Mathematics Sets Functions and Groups Online Test

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

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

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

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

5. √23 is

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

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

8. 0 (zero) is

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

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

11. QUQ’ =

12. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

13. For any set B, BUB’ is

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

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

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

17. 1/3 is a decimal.

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

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

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

21. The set (Q, .)

22. 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 =

23. Multiplicative inverse of “1” is

24. a > b, b > c ⇒ a > is a

25. The identity element with respect to subtraction is

26. (a¯¹)¯¹ =

27. 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.

28. Additive inverse of – a – b is

29. If A is any set, then

30. The square root function is defined by the equation

31. (A ∩ B)ᶜ =

32. The negation of a given number is a

33. Which of the following is true?

34. 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.

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

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

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

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

39. If A ∩ B = B, then.

40. zz = ________

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

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

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

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

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

46. (a + bi) – (c + di) =

47. The function {(x,y)|y = ½ x²} is

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

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

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

51. The set {-1, 1} is

52. If – P is true, then p is

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

54. A _________ is an ordered collection of objects.

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

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

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

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

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

60. If Z = (1,2), then Z¯¹ = ?

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

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

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

64. The set (Q, .)

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

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

67. If A and B are overlapping sets, then

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

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

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

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

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

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

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

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

76. The graph of a linear function represents

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

78. If x ϵ R, then x² + x + 1 is

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

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

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

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

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

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

85. The multiplicative inverse of -3i is

86. 202.04 is an example of

87. If A ⊆ B then A U B is

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

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

90. φ set is the __________ of all sets?

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

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

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

94. Decimal part of irrational number is

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

96. The graph of a quadratic function is

97. A subset of B x A is called a

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

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

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

101. 6 is

102. The value of i⁴ᶜ¯¹

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

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

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

106. a.a¯¹ = a¯¹.a = 1 is a

107. The inverse of A → B is

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

109. Multiplicative inverse of “1” is

110. The multiplicative inverse of x ≠ 0 is

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

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

113. A U A’ = ?

114. If z = 1/Z, then

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

116. {x|x ϵ N, x ≤ 10} is the

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

118. The set of complex numbers forms

119. 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 =

120. The symbol of irrational is

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

122. The set of students of your class is

123. {x:x ϵ Z⁺ and x <-1} is

124. 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.

125. π/3 is

126. The set of all positive even integers is

127. The set A is

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

129. i¹⁰¹ =

130. √-1 b =

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

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

133. √2 is a number.

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

135. The multiplicative inverse of 1 – 2i is

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

137. A set containing only one element is called the

138. 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

139. A semi group is monoid if

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

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

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

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

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

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

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

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

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

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

150. Associative law of multiplication

151. (7, 9) + (3, -5) =

152. In polar form of complex number

153. Multiplicative inverse of 0 is

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

155. i³ =

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

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

158. √-1b = ?

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

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

161. {x : x ϵ Z⁺ and x < 1} is

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

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

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

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

166. 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

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

168. The set of integer is

169. A ⊆ B means

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

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

172. 3/2 is

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

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

175. ∀ a, b ϵ ℜ, ab = be is a

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

177. The conjugate of √5 i is

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

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

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

181. 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

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

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

184. √–81 – √–36 = ?

185. √25 is a number

186. The square root of 2i – 20i is

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

188. The graph of a quadratic function is

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

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

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