Trigonometry · NDA previous year questions

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2010 17 questions

Q312010 · 22 Aug 2010
One of the angles of a triangle is $1/2$ radian and the other is $9 9^{\circ}$ . What is the third angle in radian measure?
1. A. $\frac{9 π - 10}{π}$
2. B. $\frac{90 π - 100}{7 π}$
3. C. $\frac{90 π - 10}{π}$
4. D.None of the above
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Answer: D
Q322010 · 22 Aug 2010
Two poles are 10 m and 20 m high. The line joining their tops makes an angle of $1 5^{\circ}$ with the horizontal. What is the approximate distance between the poles?
1. A.35.3 m
2. B.37.3 m
3. C.41 m
4. D.44 m
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Answer: B
Q332010 · 22 Aug 2010
What is the value of $sin^{- 1} \frac{4}{5} + 2 tan^{- 1} \frac{1}{3}$ ?
1. A. $\frac{π}{3}$
2. B. $\frac{π}{2}$
3. C. $\frac{π}{4}$
4. D. $\frac{π}{6}$
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Answer: B
Q342010 · 22 Aug 2010
What is $(\frac{s e c 1 8 ^{\circ}}{s e c 14 4 ^{\circ}} + \frac{cosec 1 8 ^{\circ}}{cosec 14 4 ^{\circ}})$ equal to?
1. A. $sec 1 8^{\circ}$
2. B. $cosec 1 8^{\circ}$
3. C. $- sec 1 8^{\circ}$
4. D. $- cosec 1 8^{\circ}$
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Answer: A
Q352010 · 22 Aug 2010
If $α$ and $β$ are positive angles such that $α + β = \frac{π}{4}$ , then what is $(1 + tan α) (1 + tan β)$ equal to?
1. A.0
2. B.1
3. C.2
4. D.3
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Answer: C
Q362010 · 22 Aug 2010
What is the value of $(sin 5 0^{\circ} - sin 7 0^{\circ} + sin 1 0^{\circ})$ ?
1. A.1
2. B. $\frac{1}{2}$
3. C. $\frac{3}{2}$
4. D.0
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Answer: D
Q372010 · 22 Aug 2010
If $cos A + cos B = m$ and $sin A + sin B = n$ , where $m, n \neq = 0$ , then what is $sin (A + B)$ equal to?
1. A. $\frac{mn}{m ^{2} + n ^{2}}$
2. B. $\frac{2 mn}{m ^{2} + n ^{2}}$
3. C. $\frac{m ^{2} + n ^{2}}{2 mn}$
4. D. $\frac{mn}{m + n}$
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Answer: B
Q382010 · 22 Aug 2010
If $y = sec^{2} θ + cos^{2} θ$ , where $0 < θ < \frac{π}{2}$ , then which one of the following is correct?
1. A. $y = 0$
2. B. $0 \leq y \leq 2$
3. C. $y \geq 2$
4. D.None of the above
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Answer: C
Q392010 · 22 Aug 2010
If $tan A = 3/4$ and $tan B = - 12/5$ , then how many values can $cot (A - B)$ have depending on the actual values of $A$ and $B$ ?
1. A.1
2. B.2
3. C.3
4. D.4
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Answer: A
Q402010 · 22 Aug 2010
What is the value of $sin 1 5^{\circ} sin 7 5^{\circ}$ ?
1. A. $1/4$
2. B. $1/8$
3. C. $1/16$
4. D.1
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Answer: A
Q912010 · 22 Aug 2010
From the top of a lighthouse $120$ m above the sea, the angle of depression of a boat is $1 5^{\circ}$ . What is the distance of the boat from the lighthouse?
1. A. $400$ m
2. B. $421$ m
3. C. $444$ m
4. D. $460$ m
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Answer: Dropped in the final answer key (full marks to everyone)
Q922010 · 22 Aug 2010
What is the value of $\frac{s i n θ + c o s θ - t a n θ}{s e c θ + cosec θ - c o t θ}$ when $θ = \frac{3 π}{4}$ ?
1. A. $0$
2. B. $1$
3. C. $- 1$
4. D.None of the above
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Answer: B
Q932010 · 22 Aug 2010
What is the value of $sin 292 \frac{1}{2}^{\circ}$ ?
1. A. $\frac{1}{3} 2 + 3$
2. B. $- \frac{1}{3} 2 - 3$
3. C. $\frac{1}{2} 2 + 2$
4. D. $- \frac{1}{2} 2 + 2$
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Answer: D
Q742010 · 18 Apr 2010
The angle of elevation of the tip of a flag post from a point $5 m$ away from its base is $7 5^{\circ}$ . What is the approximate height of the flag post?
1. A. $15 m$
2. B. $17 m$
3. C. $19 m$
4. D. $21 m$
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Answer: C
Q802010 · 18 Apr 2010
In a triangle ABC, $B C = 39$ , $A C = 5$ and $A B = 7$ . What is the measure of the angle A?
1. A. $\frac{π}{4}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{2}$
4. D. $\frac{π}{6}$
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Answer: B
Q1012010 · 18 Apr 2010
A balloon is pumped at the rate of $4 c m^{3}$ per second. What is the rate at which its surface area increases when its radius is $4 cm$ ?
1. A. $1 c m^{2} /sec$
2. B. $2 c m^{2} /sec$
3. C. $3 c m^{2} /sec$
4. D. $4 c m^{2} /sec$
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Answer: B
Q1022010 · 18 Apr 2010
What is the value of $\frac{1 + t a n 1 5 ^{\circ}}{1 - t a n 1 5 ^{\circ}}$ ?
1. A.1
2. B. $\frac{1}{2}$
3. C. $\frac{1}{3}$
4. D. $3$
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Answer: D