Sets, Relations & Functions · NDA previous year questions

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2021 13 questions

Q232021 · 14 Nov 2021
What is the period of the function $f (x) = ln (2 + sin^{2} x)$ ?
1. A. $\frac{π}{2}$
2. B. $π$
3. C. $2 π$
4. D. $3 π$
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Answer: B
Q372021 · 14 Nov 2021
Consider the following statements in respect of sets: 1. The union over the intersection of sets is distributive. 2. The complement of the union of two sets is equal to the intersection of their complements. 3. If the difference between the two sets is equal to the empty set, then the two sets must be equal. Which of the above statements are correct?
1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3
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Answer: A
Q382021 · 14 Nov 2021
Consider three sets X, Y and Z having 6, 5 and 4 elements respectively. All these 15 elements are distinct. Let S = (X - Y) ∪ Z. How many proper subsets does S have?
1. A.255
2. B.256
3. C.1023
4. D.1024
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Answer: C
Q392021 · 14 Nov 2021
Consider the following statements in respect of relations and functions: 1. All relations are functions but all functions are not relations. 2. A relation from A to B is a subset of Cartesian product A × B. 3. A relation in A is a subset of Cartesian product A × A. Which of the above statements are correct?
1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3
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Answer: B
Q432021 · 14 Nov 2021
Suppose set A consists of first 250 natural numbers that are multiple of 3 and set B consists of first 200 even natural numbers. How many elements does A ∪ B have?
1. A.342
2. B.364
3. C.384
4. D.400
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Answer: C
Q732021 · 14 Nov 2021
Let f(x) be a polynomial function such that $f \circ f (x) = x^{4}$ . What is f'(1) equal to ?
1. A.0
2. B.1
3. C.2
4. D.4
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Answer: C
Q792021 · 14 Nov 2021
What is the range of the function f(x) = 1 - sinx defined on entire real line?
1. A.(0, 2)
2. B.[0, 2]
3. C.(-1, 1)
4. D.[-1, 1]
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Answer: B
Q202021 · 18 Apr 2021
Consider the following statements: 1. A = {1, 3, 5} and B = {2, 4, 7} are equivalent sets. 2. A = {1, 5, 9} and B = {1, 5, 5, 9, 9} are equal sets. Which of the above statements is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: C
Q212021 · 18 Apr 2021
Consider the following statements: 1. The null set is a subset of every set. 2. Every set is a subset of itself. 3. If a set has 10 elements, then its power set will have 1024 elements. Which of the above statements are correct?
1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3
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Answer: D
Q222021 · 18 Apr 2021
Let R be a relation defined as xRy if and only if 2x + 3y = 20, where x, y ∈ N. How many elements of the form (x, y) are there in R?
1. A.2
2. B.3
3. C.4
4. D.6
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Answer: B
Q232021 · 18 Apr 2021
Consider the following statements: 1. A function f : Z → Z, defined by f(x) = x + 1, is one-one as well as onto. 2. A function f : N → N, defined by f(x) = x + 1, is one-one but not onto. Which of the above statements is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: C
Q712021 · 18 Apr 2021
The average of a set of 15 observations is recorded, but later it is found that for one observation, the digit in the tens place was wrongly recorded as 8 instead of 3. After correcting the observation, the average is
1. A.reduced by $\frac{1}{3}$
2. B.increased by $\frac{10}{3}$
3. C.reduced by $\frac{10}{3}$
4. D.reduced by 50
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Answer: C
Q802021 · 18 Apr 2021
What is the domain of the function $f (x) = 3^{x}$ ?
1. A. $(- \infty, \infty)$
2. B. $(0, \infty)$
3. C. $[0, \infty)$
4. D. $(- \infty, \infty) - {0}$
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Answer: A