NDA & NA Exam (II)- 2014 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2014 - Mathematics

NDA & NA Exam (II)- 2014 - Mathematics Defence Questions

41.
The line \( y = \sqrt{3} \) meets the graph \( y = \tan x \), where \( x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \), in k points. What is k equal to?
A.
One
B.
Two
C.
Three
D.
Infinity
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ANSWER :
A. One
42.
Which one of the following is one of the solutions of the equation \( \tan 2\theta \cdot \tan\theta = 1 \)?
A.
\( \frac{\pi}{12} \)
B.
\( \frac{\pi}{6} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{3} \)
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ANSWER :
B. \( \frac{\pi}{6} \)
43.
For the next three (03) items that follow:
Given that \( 16\sin^{5} x = p\sin 5x + q\sin 3x + r\sin x \).

What is the value of p?
A.
1
B.
2
C.
−1
D.
−2
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ANSWER :
A. 1
44.
What is the value of q?
A.
3
B.
5
C.
10
D.
−5
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ANSWER :
D. −5
45.
What is the value of r?
A.
5
B.
8
C.
10
D.
−10
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ANSWER :
C. 10
46.
For the next two (02) items that follow:
Let \( S_{n} \) denote the sum of first n terms of an AP and \( 3S_{n} = S_{2n} \).

What is \( S_{3n} : S_{n} \) equal to?
A.
4 : 1
B.
6 : 1
C.
8 : 1
D.
10 : 1
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ANSWER :
B. 6 : 1
47.
What is \( S_{3n} : S_{2n} \) equal to?
A.
2 : 1
B.
3 : 1
C.
4 : 1
D.
5 : 1
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ANSWER :
A. 2 : 1
48.
What is the length of latus rectum of the ellipse \( 25x^{2} + 16y^{2} = 400 \)?
A.
\( \frac{25}{2} \)
B.
\( \frac{25}{4} \)
C.
\( \frac{16}{5} \)
D.
\( \frac{32}{5} \)
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ANSWER :
D. \( \frac{32}{5} \)
49.
For the next two (02) items that follow:
Consider the circles \( x^{2} + y^{2} + 2ax + c = 0 \) and \( x^{2} + y^{2} + 2by + c = 0 \).

What is the distance between the centres of the two circles?
A.
\( \sqrt{a^{2} + b^{2}} \)
B.
\( a^{2} + b^{2} \)
C.
a + b
D.
2(a + b)
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ANSWER :
A. \( \sqrt{a^{2} + b^{2}} \)
50.
The two circles touch each other if
A.
\( c = \sqrt{a^{2} + b^{2}} \)
B.
\( \frac{1}{c} = \frac{1}{a^{2}} + \frac{1}{b^{2}} \)
C.
\( c = \frac{1}{a^{2}} + \frac{1}{b^{2}} \)
D.
\( c = \frac{1}{a^{2} + b^{2}} \)
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ANSWER :
B. \( \frac{1}{c} = \frac{1}{a^{2}} + \frac{1}{b^{2}} \)
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