NDA & NA Exam (I)- 2018 - Mathematics Defence Question Paper

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NDA & NA Exam (I)- 2018 - Mathematics

NDA & NA Exam (I)- 2018 - Mathematics Defence Questions

31.
What is the sum of all two-digit numbers which when divided by 3 leave 2 as the remainder?
A.
1565
B.
1585
C.
1635
D.
1655
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ANSWER :
C. 1635
32.
If 0 < a < 1, the value of \( \log_{10} a \) is negative. This is justified by
A.
Negative power of 10 is less than 1
B.
Negative power of 10 is greater than 1
C.
Negative power of 10 is positive
D.
Negative power of 10 is negative
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ANSWER :
A. Negative power of 10 is less than 1
33.
The third term of a GP is 3. What is the product of the first five terms?
A.
216
B.
226
C.
243
D.
Cannot be determined due to insufficient data
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ANSWER :
C. 243
34.
If x, \( \frac{3}{2} \), z are in AP and x, 3, z are in GP, then which one of the following will be in HP?
A.
x, 6, z
B.
x, 4, z
C.
x, 2, z
D.
x, 1, z
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ANSWER :
A. x, 6, z
35.
What is the value of the sum \( \sum_{n=2}^{11} (i^{n} + i^{n+1}) \), where \( i = \sqrt{-1} \)?
A.
i
B.
2i
C.
−2i
D.
1 + i
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ANSWER :
C. −2i
36.
If \( \sin x = \frac{1}{\sqrt{5}} \), \( \sin y = \frac{1}{\sqrt{10}} \), where \( 0 < x < \frac{\pi}{2} \), \( 0 < y < \frac{\pi}{2} \), then what is (x + y) equal to?
A.
\( \pi \)
B.
\( \frac{\pi}{2} \)
C.
\( \frac{\pi}{4} \)
D.
0
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ANSWER :
C. \( \frac{\pi}{4} \)
37.
What is \( \frac{\sin 5x - \sin 3x}{\cos 5x + \cos 3x} \) equal to?
A.
sin x
B.
cos x
C.
tan x
D.
cot x
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ANSWER :
C. tan x
38.
What is \( \sin 105^{\circ} + \cos 105^{\circ} \) equal to?
A.
\( \sin 50^{\circ} \)
B.
\( \cos 50^{\circ} \)
C.
\( \frac{1}{\sqrt{2}} \)
D.
0
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ANSWER :
C. \( \frac{1}{\sqrt{2}} \)
39.
In a triangle ABC, if a = 2, b = 3 and \( \sin A = \frac{2}{3} \), then what is the angle B equal to?
A.
\( \frac{\pi}{4} \)
B.
\( \frac{\pi}{2} \)
C.
\( \frac{\pi}{3} \)
D.
\( \frac{\pi}{6} \)
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ANSWER :
B. \( \frac{\pi}{2} \)
40.
What is the principal value of \( \sin^{-1}\left(\sin\frac{2\pi}{3}\right) \)?
A.
\( \frac{\pi}{4} \)
B.
\( \frac{\pi}{2} \)
C.
\( \frac{\pi}{3} \)
D.
\( \frac{2\pi}{3} \)
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ANSWER :
C. \( \frac{\pi}{3} \)
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