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) 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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| 2) 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)
( ) |
| 3) 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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| 4) For any two sets A and B, {(A\B)∪(B\A)} ∩ (A∩B) is _____ (A) ∅ (B) (A∪B) (C) (A∩B) (D) A‘∩B‘
{(A\B)∪(B\A)} ∩ (A∩B) = {(A∪B)∖(A∩B)}∩(A∩B) = ∅ Ans (A) = ∅ ( ) |
| 5) If n(A) = 40, n(B) = 60 and n(A∪B) = 30, then n(A∩B) is equal to _______
( ) |
| 6) If A = {p,q,r,s}, B = {r,s,t,u} then A\B is ______ (A) {p,q} (B) {t,u} (C) {r,s} (D) {p,q,r,s}
( ) |
| 7) 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 ________
( ) |
| 8) If A = {7,8,9}, B = {3,4,5,6,7} and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___
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| 9) If {(7,14), (3,h)} represent a constant function, then the value of 'h' is _______ (A) 7 (B) 14 (C) 3 (D) 8
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| 10) If n[p(A)] = 32, then n(A) is _____ (A) 2 (B) 4 (C) 6 (D) 3
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| 1) 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: 3 SOLUTION 1 : Intersection distribution over union A∪(B∩C) = (A∩B)∪(A∩C) Ans (B) (A∩B)∪(A∩C) |
| 2) 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: 1 SOLUTION 1 : B∖(A∪C) = (B∖A) ∩ (B∖C) Ans (B) ⇒ (B∖A) ∩ (B∖C) |
| 3) 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: 3 SOLUTION 1 : By the definition, A∪B =A ⇔ B⊆A |
| 4) For any two sets A and B, {(A\B)∪(B\A)} ∩ (A∩B) is _____ (A) ∅ (B) (A∪B) (C) (A∩B) (D) A‘∩B‘
Answer: 2 {(A\B)∪(B\A)} ∩ (A∩B) = {(A∪B)∖(A∩B)}∩(A∩B) = ∅ Ans (A) = ∅ SOLUTION 1 : {(A∖B)∪(B∖A)} ∩ (A∩B) = {(A∪B)∖(A∩B)}∩(A∩B) = ∅ Ans (A) = ∅ |
| 5) If n(A) = 40, n(B) = 60 and n(A∪B) = 30, then n(A∩B) is equal to _______
Answer: 4
SOLUTION 1 : n(A∪B) = n(A) + n(B) - n(A∩B) 30 = 40 + 60 - n(A∩B) n(A∩B) = 100 - 30 n(A∩B) = 70 Ans (B) ⇒ 70 |
| 6) If A = {p,q,r,s}, B = {r,s,t,u} then A\B is ______ (A) {p,q} (B) {t,u} (C) {r,s} (D) {p,q,r,s}
Answer: 4 SOLUTION 1 : A|B = {p,q,r,s} {r,s,t,u} = {p,q} |
| 7) 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: 1 SOLUTION 1 : Each element in A is associated to a unique element in B. ƒ is one-one function. Ans (A) one-one |
| 8) If A = {7,8,9}, B = {3,4,5,6,7} and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___
Answer: 4 SOLUTION 1 : ƒ(x) = x - 2 ƒ (7) = 7 - 2 = 5 ƒ (8) = 8 - 2 = 6 ƒ (9) = 9 - 2 = 7 Range of ƒ = {5,6,7} Ans (D) {5,6,7}. |
| 9) If {(7,14), (3,s)} represent a constant function, then the value of 's' is _______ (A) 7 (B) 14 (C) 3 (D) 8
Answer: 4 SOLUTION 1 : If {(7,14), (3,s)} represent a constant function, then the value of s = 14 Ans (B) ⇒ 14 |
| 10) If n[p(A)] = 32, then n(A) is _____ (A) 2 (B) 4 (C) 6 (D) 3
Answer: 3 SOLUTION 1 : n[p(A)] = 32 2n(A) = 32 2n(A) = 25 n(A) = 5 Ans(A)5 |