NDA & NA Exam (II)- 2022 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (II)- 2022 - Mathematics

NDA & NA Exam (II)- 2022 - Mathematics Defence Questions

41.
What is \( \frac{AB}{\sin C} \) equal to?
A.
17 m
B.
\( \frac{50}{3} \) m
C.
\( \frac{40}{3} \) m
D.
16 m
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ANSWER :
B. \( \frac{50}{3} \) m
42.
What is \( \cos A + \cos B + \cos C \) equal to?
A.
1
B.
\( \frac{41}{25} \)
C.
\( \frac{37}{25} \)
D.
\( \frac{33}{25} \)
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ANSWER :
D. \( \frac{33}{25} \)
43.
Directions (Qn. 43-45): Consider the following for the next three (03) items that follow:
There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance \( x \) and Q is at a distance \( y \) from the foot of the tower \( (x > y) \). The angles of elevation of the top of the tower from P and Q are \( 15^{\circ} \) and \( 75^{\circ} \) respectively.

At what height is the top of the tower above the ground level?
A.
\( \frac{x - y}{2\sqrt{3}} \)
B.
\( \frac{x - y}{4\sqrt{3}} \)
C.
\( \frac{x - y}{4} \)
D.
\( \frac{x - y}{2} \)
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ANSWER :
A. \( \frac{x - y}{2\sqrt{3}} \)
44.
If \( \theta \) is the inclination of the tower to the horizontal, then what is \( \cot \theta \) equal to?
A.
\( 2 + \frac{\sqrt{3}(x - y)}{x + y} \)
B.
\( 2 - \frac{\sqrt{3}(x - y)}{x + y} \)
C.
\( 2 + \frac{\sqrt{3}(x + y)}{x - y} \)
D.
\( 2 - \frac{\sqrt{3}(x + y)}{x - y} \)
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ANSWER :
D. \( 2 - \frac{\sqrt{3}(x + y)}{x - y} \)
45.
What is the length of the tower?
A.
\( \frac{x - y}{2\sqrt{3}} \sqrt{1 + \left\{2 + \frac{\sqrt{3}(x + y)}{x - y}\right\}^{2}} \)
B.
\( \frac{x - y}{2\sqrt{3}} \sqrt{1 + \left\{2 - \frac{\sqrt{3}(x + y)}{x - y}\right\}^{2}} \)
C.
\( \frac{x - y}{4\sqrt{3}} \sqrt{1 + \left\{2 + \frac{\sqrt{3}(x + y)}{x - y}\right\}^{2}} \)
D.
\( \frac{x - y}{4\sqrt{3}} \sqrt{1 + \left\{2 - \frac{\sqrt{3}(x + y)}{x - y}\right\}^{2}} \)
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ANSWER :
B. \( \frac{x - y}{2\sqrt{3}} \sqrt{1 + \left\{2 - \frac{\sqrt{3}(x + y)}{x - y}\right\}^{2}} \)
46.
What is the value of \( cosec\left(-\frac{73\pi}{3}\right) \)?
A.
\( \frac{2}{\sqrt{3}} \)
B.
\( -\frac{2}{\sqrt{3}} \)
C.
2
D.
−2
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ANSWER :
B. \( -\frac{2}{\sqrt{3}} \)
47.
What is the value of
\( \cos\left(\frac{5\pi}{17}\right) + \cos\left(\frac{7\pi}{17}\right) + 2 \cos\left(\frac{11\pi}{17}\right) \cos\left(\frac{\pi}{17}\right) \)?
A.
0
B.
1
C.
\( 4 \cos\left(\frac{6\pi}{17}\right) \cos\left(\frac{\pi}{17}\right) \)
D.
\( 4 \cos\left(\frac{11\pi}{17}\right) \cos\left(\frac{\pi}{17}\right) \)
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ANSWER :
A. 0
48.
What is the value of \( \tan\left(\frac{3\pi}{8}\right) \)?
A.
\( \sqrt{2} - 1 \)
B.
\( \sqrt{2} + 1 \)
C.
\( 1 - \sqrt{2} \)
D.
\( -(\sqrt{2} + 1) \)
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ANSWER :
B. \( \sqrt{2} + 1 \)
49.
What is \( \tan^{-1} \cot(cosec^{-1} 2) \) equal to?
A.
\( \frac{\pi}{8} \)
B.
\( \frac{\pi}{6} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{3} \)
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ANSWER :
D. \( \frac{\pi}{3} \)
50.
In a triangle ABC, \( a = 4, b = 3, c = 2 \). What is \( \cos 3C \) equal to?
A.
\( \frac{7}{128} \)
B.
\( \frac{11}{128} \)
C.
\( \frac{7}{64} \)
D.
\( \frac{11}{64} \)
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ANSWER :
A. \( \frac{7}{128} \)
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