CDS Exam (II)- 2025 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2025 - Elementary Mathematics

CDS Exam (II)- 2025 - Elementary Mathematics Defence Questions

41.
For the following two (02) items:
Let \( p \sin^{2} \alpha + q \cos^{2} \alpha = m \), \( q \sin^{2} \beta + p \cos^{2} \beta = n \); \( p \neq m, n \) and \( q \neq m, n \).

What is \( \left(\frac{\tan \alpha}{\tan \beta}\right)^{2} \) equal to?
A.
\( -\frac{(m - q)(n - q)}{(m - p)(n - p)} \)
B.
\( -\frac{(m - q)(n - p)}{(m - p)(n - q)} \)
C.
\( \frac{(m - q)(n - q)}{(m - p)(n - p)} \)
D.
\( \frac{(m - q)(n - p)}{(m - p)(n - q)} \)
😑 View Answer Error
ANSWER :
C. \( \frac{(m - q)(n - q)}{(m - p)(n - p)} \)
42.
If \( \alpha \) and \( \beta \) are complementary angles, then which one of the following is correct?
A.
\( mn - 1 = 0 \)
B.
\( mn + 1 = 0 \)
C.
\( m + n = 0 \)
D.
\( m - n = 0 \)
😑 View Answer Error
ANSWER :
D. \( m - n = 0 \)
43.
For the following two (02) items:
Let \( \mathrm{cosec} \theta - \sin \theta = p \) and \( \sec \theta - \cos \theta = q \).

What is \( (p \sin \theta + q \cos \theta) \) equal to?
A.
-1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
C. 1
44.
What is \( p^{2}q^{2}(p^{2} + q^{2} + 3) \) equal to?
A.
0
B.
1
C.
2
D.
4
😑 View Answer Error
ANSWER :
B. 1
45.
For the following two (02) items:
Let \( \frac{\sin \alpha}{\sin \beta} = \frac{4\sqrt{2}}{3} \) and \( \frac{\cos \alpha}{\cos \beta} = \frac{2\sqrt{3}}{9} \).

What is \( \tan^{2} \alpha \) equal to?
A.
8
B.
6
C.
4
D.
3
😑 View Answer Error
ANSWER :
A. 8
46.
What is \( \tan^{2} \beta \) equal to?
A.
\( 1/\sqrt{2} \)
B.
\( 3/\sqrt{2} \)
C.
1/3
D.
2/3
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ANSWER :
C. 1/3
47.
For the following two (02) items:
Let \( \frac{1 + \sin \theta}{\cos \theta} = p + \sqrt{p^{2} + 1} \).

What is \( \sec \theta \) equal to?
A.
\( p \)
B.
\( \sqrt{p^{2} + 1} \)
C.
\( \frac{1}{\sqrt{p^{2} + 1}} \)
D.
\( \frac{p}{\sqrt{p^{2} + 1}} \)
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ANSWER :
B. \( \sqrt{p^{2} + 1} \)
48.
What is \( \tan \theta \) equal to?
A.
\( p \)
B.
\( \sqrt{p^{2} + 1} \)
C.
\( \frac{1}{\sqrt{p^{2} + 1}} \)
D.
\( \frac{p}{\sqrt{p^{2} + 1}} \)
😑 View Answer Error
ANSWER :
A. \( p \)
49.
For the following two (02) items:
Let \( \sin \theta + \cos \theta = p \) and \( \sec \theta + \mathrm{cosec} \theta = q \), where \( p \neq 1 \).

What is the relation between \( p \) and \( q \)?
A.
\( p = q(p^{2} - 1) \)
B.
\( 2p = q(p^{2} - 1) \)
C.
\( q = p^{2} - 1 \)
D.
\( 2q = p(p^{2} - 1) \)
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ANSWER :
B. \( 2p = q(p^{2} - 1) \)
50.
What is \( \tan \theta + \cot \theta \) equal to?
A.
\( \frac{p}{q} \)
B.
\( \frac{q}{p} \)
C.
\( \frac{2p}{q} \)
D.
\( \frac{2q}{p} \)
😑 View Answer Error
ANSWER :
B. \( \frac{q}{p} \)
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