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 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}
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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)
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| 3) 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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| 4) If n(A) = 40, n(B) = 60 and n(A∪B) = 20, then n(A∩B) is equal to _______
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| 5) 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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| 6) If {(x,4)}, (6,y)} represent an identity function, then (x,y) is _______ (A) (4,6) (B) (6,4) (C) (4,4) (D) (6,6)
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| 7) If {(5,15), (2,z)} represent a constant function, then the value of 'z' is _______ (A) 5 (B) 15 (C) 2 (D) 10
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| 8) If A = {8,9,10}, B = {4,5,6,7,8} and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___
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| 9) If the range of a function is a singleton set, then it is _____
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| 10) 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) = ∅ ( ) |
| 1) 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: 3 SOLUTION 1 : A|B = {p,q,r,s} {r,s,t,u} = {p,q} |
| 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: 2 SOLUTION 1 : B∖(A∪C) = (B∖A) ∩ (B∖C) Ans (B) ⇒ (B∖A) ∩ (B∖C) |
| 3) 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 |
| 4) If n(A) = 40, n(B) = 60 and n(A∪B) = 20, then n(A∩B) is equal to _______
Answer: 3
SOLUTION 1 : n(A∪B) = n(A) + n(B) - n(A∩B) 20 = 40 + 60 - n(A∩B) n(A∩B) = 100 - 20 n(A∩B) = 80 Ans (B) ⇒ 80 |
| 5) 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 |
| 6) If {(x,4)}, (6,y)} represent an identity function, then (x,y) is _______ (A) (4,6) (B) (6,4) (C) (4,4) (D) (6,6)
Answer: 2 SOLUTION 1 : If {(x,4)}, (6,y)} represent an identity function the x = 4, y = 6 (x,y) = (4,6) Ans (A) ⇒(4,6) |
| 7) If {(5,15), (2,p)} represent a constant function, then the value of 'p' is _______ (A) 5 (B) 15 (C) 2 (D) 10
Answer: 2 SOLUTION 1 : If {(5,15), (2,p)} represent a constant function, then the value of p = 15 Ans (B) ⇒ 15 |
| 8) If A = {8,9,10}, B = {4,5,6,7,8} 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 (8) = 8 - 2 = 6 ƒ (9) = 9 - 2 = 7 ƒ (10) = 10 - 2 = 8 Range of ƒ = {6,7,8} Ans (D) {6,7,8}. |
| 9) If the range of a function is a singleton set, then it is _____
Answer: 1 SOLUTION 1 : Range of a function is a singleton set ⇒ all elements of a domain is associated to unique element in the codomain. It is a constant function. Ans ⇒ a constant function. |
| 10) 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: 1 {(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) = ∅ |