NDA & NA Exam (I)- 2026 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2026 - Mathematics

NDA & NA Exam (I)- 2026 - Mathematics Defence Questions

31.
If \( \theta \) lies in the fourth quadrant and \( 3 \cot \theta + 4 = 0 \), then what is the value of \( \sin 2\theta + \cos 2\theta \)?
A.
\( -\frac{31}{25} \)
B.
\( -\frac{17}{25} \)
C.
0
D.
1
😑 View Answer Error
ANSWER :
B. \( -\frac{17}{25} \)
32.
If \( \cos \alpha + \cos \beta = 0 = \sin \alpha + \sin \beta \), \( \alpha \neq \beta \), then what is a value of \( \cos 2\alpha + \cos 2\beta + 2\cos(\alpha + \beta) \)?
A.
0
B.
1
C.
2
D.
4
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ANSWER :
A. 0
33.
In a triangle ABC, \( \sin A = \cos B + \cos C \), where \( B > C \), then what is \( \tan\left(\frac{B}{2}\right) + \cot\left(\frac{B}{2}\right) \) equal to?
A.
1
B.
\( \sqrt{2} \)
C.
\( \sqrt{3} \)
D.
2
😑 View Answer Error
ANSWER :
D. 2
34.
Consider the following in respect of inverse circular functions:
I. \( \sin^{-1}(-x) = -\sin^{-1} x \)
II. \( \cos^{-1}(-x) = \cos^{-1} x \)
III. \( \tan^{-1}(-x) = \pi - \tan^{-1} x \)
IV. \( \cot^{-1}(-x) = \pi - \cot^{-1} x \)
How many of the above are correct?
A.
One
B.
Two
C.
Three
D.
All the four
😑 View Answer Error
ANSWER :
B. Two
35.
What is \( \tan\left(2\tan^{-1}\frac{1}{5} - \frac{\pi}{4}\right) \) equal to?
A.
\( -\frac{7}{17} \)
B.
0
C.
\( \frac{1}{5} \)
D.
\( \frac{1}{7} \)
😑 View Answer Error
ANSWER :
A. \( -\frac{7}{17} \)
36.
The angles A, B and C of a triangle are in the ratio 1 : 1 : 4. If the longest side of the triangle is 3 units, then what is the perimeter of the triangle?
A.
\( 3 + \sqrt{3} \) units
B.
\( 3 + 2\sqrt{3} \) units
C.
\( 3 + 3\sqrt{3} \) units
D.
\( 6 + \sqrt{3} \) units
😑 View Answer Error
ANSWER :
B. \( 3 + 2\sqrt{3} \) units
37.
In a triangle ABC, if a, b and c are the lengths of the sides opposite to the angles A, B and C respectively, then what is \( \frac{\sin(A - B)}{\sin(A + B)} \) equal to?
A.
\( \frac{a^{2}}{a^{2} - b^{2}} \)
B.
\( \frac{a^{2}}{a^{2} + b^{2}} \)
C.
\( \frac{a^{2} - b^{2}}{c^{2}} \)
D.
\( \frac{a^{2} - b^{2}}{b^{2}} \)
😑 View Answer Error
ANSWER :
C. \( \frac{a^{2} - b^{2}}{c^{2}} \)
38.
What is the smallest positive x satisfying \( \log_{\frac{1}{\sqrt{2}}} \cos x + \log_{\frac{1}{\sqrt{2}}} \sin x = 2 \)?
A.
\( \frac{\pi}{2} \)
B.
\( \frac{\pi}{3} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{6} \)
😑 View Answer Error
ANSWER :
C. \( \frac{\pi}{4} \)
39.
A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of \( 67.5^{\circ} \). What is the height of the plane above the ground?
A.
\( 10\sqrt{2 + \sqrt{2}} \) km
B.
\( 10\sqrt{2 - \sqrt{2}} \) km
C.
\( 5\sqrt{2 + \sqrt{2}} \) km
D.
\( 5\sqrt{2 - \sqrt{2}} \) km
😑 View Answer Error
ANSWER :
C. \( 5\sqrt{2 + \sqrt{2}} \) km
40.
What is the length of the chord of a unit circle which subtends at the centre of the circle an angle of \( 45^{\circ} \)?
A.
\( 2\sqrt{2 + \sqrt{2}} \) units
B.
\( 2\sqrt{2 - \sqrt{2}} \) units
C.
\( \sqrt{2 + \sqrt{2}} \) units
D.
\( \sqrt{2 - \sqrt{2}} \) units
😑 View Answer Error
ANSWER :
D. \( \sqrt{2 - \sqrt{2}} \) units
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