Trigonometry · NDA previous year questions

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2012 15 questions

Q202012 · 19 Aug 2012
The angles of a triangle are in AP and the least angle is $3 0^{\circ}$ . What is the greatest angle (in radian)?
1. A. $\frac{π}{2}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{4}$
4. D. $π$
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Answer: A
Q402012 · 19 Aug 2012
From the top of a lighthouse 70 m high with its base at sea level, the angle of depression of a boat is $1 5^{\circ}$ . The distance of the boat from the foot of the lighthouse is:
1. A. $70 (2 - 3) m$
2. B. $70 (2 + 3) m$
3. C. $70 (3 - 3) m$
4. D. $70 (3 + 3) m$
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Answer: B
Q352012 · 15 Apr 2012
The angle of elevation of a tower at a level ground is $3 0^{\circ}$ . The angle of elevation becomes $θ$ when moved 10 m towards the tower. If the height of tower is $53 m$ , then what is $θ$ equal to?
1. A. $4 5^{\circ}$
2. B. $6 0^{\circ}$
3. C. $7 5^{\circ}$
4. D.None of the above
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Answer: B
Q362012 · 15 Apr 2012
In a triangle ABC if the angles A, B, C are in AP, then which one of the following is correct?
1. A. $c = a + b$
2. B. $c^{2} = a^{2} + b^{2} - ab$
3. C. $a^{2} = b^{2} + c^{2} - b c$
4. D. $b^{2} = a^{2} + c^{2} - a c$
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Answer: D
Q372012 · 15 Apr 2012
If $sin^{- 1} 1 + sin^{- 1} \frac{4}{5} = sin^{- 1} x$ , then what is x equal to?
1. A.3/5
2. B.4/5
3. C.1
4. D.0
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Answer: Dropped in the final answer key (full marks to everyone)
Q382012 · 15 Apr 2012
If $cosec θ - cot θ = \frac{1}{3}$ where $θ \neq = 0$ , then what is the value of $cos θ$ ?
1. A.0
2. B. $\frac{3}{2}$
3. C. $\frac{1}{2}$
4. D. $\frac{1}{2}$
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Answer: C
Q392012 · 15 Apr 2012
From the top of a building of height h meter, the angle of depression of an object on the ground is $θ$ . What is the distance (in meter) of the object from the foot of the building?
1. A. $h cot θ$
2. B. $h tan θ$
3. C. $h cos θ$
4. D. $h sin θ$
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Answer: A
Q402012 · 15 Apr 2012
If $tan^{- 1} 2, tan^{- 1} 3$ are two angles of a triangle, then what is the third angle?
1. A. $tan^{- 1} 2$
2. B. $tan^{- 1} 4$
3. C. $π /4$
4. D. $π /3$
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Answer: C
Q462012 · 15 Apr 2012
The angle of elevation of the tip of a flag staff from a point 10 m due South of its base is $6 0^{\circ}$ . What is the height of the flag staff correct to the nearest meter?
1. A.15 m
2. B.16 m
3. C.17 m
4. D.18 m
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Answer: C
Q472012 · 15 Apr 2012
What is $\frac{s i n θ}{cosec θ} + \frac{c o s θ}{s e c θ}$ equal to?
1. A.1
2. B.1/2
3. C.1/3
4. D.2
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Answer: A
Q482012 · 15 Apr 2012
If $tan θ + sec θ = 4$ , then what is the value of $sin θ$ ?
1. A.8/17
2. B.8/15
3. C.15/17
4. D.23/32
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Answer: C
Q492012 · 15 Apr 2012
What is the value of $cos {cos^{- 1} \frac{4}{5} + cos^{- 1} \frac{12}{13}}$ ?
1. A.63/65
2. B.33/65
3. C.22/65
4. D.11/65
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Answer: B
Q502012 · 15 Apr 2012
What is the angle subtended by 1 m pole at a distance 1 km on the ground in sexagesimal measure?
1. A. $\frac{9}{50 π}$ degree
2. B. $\frac{9}{5 π}$ degree
3. C.3.4 minute
4. D.3.5 minute
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Answer: A
Q512012 · 15 Apr 2012
If $cot A \cdot cot B = 2$ , then what is the value of $cos (A + B) \cdot sec (A - B)$ ?
1. A.1/3
2. B.2/3
3. C.1
4. D. $- 1$
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Answer: A
Q1072012 · 15 Apr 2012
Consider the following statements : 1. $1^{\circ}$ in radian measure is less than 0.02 radians. 2. 1 radian in degree measure is greater than $4 5^{\circ}$ . 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
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Answer: C