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

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

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

31.
If \( \tan \theta = -\frac{5}{12} \), then what can be the value of \( \sin \theta \)?
A.
\( \frac{5}{13} \) but cannot be \( -\frac{5}{13} \)
B.
\( -\frac{5}{13} \) but cannot be \( \frac{5}{13} \)
C.
\( \frac{5}{13} \) or \( -\frac{5}{13} \)
D.
None of the above
😑 View Answer Error
ANSWER :
C. \( \frac{5}{13} \) or \( -\frac{5}{13} \)
32.
What is the value of
\( \cos^{4} \frac{47\pi}{8} + \cos^{4} \frac{45\pi}{8} \)?
A.
\( \frac{3}{2} \)
B.
\( \frac{3}{4} \)
C.
\( \frac{3}{8} \)
D.
\( \frac{3}{16} \)
😑 View Answer Error
ANSWER :
B. \( \frac{3}{4} \)
33.
What is \( \sin^{2}\left(\frac{\pi}{4} + \theta\right) - \sin^{2}\left(\frac{\pi}{4} - \theta\right) \) equal to?
A.
\( \sin 2\theta \)
B.
\( \cos 2\theta \)
C.
\( 2 \sin \theta \)
D.
\( 2 \cos \theta \)
😑 View Answer Error
ANSWER :
A. \( \sin 2\theta \)
34.
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height \( h \). At a point on the plane the angles of elevation of the bottom and top of the flagstaff are \( \theta \) and \( 2\theta \) respectively. What is the height of the tower?
A.
\( h \cos \theta \)
B.
\( h \sin \theta \)
C.
\( h \cos 2\theta \)
D.
\( h \sin 2\theta \)
😑 View Answer Error
ANSWER :
C. \( h \cos 2\theta \)
35.
The shadow of a tower becomes \( x \) metre longer, when the angle of elevation of sun changes from \( 60^{\circ} \) to \( \theta \). If the height of the tower is \( \sqrt{3}x \) metre, then which one of the following is correct?
A.
\( 0^{\circ} < \theta < 30^{\circ} \)
B.
\( 30^{\circ} < \theta < 45^{\circ} \)
C.
\( 45^{\circ} < \theta < 60^{\circ} \)
D.
\( 60^{\circ} < \theta < 90^{\circ} \)
😑 View Answer Error
ANSWER :
B. \( 30^{\circ} < \theta < 45^{\circ} \)
36.
If \( \tan^{-1}\left(\frac{x}{2}\right) + \tan^{-1}\left(\frac{x}{3}\right) = \frac{\pi}{4} \), where \( 0 < x < \sqrt{6} \), then what is \( x \) equal to?
A.
1
B.
2
C.
3
D.
5
😑 View Answer Error
ANSWER :
A. 1
37.
If \( 3 \sin^{-1} x + \cos^{-1} x = \pi \), then what is \( x \) equal to?
A.
0
B.
\( \frac{1}{2} \)
C.
\( \frac{1}{\sqrt{2}} \)
D.
\( \frac{1}{3} \)
😑 View Answer Error
ANSWER :
C. \( \frac{1}{\sqrt{2}} \)
38.
If \( \tan \alpha + \tan \beta = 1 - \tan \alpha \tan \beta \), where \( \tan \alpha \tan \beta \neq 1 \), then which of the following is one of the values of \( (\alpha + \beta) \)?
A.
\( \frac{\pi}{6} \)
B.
\( \frac{\pi}{4} \)
C.
\( \frac{\pi}{3} \)
D.
\( \frac{\pi}{2} \)
😑 View Answer Error
ANSWER :
B. \( \frac{\pi}{4} \)
39.
If \( (1 + \tan \theta)(1 + \tan 9\theta) = 2 \), then what is the value of \( \tan(10\theta) \)?
A.
0
B.
1
C.
2
D.
Infinite
😑 View Answer Error
ANSWER :
B. 1
40.
What is the value of \( \sin 0^{\circ} + \sin 10^{\circ} + \sin 20^{\circ} + \sin 30^{\circ} + \ldots + \sin 360^{\circ} \)?
A.
−1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
B. 0
Prev Next page