NDA & NA Exam (I)- 2021 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2021 - Mathematics

NDA & NA Exam (I)- 2021 - Mathematics Defence Questions

21.
The equation \( \sin^{-1} x - \cos^{-1} x = \frac{\pi}{6} \) has
A.
no solution
B.
unique solution
C.
two solutions
D.
infinite number of solutions
😑 View Answer Error
ANSWER :
B. unique solution
22.
What is the value of the following?
\( (\sin 24^{\circ} + \cos 66^{\circ})(\sin 24^{\circ} - \cos 66^{\circ}) \)
A.
−1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
B. 0
23.
A chord subtends an angle \( 120^{\circ} \) at the centre of a unit circle. What is the length of the chord?
A.
\( \sqrt{2} - 1 \) units
B.
\( \sqrt{3} - 1 \) units
C.
\( \sqrt{2} \) units
D.
\( \sqrt{3} \) units
😑 View Answer Error
ANSWER :
D. \( \sqrt{3} \) units
24.
What is \( (1 + \cot \theta - cosec \theta)(1 + \tan \theta + \sec \theta) \) equal to?
A.
1
B.
2
C.
3
D.
4
😑 View Answer Error
ANSWER :
B. 2
25.
What is
\( \frac{1 + \tan^{2} \theta}{1 + \cot^{2} \theta} - \left(\frac{1 - \tan \theta}{1 - \cot \theta}\right)^{2} \)
equal to?
A.
0
B.
1
C.
\( 2 \tan \theta \)
D.
\( 2 \cot \theta \)
😑 View Answer Error
ANSWER :
A. 0
26.
What is the interior angle of a regular octagon of side length 2 cm?
A.
\( \frac{\pi}{2} \)
B.
\( \frac{3\pi}{4} \)
C.
\( \frac{3\pi}{5} \)
D.
\( \frac{2\pi}{3} \)
😑 View Answer Error
ANSWER :
B. \( \frac{3\pi}{4} \)
27.
If \( 7 \sin \theta + 24 \cos \theta = 25 \), then what is the value of \( (\sin \theta + \cos \theta) \)?
A.
1
B.
\( \frac{26}{25} \)
C.
\( \frac{6}{5} \)
D.
\( \frac{31}{25} \)
😑 View Answer Error
ANSWER :
D. \( \frac{31}{25} \)
28.
A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the top of the flagstaff is \( 75^{\circ} \). What is the height of the flagstaff?
A.
12 m
B.
9 m
C.
\( (6 + \sqrt{3}) \) m
D.
\( (6 + 3\sqrt{3}) \) m
😑 View Answer Error
ANSWER :
D. \( (6 + 3\sqrt{3}) \) m
29.
The shadow of a tower is found to be \( x \) metre longer, when the angle of elevation of the sun changes from \( 60^{\circ} \) to \( 45^{\circ} \). If the height of the tower is \( 5(3 + \sqrt{3}) \) m, then what is \( x \) equal to?
A.
8 m
B.
10 m
C.
12 m
D.
15 m
😑 View Answer Error
ANSWER :
B. 10 m
30.
If \( 3 \cos \theta = 4 \sin \theta \), then what is the value of \( \tan(45^{\circ} + \theta) \)?
A.
10
B.
7
C.
\( \frac{7}{5} \)
D.
\( \frac{7}{4} \)
😑 View Answer Error
ANSWER :
B. 7
Prev Next page