NDA & NA Exam (II)- 2014 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2014 - Mathematics

NDA & NA Exam (II)- 2014 - Mathematics Defence Questions

31.
What is \( \sqrt{1 + \sin 2\theta} \) equal to?
A.
\( \cos\theta - \sin\theta \)
B.
\( \cos\theta + \sin\theta \)
C.
\( 2\cos\theta + \sin\theta \)
D.
\( \cos\theta + 2\sin\theta \)
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ANSWER :
B. \( \cos\theta + \sin\theta \)
32.
A lamp post stands on a horizontal plane. From a point situated at a distance 150 m from its foot, the angle of elevation of the top is \( 30^{\circ} \). What is the height of the lamp post?
A.
50 m
B.
\( 50\sqrt{3} \) m
C.
\( \frac{50}{\sqrt{3}} \) m
D.
100 m
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ANSWER :
B. \( 50\sqrt{3} \) m
33.
If \( \cot A = 2 \) and \( \cot B = 3 \), then what is the value of \( A + B \)?
A.
\( \frac{\pi}{6} \)
B.
\( \pi \)
C.
\( \frac{\pi}{2} \)
D.
\( \frac{\pi}{4} \)
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ANSWER :
D. \( \frac{\pi}{4} \)
34.
What is \( \sin^{2} 66\frac{1}{2}^{\circ} - \sin^{2} 23\frac{1}{2}^{\circ} \) equal to?
A.
\( \sin 47^{\circ} \)
B.
\( \cos 47^{\circ} \)
C.
\( 2\sin 47^{\circ} \)
D.
\( 2\cos 47^{\circ} \)
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ANSWER :
B. \( \cos 47^{\circ} \)
35.
What is \( \sin^{-1}\frac{3}{5} + \sin^{-1}\frac{4}{5} \) equal to?
A.
\( \frac{\pi}{2} \)
B.
\( \frac{\pi}{3} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{6} \)
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ANSWER :
A. \( \frac{\pi}{2} \)
36.
What is \( \frac{\cos 7x - \cos 3x}{\sin 7x - 2\sin 5x + \sin 3x} \) equal to?
A.
\( \tan x \)
B.
\( \cot x \)
C.
\( \tan 2x \)
D.
\( \cot 2x \)
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ANSWER :
B. \( \cot x \)
37.
In a triangle ABC, \( c = 2 \), \( A = 45^{\circ} \), \( a = 2\sqrt{2} \), then what is C equal to?
A.
\( 30^{\circ} \)
B.
\( 15^{\circ} \)
C.
\( 45^{\circ} \)
D.
None of the above
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ANSWER :
A. \( 30^{\circ} \)
38.
In a triangle ABC, \( \sin A - \cos B = \cos C \), then what is B equal to?
A.
\( \pi \)
B.
\( \frac{\pi}{3} \)
C.
\( \frac{\pi}{2} \)
D.
\( \frac{\pi}{4} \)
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ANSWER :
C. \( \frac{\pi}{2} \)
39.
If \( \frac{\sin(x+y)}{\sin(x-y)} = \frac{a+b}{a-b} \), then what is \( \frac{\tan x}{\tan y} \) equal to?
A.
\( \frac{b}{a} \)
B.
\( \frac{a}{b} \)
C.
ab
D.
1
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ANSWER :
B. \( \frac{a}{b} \)
40.
If \( \sin A \sin(60^{\circ} - A) \sin(60^{\circ} + A) = k \sin 3A \), then what is k equal to?
A.
\( \frac{1}{4} \)
B.
\( \frac{1}{2} \)
C.
1
D.
4
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ANSWER :
A. \( \frac{1}{4} \)
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