NDA & NA Exam (I)- 2019 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2019 - Mathematics

NDA & NA Exam (I)- 2019 - Mathematics Defence Questions

31.
What is the value of \( \frac{\sin 34^{\circ} \cos 236^{\circ} - \sin 56^{\circ} \sin 124^{\circ}}{\cos 28^{\circ} \cos 88^{\circ} + \cos 178^{\circ} \sin 208^{\circ}} \)?
A.
−2
B.
−1
C.
2
D.
1
😑 View Answer Error
ANSWER :
A. −2
32.
\( \tan 54^{\circ} \) can be expressed as
A.
\( \frac{\sin 9^{\circ} + \cos 9^{\circ}}{\sin 9^{\circ} - \cos 9^{\circ}} \)
B.
\( \frac{\sin 9^{\circ} - \cos 9^{\circ}}{\sin 9^{\circ} + \cos 9^{\circ}} \)
C.
\( \frac{\cos 9^{\circ} + \sin 9^{\circ}}{\cos 9^{\circ} - \sin 9^{\circ}} \)
D.
\( \frac{\sin 36^{\circ}}{\cos 36^{\circ}} \)
😑 View Answer Error
ANSWER :
C. \( \frac{\cos 9^{\circ} + \sin 9^{\circ}}{\cos 9^{\circ} - \sin 9^{\circ}} \)
33.
Consider the following for the next 03 (three) items:
If \( p = X \cos \theta - Y \sin \theta \), \( q = X \sin \theta + Y \cos \theta \) and \( p^{2} + 4pq + q^{2} = AX^{2} + BY^{2} \), \( 0 \leq \theta \leq \frac{\pi}{2} \).

What is the value of \( \theta \)?
A.
\( \frac{\pi}{2} \)
B.
\( \frac{\pi}{3} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{8} \)
😑 View Answer Error
ANSWER :
C. \( \frac{\pi}{4} \)
34.
What is the value of A?
A.
4
B.
3
C.
2
D.
1
😑 View Answer Error
ANSWER :
B. 3
35.
What is the value of B?
A.
−1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
A. −1
36.
Consider the following for the next 02 (two) items:
It is given that \( \cos(\theta - \alpha) = a \), \( \cos(\theta - \beta) = b \).

What is \( \cos(\alpha - \beta) \) equal to?
A.
\( ab + \sqrt{1 - a^{2}} \sqrt{1 - b^{2}} \)
B.
\( ab - \sqrt{1 - a^{2}} \sqrt{1 - b^{2}} \)
C.
\( a \sqrt{1 - b^{2}} - b \sqrt{1 - a^{2}} \)
D.
\( a \sqrt{1 - b^{2}} + b \sqrt{1 - a^{2}} \)
😑 View Answer Error
ANSWER :
A. \( ab + \sqrt{1 - a^{2}} \sqrt{1 - b^{2}} \)
37.
What is \( \sin^{2}(\alpha - \beta) + 2ab \cos(\alpha - \beta) \) equal to?
A.
\( a^{2} + b^{2} \)
B.
\( a^{2} - b^{2} \)
C.
\( b^{2} - a^{2} \)
D.
\( -(a^{2} + b^{2}) \)
😑 View Answer Error
ANSWER :
A. \( a^{2} + b^{2} \)
38.
If \( \sin \alpha + \cos \alpha = p \), then what is \( \cos^{2}(2\alpha) \) equal to?
A.
\( p^{2} \)
B.
\( p^{2} - 1 \)
C.
\( p^{2}(2 - p^{2}) \)
D.
\( p^{2} + 1 \)
😑 View Answer Error
ANSWER :
C. \( p^{2}(2 - p^{2}) \)
39.
What is the value of \( \sin^{-1} \frac{4}{5} + \sec^{-1} \frac{5}{4} - \frac{\pi}{2} \)?
A.
\( \pi \)
B.
\( \frac{\pi}{2} \)
C.
\( \frac{\pi}{3} \)
D.
0
😑 View Answer Error
ANSWER :
D. 0
40.
If \( \sin^{-1} \left(\frac{2p}{1 + p^{2}}\right) - \cos^{-1} \left(\frac{1 - q^{2}}{1 + q^{2}}\right) = \tan^{-1} \left(\frac{2x}{1 - x^{2}}\right) \), then what is x equal to?
A.
\( \frac{p - q}{1 + pq} \)
B.
\( \frac{p + q}{1 + pq} \)
C.
\( \frac{pq}{1 + pq} \)
D.
\( \frac{p + q}{1 - pq} \)
😑 View Answer Error
ANSWER :
A. \( \frac{p - q}{1 + pq} \)
Prev Next page