Written Instructions:
For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
| 1) If n(A) = 20, n(B) = 60 and n(A∪B) = 30, then n(A∩B) is equal to _______
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| 2) Let A = {1,3,4,7,11}, B = {-1,1,2,5,7,9} and ƒ: A"B be given by ƒ = {(1,-1),(3,2),(4,1),(7,5),(11,9)}. Then ƒis ________
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| 3) For any three sets A,B and C, B\(A∪C) is ______ (A) (A\B) ∩ (A\C) (B) (B∖A) ∩ (B∖C) (C) (B\A) ∩ (A\C) (C) (A\B) ∩ (B\C)
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| 4) If ƒ: A" B is a bijective function and if n(A) = 10, then n(B) is equal to ____
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| 5) Which one of the following is not true (A) A∖B = A∩B‘ (B) A\B = A∩B (C) A\B = (A∪B)∩B‘ (D) = A\B = (A∪B)\B
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| 6) For any three sets A,B and C, A∪(B∩C) is ______ (A) (A∪B)∪(B∩C) (B) (A∩B)∪(A∩C) (C) A∪(BC) (D) (A∪B)∩(B∪C)
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| 7) If A = {6,7,8}, B = {2,3,4,5,6} and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___
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| 8) For any two sets P and Q, P∩Q is ______ (A) {x:x∈P or x∈Q} (B) {x:x∈ P and∉Q} (C) {x:x∈P and x∈Q} (D) {x:x∉ P and∈Q}
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| 9) If {(5,12), (2,x)} represent a constant function, then the value of 'x' is _______ (A) 5 (B) 12 (C) 2 (D) 8
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| 10) For the sets A and B, A∪B =A if and only if __________ (A) B⊆A (B) A⊆B (C) A≠B (D) A∩B
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| 1) If n(A) = 20, n(B) = 60 and n(A∪B) = 30, then n(A∩B) is equal to _______
Answer: 3
SOLUTION 1 : n(A∪B) = n(A) + n(B) - n(A∩B) 30 = 20 + 60 - n(A∩B) n(A∩B) = 80 - 30 n(A∩B) = 50 Ans (B) ⇒ 50 |
| 2) Let A = {1,3,4,7,11}, B = {-1,1,2,5,7,9} and ƒ: A"B be given by ƒ = {(1,-1),(3,2),(4,1),(7,5),(11,9)}. Then ƒis ________
Answer: 3 SOLUTION 1 : Each element in A is associated to a unique element in B. ƒ is one-one function. Ans (A) one-one |
| 3) For any three sets A,B and C, B\(A∪C) is ______ (A) (A\B) ∩ (A\C) (B) (B∖A) ∩ (B∖C) (C) (B\A) ∩ (A\C) (C) (A\B) ∩ (B\C)
Answer: 3 SOLUTION 1 : B∖(A∪C) = (B∖A) ∩ (B∖C) Ans (B) ⇒ (B∖A) ∩ (B∖C) |
| 4) If ƒ: A" B is a bijective function and if n(A) = 10, then n(B) is equal to ____
Answer: 3 SOLUTION 1 : ƒ: A" B is bijective ⇒ ƒ is one-one and onto. ƒ(A) = n(B) ⇒ n(B) = 10 Ans 10 |
| 5) Which one of the following is not true (A) A∖B = A∩B‘ (B) A\B = A∩B (C) A\B = (A∪B)∩B‘ (D) = A\B = (A∪B)\B
Answer: 4
SOLUTION 1 : A∖B ≠ A∩B Ans (B) ⇒ AB = A∩B |
| 6) For any three sets A,B and C, A∪(B∩C) is ______ (A) (A∪B)∪(B∩C) (B) (A∩B)∪(A∩C) (C) A∪(BC) (D) (A∪B)∩(B∪C)
Answer: 4 SOLUTION 1 : Intersection distribution over union A∪(B∩C) = (A∩B)∪(A∩C) Ans (B) (A∩B)∪(A∩C) |
| 7) If A = {6,7,8}, B = {2,3,4,5,6} and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___
Answer: 3 SOLUTION 1 : ƒ(x) = x - 2 ƒ (6) = 6 - 2 = 4 ƒ (7) = 7 - 2 = 5 ƒ (8) = 8 - 2 = 6 Range of ƒ = {4,5,6} Ans (D) {4,5,6}. |
| 8) For any two sets P and Q, P∩Q is ______ (A) {x:x∈P or x∈Q} (B) {x:x∈ P and∉Q} (C) {x:x∈P and x∈Q} (D) {x:x∉ P and∈Q}
Answer: 4 SOLUTION 1 : P∩Q = {x:x∈P and x∈Q} |
| 9) If {(5,12), (2,i)} represent a constant function, then the value of 'i' is _______ (A) 5 (B) 12 (C) 2 (D) 8
Answer: 4 SOLUTION 1 : If {(5,12), (2,i)} represent a constant function, then the value of i = 12 Ans (B) ⇒ 12 |
| 10) For the sets A and B, A∪B =A if and only if __________ (A) B⊆A (B) A⊆B (C) A≠B (D) A∩B
Answer: 2 SOLUTION 1 : By the definition, A∪B =A ⇔ B⊆A |