NDA & NA Exam (I) & (II)- 2020 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I) & (II)- 2020 - Mathematics

NDA & NA Exam (I) & (II)- 2020 - Mathematics Defence Questions

31.
Directions for the following three (03) items:
Read the following information and answer the three items that follow:
Let \( a \sin^{2} x + b \cos^{2} x = c \); \( b \sin^{2} y + a \cos^{2} y = d \) and \( p \tan x = q \tan y \).

What is \( \tan^{2} x \) equal to?
A.
\( \frac{c - b}{a - c} \)
B.
\( \frac{a - c}{c - b} \)
C.
\( \frac{c - a}{c - b} \)
D.
\( \frac{c - b}{c - a} \)
😑 View Answer Error
ANSWER :
A. \( \frac{c - b}{a - c} \)
32.
What is \( \frac{d - a}{b - d} \) equal to?
A.
\( \sin^{2} y \)
B.
\( \cos^{2} y \)
C.
\( \tan^{2} y \)
D.
\( \cot^{2} y \)
😑 View Answer Error
ANSWER :
C. \( \tan^{2} y \)
33.
What is \( \frac{p^{2}}{q^{2}} \) equal to?
A.
\( \frac{(b - c)(b - d)}{(a - d)(a - c)} \)
B.
\( \frac{(a - d)(c - a)}{(b - c)(d - b)} \)
C.
\( \frac{(d - a)(c - a)}{(b - c)(d - b)} \)
D.
\( \frac{(b - c)(b - d)}{(c - a)(a - d)} \)
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ANSWER :
B. \( \frac{(a - d)(c - a)}{(b - c)(d - b)} \)
34.
Directions for the following three (03) items:
Read the following information and answer the three items that follow:
Let \( t_{n} = \sin^{n} \theta + \cos^{n} \theta \).

What is \( \frac{t_{3} - t_{5}}{t_{5} - t_{7}} \) equal to?
A.
\( \frac{t_{1}}{t_{3}} \)
B.
\( \frac{t_{3}}{t_{5}} \)
C.
\( \frac{t_{5}}{t_{7}} \)
D.
\( \frac{t_{7}}{t_{3}} \)
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ANSWER :
A. \( \frac{t_{1}}{t_{3}} \)
35.
What is \( t_{1}^{2} - t_{2} \) equal to?
A.
\( \cos 2\theta \)
B.
\( \sin 2\theta \)
C.
\( 2 \cos \theta \)
D.
\( 2 \sin \theta \)
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ANSWER :
B. \( \sin 2\theta \)
36.
What is the value of \( t_{10} \), where \( \theta = 45^{\circ} \)?
A.
1
B.
\( \frac{1}{4} \)
C.
\( \frac{1}{16} \)
D.
\( \frac{1}{32} \)
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ANSWER :
C. \( \frac{1}{16} \)
37.
Directions for the following three (03) items:
Read the following information and answer the three items that follow:
Let \( \alpha = \beta = 15^{\circ} \).

What is the value of \( \sin \alpha + \cos \beta \)?
A.
\( \frac{1}{\sqrt{2}} \)
B.
\( \frac{1}{2\sqrt{2}} \)
C.
\( \frac{\sqrt{3}}{2\sqrt{2}} \)
D.
\( \frac{\sqrt{3}}{\sqrt{2}} \)
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ANSWER :
D. \( \frac{\sqrt{3}}{\sqrt{2}} \)
38.
What is the value of \( \sin 7\alpha - \cos 7\beta \)?
A.
\( \frac{1}{\sqrt{2}} \)
B.
\( \frac{1}{2\sqrt{2}} \)
C.
\( \frac{\sqrt{3}}{2\sqrt{2}} \)
D.
\( \frac{\sqrt{3}}{\sqrt{2}} \)
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ANSWER :
D. \( \frac{\sqrt{3}}{\sqrt{2}} \)
39.
What is \( \sin(\alpha + 1^{\circ}) + \cos(\beta + 1^{\circ}) \) equal to?
A.
\( \sqrt{3} \cos 1^{\circ} + \sin 1^{\circ} \)
B.
\( \sqrt{3} \cos 1^{\circ} - \sin 1^{\circ} \)
C.
\( \frac{1}{\sqrt{2}} (\sqrt{3} \cos 1^{\circ} - \sin 1^{\circ}) \)
D.
\( \frac{1}{\sqrt{2}} (\sqrt{3} \cos 1^{\circ} + \sin 1^{\circ}) \)
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ANSWER :
D. \( \frac{1}{\sqrt{2}} (\sqrt{3} \cos 1^{\circ} + \sin 1^{\circ}) \)
40.
If \( \sin x + \sin y = \cos y - \cos x \), where \( 0 < y < x < \frac{\pi}{2} \), then what is \( \tan \left(\frac{x - y}{2}\right) \) equal to?
A.
0
B.
\( \frac{1}{2} \)
C.
1
D.
2
😑 View Answer Error
ANSWER :
C. 1
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