NDA & NA Exam (I)- 2022 - Mathematics Defence Question Paper

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NDA & NA Exam (I)- 2022 - Mathematics

NDA & NA Exam (I)- 2022 - Mathematics Defence Questions

21.
What is the maximum value of \( n \) such that \( 5^{n} \) divides \( (30! + 35!) \), where \( n \) is a natural number?
A.
4
B.
6
C.
7
D.
8
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ANSWER :
C. 7
22.
What is the value of
\( 2(2 \times 1) + 3(3 \times 2 \times 1) + 4(4 \times 3 \times 2 \times 1) + \ldots + 9(9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1) + 2 \)?
A.
\( 11! \)
B.
\( 10! \)
C.
\( 10 + 10! \)
D.
\( 11 + 10! \)
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ANSWER :
B. \( 10! \)
23.
If \( A = \{\{1, 2, 3\}\} \), then how many elements are there in the power set of \( A \)?
A.
1
B.
2
C.
4
D.
8
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ANSWER :
B. 2
24.
If \( a, b, c \) are in GP where \( a > 0, b > 0, c > 0 \), then which of the following are correct?
1. \( a^{2}, b^{2}, c^{2} \) are in GP
2. \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) are in GP
3. \( \sqrt{a}, \sqrt{b}, \sqrt{c} \) are in GP
Select the correct answer using the code given below:
A.
1 and 2 only
B.
2 and 3 only
C.
1 and 3 only
D.
1, 2 and 3
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ANSWER :
D. 1, 2 and 3
25.
If \( \frac{a + b}{2}, b, \frac{b + c}{2} \) are in HP, then which one of the following is correct?
A.
\( a, b, c \) are in AP
B.
\( a, b, c \) are in GP
C.
\( a + b, b + c, c + a \) are in GP
D.
\( a + b, b + c, c + a \) are in AP
😑 View Answer Error
ANSWER :
B. \( a, b, c \) are in GP
26.
What is value of \( \cot^{2} 15^{\circ} + \tan^{2} 15^{\circ} \)?
A.
12
B.
14
C.
\( 8\sqrt{3} \)
D.
4
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ANSWER :
B. 14
27.
In a triangle ABC, \( \sin A - \cos B - \cos C = 0 \) and angle C is acute. What is angle B equal to?
A.
\( \frac{\pi}{6} \)
B.
\( \frac{\pi}{4} \)
C.
\( \frac{\pi}{3} \)
D.
\( \frac{\pi}{2} \)
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ANSWER :
D. \( \frac{\pi}{2} \)
28.
If \( \alpha + \beta = \frac{\pi}{4} \) and \( 2 \tan \alpha = 1 \), then what is \( \tan 2\beta \) equal to?
A.
\( \frac{1}{3} \)
B.
\( \frac{2}{3} \)
C.
\( \frac{3}{4} \)
D.
\( \frac{3}{5} \)
😑 View Answer Error
ANSWER :
C. \( \frac{3}{4} \)
29.
If \( \tan(45^{\circ} + \theta) = 1 + \sin 2\theta \), where \( -\frac{\pi}{4} < \theta < \frac{\pi}{4} \), then what is the value of \( \cos 2\theta \)?
A.
0
B.
\( \frac{1}{2} \)
C.
1
D.
2
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ANSWER :
C. 1
30.
Let \( \sin 2\theta = \cos 3\theta \), where \( \theta \) is acute angle. What is the value of \( 1 + 4 \sin \theta \)? (given that \( \sin 18^{\circ} = \frac{\sqrt{5} - 1}{4} \))
A.
\( \sqrt{3} \)
B.
2
C.
\( \sqrt{5} \)
D.
3
😑 View Answer Error
ANSWER :
C. \( \sqrt{5} \)
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