NDA & NA Exam (I)- 2025 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2025 - Mathematics

NDA & NA Exam (I)- 2025 - Mathematics Defence Questions

41.
Consider the following for the next three (03) items that follow:
Let \( p = \tan 2\alpha - \tan \alpha \) and \( q = \cot \alpha - \cot 2\alpha \).

What is \( \left(\frac{p}{q}\right) \) equal to?
A.
\( -\tan \alpha \tan 2\alpha \)
B.
\( -\cot \alpha \cot 2\alpha \)
C.
\( \tan \alpha \tan 2\alpha \)
D.
\( \cot \alpha \cot 2\alpha \)
😑 View Answer Error
ANSWER :
C. \( \tan \alpha \tan 2\alpha \)
42.
What is \( (p + q) \) equal to?
A.
\( \sec 4\alpha \)
B.
\( \mathrm{cosec} 4\alpha \)
C.
\( 2\sec 4\alpha \)
D.
\( 2\mathrm{cosec} 4\alpha \)
😑 View Answer Error
ANSWER :
D. \( 2\mathrm{cosec} 4\alpha \)
43.
What is \( \tan^{2} \alpha \) equal to?
A.
\( \frac{pq}{p + q} \)
B.
\( \frac{p + 2q}{p} \)
C.
\( \frac{p}{p + 2q} \)
D.
\( \frac{p}{2p + q} \)
😑 View Answer Error
ANSWER :
C. \( \frac{p}{p + 2q} \)
44.
Consider the following for the next two (02) items that follow:
Let \( 2\sin \alpha + \cos \alpha = 2 \), where \( 0 < \alpha < 90^{\circ} \).

What is \( \tan \alpha \) equal to?
A.
\( \frac{1}{2} \)
B.
1
C.
\( \frac{3}{4} \)
D.
2
😑 View Answer Error
ANSWER :
C. \( \frac{3}{4} \)
45.
What is \( 2\sin 2\alpha + \cos 2\alpha \) equal to?
A.
\( \frac{11}{10} \)
B.
\( \frac{11}{5} \)
C.
\( \frac{12}{5} \)
D.
\( \frac{13}{5} \)
😑 View Answer Error
ANSWER :
B. \( \frac{11}{5} \)
46.
Consider the following for the next two (02) items that follow:
In a triangle ABC, two sides BC and CA are in the ratio 2 : 1 and their opposite corresponding angles are in the ratio 3 : 1.

One of the angles of the triangle is
A.
\( 15^{\circ} \)
B.
\( 30^{\circ} \)
C.
\( 45^{\circ} \)
D.
\( 75^{\circ} \)
😑 View Answer Error
ANSWER :
B. \( 30^{\circ} \)
47.
Consider the following statements:
I. The triangle is right-angled.
II. One of the sides of the triangle is \( \sqrt{3} \) times the other.
III. The angles A, C and B of the triangle are in AP.
Which of the statements given above is/are correct?
A.
I only
B.
II and III only
C.
I and III only
D.
I, II and III
😑 View Answer Error
ANSWER :
D. I, II and III
48.
A man at M, standing 100 m away from the base (P) of a chimney of height 50 m, observes the angle of elevation of the highest point (Q) of the smoke to be \( 45^{\circ} \). The highest point of the chimney is at R. Further P, R and Q are in a straight line and the straight line is perpendicular to PM. What is the angle RMQ equal to?
A.
\( \tan^{-1}\left(\frac{1}{5}\right) \)
B.
\( \tan^{-1}\left(\frac{1}{3}\right) \)
C.
\( \tan^{-1}\left(\frac{2}{3}\right) \)
D.
\( \tan^{-1}\left(\frac{3}{4}\right) \)
😑 View Answer Error
ANSWER :
B. \( \tan^{-1}\left(\frac{1}{3}\right) \)
49.
If \( k \) is a root of \( x^{2} - 4x + 1 = 0 \), then what is \( \tan^{-1} k + \tan^{-1}\left(\frac{1}{k}\right) \) equal to?
A.
\( -\frac{\pi}{2} \)
B.
0
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{2} \)
😑 View Answer Error
ANSWER :
D. \( \frac{\pi}{2} \)
50.
If \( \tan^{-1} k + \tan^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{4} \), then what is the value of \( k \)?
A.
1
B.
\( \frac{1}{2} \)
C.
\( \frac{1}{3} \)
D.
\( \frac{1}{4} \)
😑 View Answer Error
ANSWER :
C. \( \frac{1}{3} \)
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