Trigonometry · NDA previous year questions

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2011 17 questions

Q12011 · 21 Aug 2011
What is the value of $(1 + i)^{5} + (1 - i)^{5}$ where $i = - 1$ ?
1. A. $- 8$
2. B. $8$
3. C. $8 i$
4. D. $- 8 i$
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Answer: A
Q22011 · 21 Aug 2011
What is the value of $tan 9^{\circ} - tan 2 7^{\circ} - tan 6 3^{\circ} + tan 8 1^{\circ}$ ?
1. A.1
2. B.2
3. C.3
4. D.4
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Answer: D
Q32011 · 21 Aug 2011
If $x = y cos (\frac{2 π}{3}) = z cos (\frac{4 π}{3})$ , then what is $x y + y z + z x$ equal to?
1. A. $- 1$
2. B.0
3. C.1
4. D.2
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Answer: B
Q42011 · 21 Aug 2011
If $sin A + sin B + sin C = 3$ then what is $cos A + cos B + cos C$ equal to?
1. A. $- 1$
2. B.0
3. C.1
4. D.3
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Answer: B
Q52011 · 21 Aug 2011
At a point 15 m away from the base of a 15 m high house, the angle of elevation of the top is
1. A. $9 0^{\circ}$
2. B. $6 0^{\circ}$
3. C. $4 5^{\circ}$
4. D. $3 0^{\circ}$
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Answer: C
Q62011 · 21 Aug 2011
The simultaneous equations $3 x + 5 y = 7$ and $6 x + 10 y = 18$ have
1. A.no solution
2. B.infinitely many solutions
3. C.unique solution
4. D.any finite number of solutions
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Answer: A
Q72011 · 21 Aug 2011
What is the principal value of $sec^{- 1} (\frac{2}{3})$ ?
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: D
Q332011 · 21 Aug 2011
In any triangle ABC, the sides are 6 cm, 10 cm and 14 cm. Then the triangle is obtuse angled with the obtuse angle equal to
1. A. $15 0^{\circ}$
2. B. $13 5^{\circ}$
3. C. $12 0^{\circ}$
4. D. $10 5^{\circ}$
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Answer: C
Q342011 · 21 Aug 2011
In a triangle ABC, if $A = tan^{- 1} 2$ and $B = tan^{- 1} 3$ , then $C$ is equal to
1. A. $\frac{π}{3}$
2. B. $\frac{π}{4}$
3. C. $\frac{π}{6}$
4. D. $\frac{π}{2}$
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Answer: B
Q442011 · 21 Aug 2011
A tower of height 15 m stands vertically on the ground. From a point on the ground the angle of elevation of the top of the tower is found to be $3 0^{\circ}$ . What is the distance of the point from the foot of the tower ?
1. A. $153$ m
2. B. $103$ m
3. C. $53$ m
4. D.30 m
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Answer: A
Q452011 · 21 Aug 2011
If $tan A - tan B = x$ and $cot B - cot A = y$ , then what is $cot (A - B)$ equal to ?
1. A. $\frac{1}{y} - \frac{1}{x}$
2. B. $\frac{1}{x} - \frac{1}{y}$
3. C. $\frac{1}{x} + \frac{1}{y}$
4. D. $- \frac{1}{x} - \frac{1}{y}$
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Answer: C
Q722011 · 21 Aug 2011
In a triangle ABC, a = 8, b = 10 and c = 12. What is angle C equal to?
1. A.A/2
2. B.2A
3. C.3A
4. D.3A/2
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Answer: B
Q732011 · 21 Aug 2011
If $sin θ = x + \frac{a}{x}$ for all $x \in R - {0}$ , then which one of the following is correct?
1. A. $a \geq 4$
2. B. $a \geq \frac{1}{2}$
3. C. $a \leq \frac{1}{4}$
4. D. $a \leq \frac{1}{2}$
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Answer: C
Q742011 · 21 Aug 2011
The equation $tan^{4} x - 2 sec^{2} x + a^{2} = 0$ will have at least one real solution if
1. A. $∣ a ∣ \leq 4$
2. B. $∣ a ∣ \leq 2$
3. C. $∣ a ∣ \leq 3$
4. D.None of the above
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Answer: C
Q752011 · 21 Aug 2011
The sides a, b, c of a triangle ABC are in arithmetic progression and 'a' is the smallest side. What is cos A equal to?
1. A. $\frac{3 c - 4 b}{2 c}$
2. B. $\frac{3 c - 4 b}{2 b}$
3. C. $\frac{4 c - 3 b}{2 c}$
4. D. $\frac{3 b - 4 c}{2 c}$
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Answer: C
Q762011 · 21 Aug 2011
If $\int_{1}^{2} {k^{2} + (4 - 4 k) x + 4 x^{3}} d x \leq 12$ , then which one of the following is correct?
1. A. $k = 3$
2. B. $0 \leq k < 3$
3. C. $k \leq 4$
4. D. $k = 0$
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Answer: A
Q72011 · 17 Apr 2011
A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is $6 0^{\circ}$ . The angle of elevation is $3 0^{\circ}$ from a point at a distance $y$ metres from the bank. What is the height of the tree?
1. A. $y$ metres
2. B. $2 y$ metres
3. C. $\frac{3 y}{2}$ metres
4. D. $\frac{y}{2}$ metres
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Answer: C