Sets, Relations & Functions · NDA previous year questions

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2026 14 questions

Q12026 · 12 Apr 2026
If $1 - lo g_{10} 2 = lo g_{10} (5^{x} + 4^{x} + 3^{x} + 2^{x} + 1)$ , then what is a value of $x$ ?
1. A.10
2. B.5
3. C.1
4. D.0
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Answer: D
Q22026 · 12 Apr 2026
Passage: Consider the curves $y = x^{2}$ and $y = 2∣ x ∣$ . Question: What is the number of points of intersection of the curves ?
1. A.4
2. B.3
3. C.2
4. D.None
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Answer: B
Q32026 · 12 Apr 2026
If $2 f (x) + f (1 - x) = x$ , then what is $f (x)$ equal to ?
1. A. $x - 1$
2. B. $x - (\frac{1}{2})$
3. C. $2 x$
4. D. $2 x - 1$
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Answer: B
Q392026 · 12 Apr 2026
A set $S$ contains $(2 n + 1)$ elements. If the number of subsets of $S$ which contain at most $n$ elements is 1024, then what is the value of $n$ ?
1. A.10
2. B.8
3. C.6
4. D.5
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Answer: D
Q612026 · 12 Apr 2026
Let $R$ be a relation on the set $N$ of natural numbers defined by $R = {(x, y) : x, y \in N and x = y^{3}}$ . Which of the following statements is/are correct ? I. $R$ is symmetric relation II. $R$ is transitive relation 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
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Answer: D
Q622026 · 12 Apr 2026
Let $A$ and $B$ be two sets. For some set $C$ , both $A \cap C$ and $B \cap C$ are empty sets and $A \cup C = B \cup C$ . Which of the following is/are true ? I. $C = φ$ II. $A = B$ III. $A \cup B = C$ Select the answer using the code given below :
1. A.I only
2. B.II only
3. C.I and II only
4. D.I, II and III
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Answer: B
Q632026 · 12 Apr 2026
What is $(((A \cap B) \cup (A - B)) - ((A \cap B) \cup (B - A))) \cup A$ equal to ?
1. A. $φ$
2. B. $A$
3. C. $B$
4. D. $A \cup B$
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Answer: B
Q642026 · 12 Apr 2026
What is $tan [2 tan^{- 1} \frac{1}{2} - \frac{π}{4}]$ equal to ?
1. A. $- 7$
2. B.0
3. C. $\frac{1}{5}$
4. D. $\frac{1}{7}$
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Answer: D
Q652026 · 12 Apr 2026
Consider the following in respect of inverse circular functions : I. $sin^{- 1} (- x) = - sin^{- 1} x$ II. $cos^{- 1} (- x) = cos^{- 1} x$ III. $tan^{- 1} (- x) = π - tan^{- 1} x$ IV. $cot^{- 1} (- x) = π - cot^{- 1} x$ How many of the above are correct ?
1. A.One
2. B.Two
3. C.Three
4. D.All the four
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Answer: B
Q812026 · 12 Apr 2026
Passage: Let $(e^{y})^{x} - y = 0$ , where $y$ is a function of $x$ whose domain is $(0, 10]$ . Question: What is $\frac{d y}{d x}$ equal to, given that $y = y_{0}$ when $x = 1$ ?
1. A. $- \frac{y _{0}}{1 + e ^{y_{0}}}$
2. B. $- \frac{y _{0} e ^{y_{0}}}{1 + e ^{y_{0}}}$
3. C. $\frac{y _{0} e ^{y_{0}}}{1 + e ^{y_{0}}}$
4. D. $\frac{y _{0} e ^{y_{0}}}{1 - e ^{y_{0}}}$
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Answer: D
Q822026 · 12 Apr 2026
1. A. $\frac{y}{1 - x y}$
2. B. $\frac{y}{1 + x y}$
3. C. $\frac{y ^{2}}{1 - x y}$
4. D. $\frac{y ^{2}}{1 + x y}$
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Answer: C
Q832026 · 12 Apr 2026
If $4 y = x + x^{2} + 4$ , then what is $x^{2} + 4 \frac{d y}{d x}$ equal to ?
1. A. $\frac{y}{4}$
2. B. $y$
3. C. $2 y$
4. D. $4 y$
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Answer: D
Q842026 · 12 Apr 2026
1. A. ${x \leq 2} \cup {x \geq 3}$
2. B. ${x < 2} \cup {x > 3}$
3. C. $(2, 3)$
4. D. $[2, 3]$
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Answer: C
Q852026 · 12 Apr 2026
1. A. ${x \leq 2} \cup {x \geq 3}$
2. B. ${x < 2} \cup {x > 3}$
3. C. $(2, 3)$
4. D. $[2, 3]$
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Answer: B