Sets, Relations & Functions · NDA previous year questions

433 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2025 27 questions

Q22025 · 14 Sept 2025
If A and B are non-empty subsets of a set, and $A^{c}$ and $B^{c}$ represent their complements, then which of the following is/are correct? I. $A - B = B^{c} - A^{c}$ II. $A - B^{c} = A^{c} - B$ Select the answer using the code given below.
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
Show answer
Answer: A
Q32025 · 14 Sept 2025
Let y=x! and z = (2x)! If (z / y) = 120 then what is the value of (3x)!?
1. A.362880
2. B.181440
3. C.90720
4. D.45360
Show answer
Answer: A
Q332025 · 14 Sept 2025
Passage
For the following two (02) items: Let ( 6 + 10 + 14 +... up to m terms) =( 1 + 3 + 5 + 7 +... up to n terms) where m < 25 and n < 25
What is the relation between m and n?
1. A. $n^{2} = m (m + 1)$
2. B. $n^{2} = m (m + 2)$
3. C. $n^{2} = 2 m (m + 1)$
4. D. $n^{2} = 2 m (m + 2)$
Show answer
Answer: D
Q342025 · 14 Sept 2025
Passage
For the following two (02) items: Let ( 6 + 10 + 14 +... up to m terms) =( 1 + 3 + 5 + 7 +... up to n terms) where m < 25 and n < 25
How many values of m are possible?
1. A.None
2. B.One
3. C.Two
4. D.More than two
Show answer
Answer: C
Q422025 · 14 Sept 2025
Set X contains 3n elements and set Y contains 2n elements, and they have n elements in common. How many elements does (X - Y) × (Y-X) have?
1. A. $5 n^{2}$
2. B. $4 n^{2}$
3. C. $3 n^{2}$
4. D. $2 n^{2}$
Show answer
Answer: D
Q432025 · 14 Sept 2025
Let A = {- 3, - 2, - 1, 0, 1, 2, 3} and B = {0, 1, 4, 9} How many elements does the subset of AB corresponding to the relation R = {(x, y) : |x| < y} have, where $x \in A$ and $y \in B$ ?
1. A.9
2. B.12
3. C.15
4. D.16
Show answer
Answer: C
Q762025 · 14 Sept 2025
For the following two (02) items: Consider the function $f (x) = \frac{x}{1 - x} (x > 0, x \neq = 1)$ What is $\frac{f ( x )}{f ( x + 1 )}$ equal to?
1. A. $- f (x^{2})$
2. B. $- f (x)$
3. C. $f (x^{2})$
4. D. $f (x - 1)$
Show answer
Answer: A
Q772025 · 14 Sept 2025
For the following two (02) items: Consider the function $f (x) = \frac{x}{1 - x} (x > 0, x \neq = 1)$ What is $(1 - x) f (x) + x f (x + 1)$ equal to?
1. A.-f(x)
2. B.f(x)
3. C.x
4. D.0
Show answer
Answer: D
Q812025 · 14 Sept 2025
For the following two (02) items: Consider the function $f (x) = 1 - 3 (x - 1)^{2}$ What is the domain of the function?
1. A. $(1, \infty)$
2. B. $(- \infty, \infty)$
3. C. $(0, \infty)$
4. D. $(- \infty, \infty) ∖ {1}$
Show answer
Answer: B
Q842025 · 14 Sept 2025
For the following two (02) items: Consider the function $f (x) = {4 (5^{x}), 8 k + x, x < 0 x \geq 0$ What is f'(-1) equal to?
1. A. $\frac{2}{5} ln 5$
2. B. $\frac{3}{5} ln 5$
3. C. $\frac{4}{5} ln 5$
4. D. $20 ln 5$
Show answer
Answer: C
Q852025 · 14 Sept 2025
For the following two (02) items: Let $u = \int e^{x} cos x d x$ and $v = \int e^{x} sin x d x$ . What is u + v equal to?
1. A. $- \frac{d u}{d x}$
2. B. $- \frac{d v}{d x}$
3. C. $\frac{d u}{d x}$
4. D. $\frac{d v}{d x}$
Show answer
Answer: D
Q862025 · 14 Sept 2025
For the following two (02) items: Let $u = \int e^{x} cos x d x$ and $v = \int e^{x} sin x d x$ . Consider the following: I. $\frac{d u}{d x} = - v$ II. $\frac{d v}{d x} = - u$ Which of the above is/are correct?
