NDA & NA Exam (I)- 2015 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2015 - Mathematics

NDA & NA Exam (I)- 2015 - Mathematics Defence Questions

31.
Let \( \theta \) be a positive angle. If the number of degrees in \( \theta \) is divided by the number of radians in \( \theta \), then an irrational number \( \frac{180}{\pi} \) results. If the number of degrees in \( \theta \) is multiplied by the number of radians in \( \theta \), then an irrational number \( \frac{125\pi}{9} \) results. The angle \( \theta \) must be equal to
A.
\( 30^{\circ} \)
B.
\( 45^{\circ} \)
C.
\( 50^{\circ} \)
D.
\( 60^{\circ} \)
😑 View Answer Error
ANSWER :
C. \( 50^{\circ} \)
32.
In a triangle ABC, \( a = (1 + \sqrt{3}) \) cm, \( b = 2 \) cm and angle \( C = 60^{\circ} \). Then the other two angles are
A.
\( 45^{\circ} \) and \( 75^{\circ} \)
B.
\( 30^{\circ} \) and \( 90^{\circ} \)
C.
\( 105^{\circ} \) and \( 15^{\circ} \)
D.
\( 100^{\circ} \) and \( 20^{\circ} \)
😑 View Answer Error
ANSWER :
A. \( 45^{\circ} \) and \( 75^{\circ} \)
33.
For the next two (2) items that follow:
Let \( \alpha \) be the root of the equation \( 25\cos^{2}\theta + 5\cos\theta - 12 = 0 \), where \( \frac{\pi}{2} < \alpha < \pi \).

What is \( \tan\alpha \) equal to?
A.
\( -\frac{3}{4} \)
B.
\( \frac{3}{4} \)
C.
\( -\frac{4}{3} \)
D.
\( -\frac{4}{5} \)
😑 View Answer Error
ANSWER :
A. \( -\frac{3}{4} \)
34.
What is \( \sin 2\alpha \) equal to?
A.
\( \frac{24}{25} \)
B.
\( -\frac{24}{25} \)
C.
\( -\frac{5}{12} \)
D.
\( -\frac{21}{25} \)
😑 View Answer Error
ANSWER :
B. \( -\frac{24}{25} \)
35.
The angle of elevation of the top of a tower from a point 20 m away from its base is \( 45^{\circ} \). What is the height of the tower?
A.
10 m
B.
20 m
C.
30 m
D.
40 m
😑 View Answer Error
ANSWER :
B. 20 m
36.
The equation \( \tan^{-1}(1 + x) + \tan^{-1}(1 - x) = \frac{\pi}{2} \) is satisfied by
A.
\( x = 1 \)
B.
\( x = -1 \)
C.
\( x = 0 \)
D.
\( x = \frac{1}{2} \)
😑 View Answer Error
ANSWER :
C. \( x = 0 \)
37.
The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are \( 43^{\circ} \) and \( 47^{\circ} \) respectively. What is the height of the tower?
A.
40 m
B.
42 m
C.
45 m
D.
47 m
😑 View Answer Error
ANSWER :
B. 42 m
38.
\( (1 - \sin A + \cos A)^{2} \) is equal to
A.
\( 2(1 - \cos A)(1 + \sin A) \)
B.
\( 2(1 - \sin A)(1 + \cos A) \)
C.
\( 2(1 - \cos A)(1 - \sin A) \)
D.
None of the above
😑 View Answer Error
ANSWER :
B. \( 2(1 - \sin A)(1 + \cos A) \)
39.
What is \( \frac{\cos\theta}{1 - \tan\theta} + \frac{\sin\theta}{1 - \cot\theta} \) equal to?
A.
\( \sin\theta - \cos\theta \)
B.
\( \sin\theta + \cos\theta \)
C.
\( 2\sin\theta \)
D.
\( 2\cos\theta \)
😑 View Answer Error
ANSWER :
B. \( \sin\theta + \cos\theta \)
40.
For the next three (3) items that follow:
Consider \( x = 4\tan^{-1}\left(\frac{1}{5}\right) \), \( y = \tan^{-1}\left(\frac{1}{70}\right) \) and \( z = \tan^{-1}\left(\frac{1}{99}\right) \).

What is x equal to?
A.
\( \tan^{-1}\left(\frac{60}{119}\right) \)
B.
\( \tan^{-1}\left(\frac{120}{119}\right) \)
C.
\( \tan^{-1}\left(\frac{90}{169}\right) \)
D.
\( \tan^{-1}\left(\frac{170}{169}\right) \)
😑 View Answer Error
ANSWER :
B. \( \tan^{-1}\left(\frac{120}{119}\right) \)
Prev Next page