Limits, Continuity & Derivatives · NDA previous year questions

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2026 34 questions

Q42026 · 12 Apr 2026
Consider the following statements in respect of the function $f (x) = x$ in the interval $(- 1, 1)$ : I. The function attains maximum value. II. The function attains minimum value. 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
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Answer: D
Q52026 · 12 Apr 2026
If $A$ and $B$ are acute angles such that $2 A + 2 B = π$ , then what is the maximum value of $sin A \cdot sin B$ ?
1. A. $\frac{1}{2}$
2. B. $\frac{1}{4}$
3. C. $\frac{3}{4}$
4. D.1
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Answer: A
Q62026 · 12 Apr 2026
In a triangle $A B C$ , $sin A = cos B + cos C$ then what is $tan (\frac{B}{2}) + cot (\frac{B}{2})$ equal to ?
1. A.1
2. B. $2$
3. C. $3$
4. D.2
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Answer: D
Q72026 · 12 Apr 2026
If $cos α + cos β = 0 = sin α + sin β, α \neq = β$ then what is a value of $cos 2 α + cos 2 β + 2 cos (α + β)$ ?
1. A.0
2. B.1
3. C.2
4. D.4
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Answer: A
Q82026 · 12 Apr 2026
If $θ$ lies in the fourth quadrant and $3 cot θ + 4 = 0$ , then what is the value of $sin 2 θ + cos 2 θ$ ?
1. A. $- \frac{31}{25}$
2. B. $- \frac{17}{25}$
3. C.0
4. D.1
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Answer: B
Q92026 · 12 Apr 2026
$cos x + 3 sin x$ is maximum when $x$ is equal to
1. A. $\frac{π}{2}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{4}$
4. D. $\frac{π}{6}$
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Answer: B
Q102026 · 12 Apr 2026
If $cos θ = \frac{1}{3}$ , then what is the value of $sin (\frac{θ}{2}) sin (\frac{3 θ}{2})$ ?
1. A. $\frac{5}{9}$
2. B. $\frac{7}{9}$
3. C. $\frac{10}{9}$
4. D. $\frac{11}{9}$
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Answer: A
Q112026 · 12 Apr 2026
If $x = sec θ - tan θ$ and $y = csc θ + cot θ$ , then which one of the following is correct ?
1. A. $x + y - x y - 1 = 0$
2. B. $x - y + x y + 1 = 0$
3. C. $x + y + x y - 1 = 0$
4. D. $x - y + x y - 1 = 0$
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Answer: B
Q122026 · 12 Apr 2026
If $α$ and $β$ are complementary angles such that $α - β = \frac{π}{6}$ and $m tan β = n tan α$ , then what is $(\frac{m + n}{m - n})$ equal to ?
1. A.2
2. B. $\frac{2}{3}$
3. C.1
4. D. $\frac{1}{3}$
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Answer: A
Q132026 · 12 Apr 2026
If $2 sec 4 β = tan 2 α + cot 2 α$ , then which one of the following is a possible value of $(α + β)$ ?
1. A. $\frac{π}{2}$
2. B. $\frac{π}{4}$
3. C. $\frac{π}{6}$
4. D. $\frac{π}{8}$
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Answer: D
Q142026 · 12 Apr 2026
What is the smallest positive $x$ satisfying $lo g_{s i n x} cos x + lo g_{c o s x} sin x = 2$ ?
1. A. $\frac{π}{2}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{4}$
4. D. $\frac{π}{6}$
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Answer: C
Q152026 · 12 Apr 2026
1. A. $\frac{a ^{2}}{c ^{2} - b ^{2}}$
2. B. $\frac{a ^{2}}{c ^{2} + b ^{2}}$
3. C. $\frac{a ^{2} - b ^{2}}{c ^{2}}$
4. D. $\frac{a ^{2} - b ^{2}}{b ^{2}}$
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Answer: C
Q162026 · 12 Apr 2026
The angles $A, B$ and $C$ of a triangle are in the ratio $1 : 1 : 4$ . If the longest side of the triangle is 3 units, then what is the perimeter of the triangle ?