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
Show answer
Answer: D
Q872025 · 14 Sept 2025
For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on the interval [0, 5]. What is $\frac{d y}{d x}$ at x = 3.5 equal to?
1. A.0
2. B.1
3. C.2
4. D.3.5
Show answer
Answer: A
Q892025 · 14 Sept 2025
For the following two (02) items: Consider the function $f (x) = \frac{1 0 ^{x} - 1 0 ^{- x}}{1 0 ^{x} + 1 0 ^{- x}}$ What is $f \circ f \circ f \circ f \circ f (0)$ equal to?
1. A.0
2. B.1
3. C.5
4. D.10
Show answer
Answer: A
Q902025 · 14 Sept 2025
For the following two (02) items: Consider the function $f (x) = \frac{1 0 ^{x} - 1 0 ^{- x}}{1 0 ^{x} + 1 0 ^{- x}}$ What is the inverse of the function?
1. A. $lo g_{10} (2 x - 1)$
2. B. $\frac{1}{2} lo g_{10} (2 x - 1)$
3. C. $\frac{1}{4} lo g_{10} (\frac{2 x}{2 - x})$
4. D. $\frac{1}{2} lo g_{10} (\frac{1 + x}{1 - x})$
Show answer
Answer: D
Q922025 · 14 Sept 2025
What is $\int_{n}^{n + 1} (x - [x]) d x$ , where [.] is the greatest integer function and n is natural number?
1. A. $\frac{4 n + 1}{2}$
2. B. $\frac{2 n + 1}{2}$
3. C.1/2
4. D.1
Show answer
Answer: C
Q932025 · 14 Sept 2025
Consider the following statements: I. $y = x e^{2 x}$ is the solution of $\frac{d y}{d x} = y (2 + \frac{1}{x})$ II. $y = x ln ∣ x ∣ + c x$ is the solution of $\frac{d y}{d x} = \frac{x + y}{x}$ Which of the statements given above is/are correct?
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
Show answer
Answer: C
Q852025 · 13 Apr 2025
Passage
Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3|
What is the domain of the function (f(x))?
1. A.(0, ∞)
2. B.(3,∞)
3. C.(-∞, ∞)
4. D.(-∞.∞)\3
Show answer
Answer: C
Q882025 · 13 Apr 2025
Passage
Consider the following for the two (02) items that follow: Let f = {(1, 1), (2, 4), (3, 7), (4, 10)}
Consider the following statements: I. f is one-one function. II. f is onto function if the codomain is the set of natural numbers. Which of the statements given above is/are correct?
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
Show answer
Answer: A
Q892025 · 13 Apr 2025
Consider the following for the two (02) items that follow : Let the function $f (x) = x^{2} - 1$ What is $lim_{x \to 1} {f \circ f (x)}$ equal to?
1. A.-1
2. B.0
3. C.1
4. D.2
Show answer
Answer: A
Q932025 · 13 Apr 2025
Consider the following for the two (02) items that follow: Let the function $f (x) = x^{2} + 9$ What is $lim_{x \to 0} \frac{f ( x ) - 3}{f ( x ) + 7 - 4}$ equal to?
1. A.2/3
2. B.1
3. C.4/3
4. D.2
Show answer
Answer: C
Q952025 · 13 Apr 2025
Consider the following for the two (02) items that follow: The function f(x) satisfies $f (\frac{x}{y}) = \frac{f ( x )}{f ( y )}$ for all positive real values of x and y, and f(2) = 3 What is $f (16)$ equal to?
1. A.18
2. B.27
3. C.54
4. D.81
Show answer
Answer: D
Q962025 · 13 Apr 2025
Consider the following for the two (02) items that follow: The function f(x) satisfies $f (x), f (\frac{x}{y}) = \frac{f ( x )}{f ( y )}$ . for all positive real values of x and y, and f(2) = 3 What is $f (1) f (4)$ equal to?
1. A.4
2. B.8
3. C.9
4. D.18
Show answer
Answer: C
Q972025 · 13 Apr 2025
Consider the following for the two (02) items that follow: A function f is such that f(xy) = f(x + y) for all real values of x and y, and f(5) = 10 What is f(0) equal to?
1. A.0
2. B.1
3. C.5
4. D.10
Show answer
Answer: D
Q982025 · 13 Apr 2025
What is f(20)+f(-20) equal to?
1. A.0
2. B.10
3. C.20
4. D.40
Show answer
Answer: C