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 ƒ: A" B is a bijective function and if n(A) = 17, then n(B) is equal to ____
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| 2) If the range of a function is a singleton set, then it is _____
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| 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) 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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| 5) 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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| 6) 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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| 7) If {(5,14), (3,r)} represent a constant function, then the value of 'r' is _______ (A) 5 (B) 14 (C) 3 (D) 8
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| 8) 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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| 9) If {(x,3)}, (9,y)} represent an identity function, then (x,y) is _______ (A) (3,9) (B) (9,3) (C) (3,3) (D) (9,9)
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| 10) If ƒ(x) = x2 + 9, then ƒ(-7) = ____
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| 1) If ƒ: A" B is a bijective function and if n(A) = 17, then n(B) is equal to ____
Answer: 1 SOLUTION 1 : ƒ: A" B is bijective ⇒ ƒ is one-one and onto. ƒ(A) = n(B) ⇒ n(B) = 17 Ans 17 |
| 2) If the range of a function is a singleton set, then it is _____
Answer: 3 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. |
| 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) 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} |
| 5) 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: 1 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}. |
| 6) 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: 4 SOLUTION 1 : B∖(A∪C) = (B∖A) ∩ (B∖C) Ans (B) ⇒ (B∖A) ∩ (B∖C) |
| 7) If {(5,14), (3,j)} represent a constant function, then the value of 'j' is _______ (A) 5 (B) 14 (C) 3 (D) 8
Answer: 1 SOLUTION 1 : If {(5,14), (3,j)} represent a constant function, then the value of j = 14 Ans (B) ⇒ 14 |
| 8) 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: 4 SOLUTION 1 : Each element in A is associated to a unique element in B. ƒ is one-one function. Ans (A) one-one |
| 9) If {(x,3)}, (9,y)} represent an identity function, then (x,y) is _______ (A) (3,9) (B) (9,3) (C) (3,3) (D) (9,9)
Answer: 1 SOLUTION 1 : If {(x,3)}, (9,y)} represent an identity function the x = 3, y = 9 (x,y) = (3,9) Ans (A) ⇒(3,9) |
| 10) If ƒ(x) = x2 + 9, then ƒ(-7) = ____
Answer: 1
SOLUTION 1 : ƒ (x) = x2 + 9 ƒ (-7) = (-7)2 + 9 = 49 + 9 = 58 Ans ⇒ 58 |