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 the range of a function is a singleton set, then it is _____
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| 2) 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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| 3) If ƒ: A" B is a bijective function and if n(A) = 9, then n(B) is equal to ____
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| 4) 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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| 5) 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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| 6) 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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| 7) 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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| 8) If ƒ(x) = x2 + 3, then ƒ(-4) = ____
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| 9) If {(x,3)}, (7,y)} represent an identity function, then (x,y) is _______ (A) (3,7) (B) (7,3) (C) (3,3) (D) (7,7)
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| 10) If {(5,13), (4,l)} represent a constant function, then the value of 'l' is _______ (A) 5 (B) 13 (C) 4 (D) 10
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| 1) 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. |
| 2) 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: 2
SOLUTION 1 : A∖B ≠ A∩B Ans (B) ⇒ AB = A∩B |
| 3) If ƒ: A" B is a bijective function and if n(A) = 9, then n(B) is equal to ____
Answer: 2 SOLUTION 1 : ƒ: A" B is bijective ⇒ ƒ is one-one and onto. ƒ(A) = n(B) ⇒ n(B) = 9 Ans 9 |
| 4) 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 |
| 5) 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: 2 SOLUTION 1 : Intersection distribution over union A∪(B∩C) = (A∩B)∪(A∩C) Ans (B) (A∩B)∪(A∩C) |
| 6) 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: 4 SOLUTION 1 : By the definition, A∪B =A ⇔ B⊆A |
| 7) 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) |
| 8) If ƒ(x) = x2 + 3, then ƒ(-4) = ____
Answer: 2
SOLUTION 1 : ƒ (x) = x2 + 3 ƒ (-4) = (-4)2 + 3 = 16 + 3 = 19 Ans ⇒ 19 |
| 9) If {(x,3)}, (7,y)} represent an identity function, then (x,y) is _______ (A) (3,7) (B) (7,3) (C) (3,3) (D) (7,7)
Answer: 1 SOLUTION 1 : If {(x,3)}, (7,y)} represent an identity function the x = 3, y = 7 (x,y) = (3,7) Ans (A) ⇒(3,7) |
| 10) If {(5,13), (4,d)} represent a constant function, then the value of 'd' is _______ (A) 5 (B) 13 (C) 4 (D) 10
Answer: 4 SOLUTION 1 : If {(5,13), (4,d)} represent a constant function, then the value of d = 13 Ans (B) ⇒ 13 |