Trigonometry · NDA previous year questions

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2024 22 questions

Q212024 · 1 Sept 2024
If $4 sin^{- 1} x + cos^{- 1} x = π$ , then what is $sin^{- 1} x + 4 cos^{- 1} x$ equal to?
1. A. $π /2$
2. B. $π$
3. C. $3 π /2$
4. D. $2 π$
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Answer: C
Q222024 · 1 Sept 2024
What is $cot^{2} (sec^{- 1} 2) + tan^{2} (cosec^{- 1} 3)$ equal to ?
1. A.11/12
2. B.11/24
3. C.7/24
4. D.1/24
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Answer: B
Q232024 · 1 Sept 2024
In a triangle ABC $\frac{a}{c o s A} = \frac{b}{c o s B} = \frac{c}{c o s C}$ . What is the area of the triangle if $a = 6 cm$ ?
1. A. $93 square cm$
2. B. $12 square cm$
3. C. $183 square cm$
4. D. $24 square cm$
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Answer: A
Q242024 · 1 Sept 2024
The roots of the equation $7 x^{2} - 6 x + 1 = 0$ are $tan α$ and $tan β$ , where $2 α$ and $2 β$ are the angles of a triangle. Which one of the following is correct?
1. A.The triangle is equilateral
2. B.The triangle is isosceles but not right-angled
3. C.The triangle is right-angled
4. D.The triangle is right-angled isosceles
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Answer: C
Q252024 · 1 Sept 2024
In a triangle ABC, ∠A = 75° and ∠B = 45°. What is 2a - b equal to?
1. A.c
2. B.√2c
3. C.2c
4. D.2√2c
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Answer: B
Q262024 · 1 Sept 2024
What is the number of solutions of the equation cot2x cot3x = 1 for 0 < x < π?
1. A.Only one
2. B.Only two
3. C.Only five
4. D.More than five
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Answer: C
Q272024 · 1 Sept 2024
What is the general solution of $cos^{100} x - sin^{100} x = 1$ ?
1. A. $nπ$
2. B. $(2 n + 1) π$
3. C. $2 nπ$
4. D. $(2 n + 1) π /2$
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Answer: A
Q282024 · 1 Sept 2024
In a triangle ABC tan A + tan B + tan C = k What is the value of cot A cot B cot C?
1. A.0.5 k
2. B.1/k
3. C.3/k
4. D. $1/ k^{3}$
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Answer: B
Q292024 · 1 Sept 2024
What is sin12° sin48° equal to?
1. A. $\frac{5 - 1}{4}$
2. B. $\frac{5 + 1}{4}$
3. C. $\frac{5 - 1}{8}$
4. D. $\frac{5 + 1}{8}$
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Answer: C
Q302024 · 1 Sept 2024
What is $\frac{c o s 1 7 ^{\circ} - s i n 1 7 ^{\circ}}{c o s 1 7 ^{\circ} + s i n 1 7 ^{\circ}}$ equal to
1. A. $tan 3 4^{\circ}$
2. B. $cot 3 4^{\circ}$
3. C. $tan 6 2^{\circ}$
4. D. $cot 6 2^{\circ}$
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Answer: D
Q312024 · 1 Sept 2024
Consider the following numbers : I. tan 22.5° II. cot 22.5° III. tan 22.5° - cot 22.5° How many of the above are irrational numbers?
1. A.None
2. B.Only one
3. C.Only two
4. D.All three
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Answer: C
Q322024 · 1 Sept 2024
If $\frac{x}{c o s θ} = \frac{y}{c o s ( \frac{2 π}{3} - θ )} = \frac{z}{c o s ( \frac{2 π}{3} + θ )}$ then what is $x + y + z$ equal to?
1. A.-1
2. B.0
3. C.1
4. D.3
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Answer: B
Q332024 · 1 Sept 2024
If p tan (θ - 30°) = q tan (θ + 120°), then what is (p + q) / (p - q) equal to?
1. A.sin 2θ
2. B.cos 2θ
3. C.2 sin 2θ
4. D.2 cos 2θ
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Answer: D
Q812024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $f \circ g (x) = cos^{2} x$ and $g \circ f (x) = ∣ cos x ∣$ . Which one of the following is f(x)?
1. A. $cos x$
2. B. $cos x^{2}$
3. C. $cos^{2} x$
4. D. $cos ∣ x ∣$
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Answer: C
Q822024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $f \circ g (x) = cos^{2} x$ and $g \circ f (x) = ∣ cos x ∣$ . Which one of the following is g(x)?
1. A. $x$
2. B. $∣ x ∣$
3. C. $x^{2}$
4. D. $x ∣ x ∣$
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Answer: A
Q832024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $f (x) = ∣ x ∣^{2} - ∣ x^{2} ∣$ What is $f (0.999) + f (1.001)$ equal to
1. A.-1
2. B.0
3. C.1
4. D.2
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Answer: B
Q932024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $f (t) = ln (t + 1 + t^{2})$ and $g (t) = tan (f (t))$ . Consider the following statements : I. f(t) is an odd function. II. g(t) is an odd function. 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
Q942024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $f (t) = ln (t + 1 + t^{2})$ and $g (t) = tan (f (t))$ . What is $\int_{- π}^{π} g (t) d t$ equal to
1. A.-1
2. B.0
3. C.1/2
4. D.1
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Answer: B
Q972024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $I = \int_{0}^{π /2} \frac{f ( x )}{g ( x )} d x$ , where $f (x) = sin x$ and $g (x) = sin x + cos x + 1$ What is $\int_{0}^{π /2} \frac{d x}{g ( x )}$ equal to
1. A. $\frac{l n 2}{2}$
2. B. $\frac{l n 2}{4}$
3. C. $ln 2$
4. D. $2 ln 2$
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Answer: C
Q982024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $I = \int_{0}^{π /2} \frac{f ( x )}{g ( x )} d x$ , where $f (x) = sin x$ and $g (x) = sin x + cos x + 1$ What is $\int_{0}^{π /2} \frac{d x}{g ( x )}$ equal to What is I equal to?
1. A. $\frac{π}{4} + ln 2$
2. B. $\frac{π}{4} - ln 2$
3. C. $\frac{π}{4} - \frac{l n 2}{2}$
4. D. $\frac{π}{4} + \frac{l n 2}{2}$
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Answer: C
Q992024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $2 \int \frac{x ^{2} - 1}{x ^{2} + 1} d x = U (x) V (x) - 3 ln {U (x) + V (x)} + c$ What is $∣ U^{2} (x) - V^{2} (x) ∣$ equal to?
1. A.0
2. B.1
3. C.2
4. D.3
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Answer: B
Q1002024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $2 \int \frac{x ^{2} - 1}{x ^{2} + 1} d x = U (x) V (x) - 3 ln {U (x) + V (x)} + c$ What is U(x) V(x) equal to?
1. A. $x^{2} + x^{4}$
2. B. $x + x^{3}$
3. C. $\frac{x ^{2} + x ^{4}}{2}$
4. D. $2 x^{2} + x^{4}$
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Answer: A