1. A. $3 + 3$ units
2. B. $3 + 23$ units
3. C. $3 + 33$ units
4. D. $6 + 3$ units
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Answer: B
Q232026 · 12 Apr 2026
For a given $k$ , what is the minimum value of $x^{2} + k x + k^{2}$ ?
1. A.0
2. B. $\frac{k ^{2}}{4}$
3. C. $\frac{3 k ^{2}}{4}$
4. D. $\frac{k ^{2}}{2}$
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Answer: C
Q322026 · 12 Apr 2026
What is the maximum number of points of intersection of 5 circles ?
1. A.10
2. B.15
3. C.20
4. D.25
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Answer: C
Q332026 · 12 Apr 2026
Passage: Let $u$ be a positive integer and $f$ be a real number lying between 0 and 1. Further, $(2 + 1)^{10} = u + f$ and $(2 - 1)^{10} = v$ . Question: What is the value of $uv$ ?
1. A.1
2. B.2
3. C. $0 < uv < 1$
4. D. $1 < uv < 2$
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Answer: C
Q342026 · 12 Apr 2026
Passage: Let $u$ be a positive integer and $f$ be a real number lying between 0 and 1. Further, $(2 + 1)^{10} = u + f$ and $(2 - 1)^{10} = v$ . Question: What is the value of $u$ ?
1. A.9725
2. B.6971
3. C.6726
4. D.6725
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Answer: D
Q352026 · 12 Apr 2026
Passage: Let $u$ be a positive integer and $f$ be a real number lying between 0 and 1. Further, $(2 + 1)^{10} = u + f$ and $(2 - 1)^{10} = v$ . Question: What is the value of $(v + f)$ ?
1. A.2
2. B.1
3. C. $0 \cdot 5$
4. D. $0 \cdot 25$
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Answer: B
Q362026 · 12 Apr 2026
Passage: Let $u$ be a positive integer and $f$ be a real number lying between 0 and 1. Further, $(2 + 1)^{10} = u + f$ and $(2 - 1)^{10} = v$ . Question: What is the multiplicative inverse of $(2 + 1)^{20}$ ?
1. A. $v$
2. B. $v^{2} - 1$
3. C. $v^{2}$
4. D. $v^{2} + 1$
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Answer: C
Q372026 · 12 Apr 2026
Passage: Let $u$ be a positive integer and $f$ be a real number lying between 0 and 1. Further, $(2 + 1)^{10} = u + f$ and $(2 - 1)^{10} = v$ . Question: Consider the following statements : I. $(u + v + f)$ is an integer. II. $(f + v)$ is an integer. 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
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Answer: C
Q382026 · 12 Apr 2026
What is the greatest value of $r$ satisfying the inequality $^{15} C_{r + 1} > 2 \times^{15} C_{r}$ ?
1. A.2
2. B.3
3. C.4
4. D.5
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Answer: C
Q752026 · 12 Apr 2026
Passage: Let $f (x) = tan (x^{2})$ and $g (x) = x ∣ x ∣$ for $∣ x ∣ < \frac{π}{2}$ . Question: If $q (x) = f \circ g (x)$ , then which of the following statements is/are correct ? I. $q (x)$ is continuous at $x = 0$ . II. $q (x)$ is differentiable at $x = 0$ . 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: C
Q762026 · 12 Apr 2026
Passage: Let $f (x) = tan (x^{2})$ and $g (x) = x ∣ x ∣$ for $∣ x ∣ < \frac{π}{2}$ . Question: If $p (x) = f (x) g (x)$ , then which of the following statements is/are correct ? I. $p (x)$ is continuous at $x = 0$ . II. $p (x)$ is differentiable at $x = 0$ . 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: C
Q772026 · 12 Apr 2026
1. A. $- 1$
2. B. $- \frac{1}{3}$
3. C. $\frac{1}{3}$
4. D.1
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Answer: A
Q782026 · 12 Apr 2026
1. A. $- 1$
2. B. $- \frac{1}{3}$
3. C. $\frac{1}{3}$
4. D.1
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Answer: C