CDS Exam (II)- 2024- Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2024- Elementary Mathematics

CDS Exam (II)- 2024- Elementary Mathematics Defence Questions

11.
What is the maximum value of \( 8\sin\theta - 4\sin^{2}\theta \)?
A.
3
B.
4
C.
8
D.
12
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ANSWER :
B. 4
12.
What is \( (1 + \tan\alpha \tan\beta)^{2} + (\tan\alpha - \tan\beta)^{2} \) equal to?
A.
\( \tan^{2}\alpha \tan^{2}\beta \)
B.
\( \sec^{2}\alpha \sec^{2}\beta \)
C.
\( \tan^{2}\alpha \cot^{2}\beta \)
D.
\( \sec^{2}\alpha \tan^{2}\beta \)
😑 View Answer Error
ANSWER :
B. \( \sec^{2}\alpha \sec^{2}\beta \)
13.
Consider the following statements:
I. \( \tan 50^{\circ} - \cot 50^{\circ} \) is positive.
II. \( \cot 25^{\circ} - \tan 25^{\circ} \) is negative.
Which of the statements are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
A. I only
14.
If \( 0 \leq (\alpha - \beta) \leq (\alpha + \beta) < \frac{\pi}{2} \), \( \tan(\alpha + \beta) = \sqrt{3} \) and \( \tan(\alpha - \beta) = \frac{1}{\sqrt{3}} \), then what is \( \tan\alpha \cdot \cot 2\beta \) equal to?
A.
1
B.
\( \sqrt{2} \)
C.
\( \sqrt{3} \)
D.
\( \frac{1}{\sqrt{3}} \)
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ANSWER :
C. \( \sqrt{3} \)
15.
What is the value of \( \sin^{2}\theta \cos^{2}\theta (\sec^{2}\theta + \mathrm{cosec}^{2}\theta) \) equal to?
A.
0
B.
1
C.
2
D.
4
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ANSWER :
B. 1
16.
If \( 64^{\sin^{2}\theta} + 64^{\cos^{2}\theta} = 16 \) where \( 0 \leq \theta \leq \frac{\pi}{2} \), then what is the value of \( \tan\theta + \cot\theta \)?
A.
1
B.
2
C.
3
D.
4
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ANSWER :
B. 2
17.
If \( \mathrm{cosec}\theta - \cot\theta = m \) and \( \sec\theta - \tan\theta = n \), then what is \( \mathrm{cosec}\theta + \sec\theta \) equal to?
A.
\( \frac{1}{2}\left(m + n + \frac{1}{m} + \frac{1}{n}\right) \)
B.
\( \left(m + n + \frac{1}{m} + \frac{1}{n}\right) \)
C.
\( \frac{1}{2}\left(m + n - \frac{1}{m} - \frac{1}{n}\right) \)
D.
\( \left(m + n - \frac{1}{m} - \frac{1}{n}\right) \)
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ANSWER :
A. \( \frac{1}{2}\left(m + n + \frac{1}{m} + \frac{1}{n}\right) \)
18.
From a point X on a bridge across a river, the angles of depression of two points P and Q on the banks on opposite side of the river are \( \alpha \) and \( \beta \), respectively. If the point X is at a height \( h \) above the surface of the river, what is the width of the river if \( \alpha \) and \( \beta \) are complementary?
A.
\( 2h(\tan\alpha + \cot\alpha) \)
B.
\( h \tan\alpha \cdot \tan\beta \)
C.
\( h \cot\alpha \cdot \cot\beta \)
D.
\( h \sec\alpha \cdot \mathrm{cosec}\alpha \)
😑 View Answer Error
ANSWER :
D. \( h \sec\alpha \cdot \mathrm{cosec}\alpha \)
19.
In a triangle ABC, \( \angle ABC = 60^{\circ} \) and AD is the altitude. If AB = 6 cm and BC = 8 cm, then what is the area of the triangle?
A.
12 square cm
B.
\( 12\sqrt{3} \) square cm
C.
24 square cm
D.
\( 24\sqrt{3} \) square cm
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ANSWER :
B. \( 12\sqrt{3} \) square cm
20.
If \( p \) and \( q \) are the roots of the equation \( x^{2} - \sin^{2}\theta x - \cos^{2}\theta = 0 \), then what is the minimum value of \( p^{2} + q^{2} \)?
A.
\( \frac{1}{2} \)
B.
1
C.
\( \frac{3}{2} \)
D.
2
😑 View Answer Error
ANSWER :
B. 1
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