

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

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

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

134. 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 =

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

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

137. Which of the following is true?

138. The set of students of your class is

139. The set A is

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

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

142. ∀ a, b ϵ ℜ, ab = be is a

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

144. A semi group is monoid if

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

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

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

148. √-1 b =

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

150. The multiplicative inverse of -3i is

151. zz = ________

152. The set of integer is

153. The multiplicative inverse of x ≠ 0 is

154. The set (Q, .)

155. 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 =

156. √-1b = ?

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

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

159. If A ∩ B = B, then.

160. √23 is

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

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

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

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

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

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

167. The negation of a given number is a

168. The graph of a quadratic function is

169. (A ∩ B)ᶜ =

170. If A and B are overlapping sets, then

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

172. The conjugate of √5 i is

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

174. The set (Q, .)

175. a.a¯¹ = a¯¹.a = 1 is a

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

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

178. If A is any set, then

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

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

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

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

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

184. The set {-1, 1} is

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

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

187. 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

188. For any set B, BUB’ is

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

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

191. The function {(x,y)|y = ½ x²} is