ECAT Mathematics Sets Functions and Groups Online Test

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

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

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

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

5. The set of students of your class is

6. The set of all positive even integers is

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

8. i³ =

9. The identity element with respect to subtraction is

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

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

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

13. Multiplicative inverse of 0 is

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

15. 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

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

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

18. Multiplicative inverse of “1” is

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

20. √-1b = ?

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

22. 3/2 is

23. The function {(x,y)|y = ½ x²} is

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

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

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

27. The negation of a given number is a

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

29. 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 =

30. A set containing only one element is called the

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

32. A ⊆ B means

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

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

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

36. (a¯¹)¯¹ =

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

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

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

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

41. Decimal part of irrational number is

42. a > b ⇒ a + c > b + c is known as

43. QUQ’ =

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

45. The conjugate of √5 i is

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

47. If A ∩ B = B, then.

48. π/3 is

49. √25 is a number

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

51. Which of the following is true?

52. The square root function is defined by the equation

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

54. The graph of a quadratic function is

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

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

57. The set (Q, .)

58. 0 (zero) is

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

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

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

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

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

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

65. √2 is a number.

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

67. 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 =

68. If A is any set, then

69. The set of integer is

70. a/b = ka/kb , (k ≠ 0) is known as

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

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

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

74. The set A is

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

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

77. a > b, b > c ⇒ a > is a

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

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

80. If Z = (1,2), then Z¯¹ = ?

81. 1/3 is a decimal.

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

83. φ set is the __________ of all sets?

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

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

86. If A ⊆ B then A U B is

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

88. A _________ is an ordered collection of objects.

89. 6 is

90. The set of complex numbers forms

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

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

93. √23 is

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

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

96. (a + bi) – (c + di) =

97. The graph of a quadratic function is

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

99. The multiplicative inverse of x ≠ 0 is

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

101. The inverse of A → B is

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

103. {x : x ϵ Z⁺ and x < 1} is

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

105. If x ϵ R, then x² + x + 1 is

106. (A ∩ B)ᶜ =

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

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

109. If A and B are overlapping sets, then

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

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

112. The multiplicative inverse of -3i is

113. The multiplicative inverse of 1 – 2i is

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

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

116. A U A’ = ?

117. (7, 9) + (3, -5) =

118. zz = ________

119. If – P is true, then p is

120. √-1 b =

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

122. i¹⁰¹ =

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

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

125. 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

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

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

128. The set (Q, .)

129. 202.04 is an example of

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

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

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

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

134. Additive inverse of – a – b is

135. 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.

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

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

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

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

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

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

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

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

144. √–81 – √–36 = ?

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

146. {x:x ϵ Z⁺ and x <-1} is

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

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

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

150. For any set B, BUB’ is

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

152. The square root of 2i – 20i is

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

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

155. The graph of a linear function represents

156. The value of i⁴ᶜ¯¹

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

158. 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.

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

160. (√3 + √5) + √7 = √3 + (√5 + √7) property used in above is

161. The symbol of irrational is

162. {x|x ϵ N, x ≤ 10} is the

163. 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.

164. ∀ a, b ϵ ℜ, ab = be is a

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

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

167. 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

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

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

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

171. A semi group is monoid if

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

173. If z = 1/Z, then

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

175. Associative law of multiplication

176. In polar form of complex number

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

178. The set {-1, 1} is

179. a.a¯¹ = a¯¹.a = 1 is a

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

181. Multiplicative inverse of “1” is

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

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

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

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

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

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

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

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

190. A subset of B x A is called a

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