Trigonometry · NDA previous year questions

273 questions asked across 17 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2021 27 questions

Q242021 · 14 Nov 2021
If $sin (A + B) = 1$ and $2 sin (A - B) = 1$ , where $0 < A, B < \frac{π}{2}$ , then what is $tan A : tan B$ equal to?
1. A. $1 : 2$
2. B. $2 : 1$
3. C. $1 : 3$
4. D. $3 : 1$
Show answer
Answer: D
Q282021 · 14 Nov 2021
Let $sin^{- 1} x + sin^{- 1} y + sin^{- 1} z = \frac{3 π}{2}$ for $0 \leq x, y, z \leq 1$ . What is the value of $x^{1000} + y^{1001} + z^{1002}$ ?
1. A.0
2. B.1
3. C.3
4. D.6
Show answer
Answer: C
Q292021 · 14 Nov 2021
Let $sin x + sin y = cos x + cos y$ for all $x, y \in R$ . What is $tan (\frac{x}{2} + \frac{y}{2})$ equal to?
1. A.1
2. B.2
3. C. $2$
4. D. $22$
Show answer
Answer: A
Q412021 · 14 Nov 2021
Let ABC be a triangle. If cos2A + cos2B + cos2C = -1 then which one of the following is correct?
1. A.sin A sin B sin C = 0
2. B.sin A sin B cos C = 0
3. C.cos A sin B sin C = 0
4. D.cos A cos B cos C = 0
Show answer
Answer: D
Q572021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. The equations of the sides AB, BC and CA of a triangle ABC are x - 2 = 0, y + 1 = 0 and x + 2y - 4 = 0 respectively.
What is the equation of the altitude through B on AC?
1. A.x - 3y + 1 = 0
2. B.x - 3y + 4 = 0
3. C.2x - y + 4 = 0
4. D.2x - y - 5 = 0
Show answer
Answer: D
Q722021 · 14 Nov 2021
If $y = cos x \cdot cos 4 x \cdot cos 8 x$ , then what is $\frac{1}{y} \frac{d y}{d x}$ at $x = \frac{π}{4}$ equal to?
1. A.-1
2. B.0
3. C.1
4. D.3
Show answer
Answer: A
Q172021 · 18 Apr 2021
If $tan A = \frac{1}{7}$ , then what is $cos 2 A$ equal to?
1. A. $\frac{24}{25}$
2. B. $\frac{18}{25}$
3. C. $\frac{12}{25}$
4. D. $\frac{6}{25}$
Show answer
Answer: A
Q182021 · 18 Apr 2021
The sides of a triangle are $m$ , $n$ and $m^{2} + n^{2} + mn$ . What is the sum of the acute angles of the triangle?
1. A. $4 5^{\circ}$
2. B. $6 0^{\circ}$
3. C. $7 5^{\circ}$
4. D. $9 0^{\circ}$
Show answer
Answer: B
Q192021 · 18 Apr 2021
What is the area of the triangle ABC with sides a = 10cm and c = 4cm angle B = 30°?
1. A. $16 c m^{2}$
2. B. $12 c m^{2}$
3. C. $10 c m^{2}$
4. D. $8 c m^{2}$
Show answer
Answer: C
Q312021 · 18 Apr 2021
If $tan x = - \frac{3}{4}$ and $x$ is in the second quadrant, then what is the value of $sin x \cdot cos x$ ?
1. A. $\frac{6}{25}$
2. B. $\frac{12}{25}$
3. C. $- \frac{6}{25}$
4. D. $- \frac{12}{25}$
Show answer
Answer: D
Q322021 · 18 Apr 2021
What is the value of the following? $cosec (\frac{7 π}{6}) sec (\frac{5 π}{3})$
1. A. $\frac{4}{3}$
2. B.4
3. C.-4
4. D. $- \frac{4}{3}$
Show answer
Answer: C
Q342021 · 18 Apr 2021
What is the value of the following? tan 31° tan 33° tan 35° _ _ _ _ _ tan 57° tan 59°
1. A.-1
2. B.0
3. C.1
4. D.2
Show answer
Answer: C
Q352021 · 18 Apr 2021
If then what is f(-1) + f(0) + f(1) equal to?
1. A.0
2. B.1
3. C.100
4. D.-100
Show answer
Answer: A
Q372021 · 18 Apr 2021
What is the value of the following? (sin 24° + cos 66°)(sin 24° - cos 66°)
1. A.-1
2. B.0
3. C.1
4. D.2
Show answer
Answer: B
Q392021 · 18 Apr 2021
What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?
1. A.1
2. B.2
3. C.3
4. D.4
Show answer
Answer: B
Q402021 · 18 Apr 2021
What is $\frac{1 + t a n ^{2} θ}{1 + c o t ^{2} θ} - (\frac{1 - t a n θ}{1 - c o t θ})^{2}$ equal to?
1. A.0
2. B.1
3. C. $2 tan θ$
4. D. $2 cot θ$
Show answer
Answer: A
Q412021 · 18 Apr 2021
What is the interior angle of a regular octagon of side length 2 cm?
1. A. $\frac{π}{2}$
2. B. $\frac{3 π}{4}$
3. C. $\frac{3 π}{5}$
4. D. $\frac{3 π}{8}$
Show answer
Answer: B
Q422021 · 18 Apr 2021
If 7 sinθ + 24 cosθ = 25, then what is the value of (sin θ + cos θ)?
1. A.1
2. B. $\frac{26}{25}$
3. C. $\frac{6}{5}$
4. D. $\frac{31}{25}$
Show answer
Answer: D
Q432021 · 18 Apr 2021
A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the top of the flagstaff is 75°. What is the height of the Flagstaff?
1. A.11 m
2. B.9 m
3. C.(6 + √3) m
4. D.(6 + 3√3) m
Show answer
Answer: D
Q442021 · 18 Apr 2021
The shadow of a tower is found to be x meter longer, when the angle of elevation of the sun changes from 60° to 45°. If the height of the tower is 5(3 + √3) m, then what is x equal to?
1. A.8 m
2. B.10 m
3. C.12 m
4. D.15 m
Show answer
Answer: B
Q452021 · 18 Apr 2021
If 3cosθ = 4sinθ, then what is the value of tan (45° + θ)?
1. A.10
2. B.7
3. C. $\frac{7}{2}$
4. D. $\frac{7}{4}$
Show answer
Answer: B
Q462021 · 18 Apr 2021
The smallest positive integer n for which where i = √-1, is
1. A.2
2. B.4
3. C.6
4. D.8
Show answer
Answer: A
Q472021 · 18 Apr 2021
The value of x, satisfying the equation $lo g_{c o s x} sin x = 1$ , where $0 < x < \frac{π}{2}$ , is
1. A. $\frac{π}{12}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{4}$
4. D. $\frac{π}{6}$
Show answer
Answer: C
Q602021 · 18 Apr 2021
What is cot 2x cot 4x - cot 4x cot 6x - cot 6x cot 2x equal to
1. A.-1
2. B.0
3. C.1
4. D.2
Show answer
Answer: C
Q792021 · 18 Apr 2021
Consider the following statements in respect of the function $f (x) = sin x$ : 1. $f (x)$ increases in the interval $(0, π)$ . 2. $f (x)$ decreases in the interval $(\frac{5 π}{2}, 3 π)$ . 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
Show answer
Answer: B