CDS Exam (II)- 2026 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2026 - Elementary Mathematics

CDS Exam (II)- 2026 - Elementary Mathematics Defence Questions

41.
If \( \cot \theta + \cos \theta = m \), \( \cot \theta - \cos \theta = n \), where \( 0 < \theta < \frac{\pi}{2} \), then what is \( \frac{m^{2} - n^{2}}{\sqrt{mn}} \) equal to?
A.
1
B.
2
C.
\( 2\sqrt{2} \)
D.
4
😑 View Answer Error
ANSWER :
D. 4
42.
If \( \frac{1}{\mathrm{cosec} \theta + \cot \theta} - \frac{1}{\sin \theta} = p \), then what is \( \frac{1}{\sin \theta} - \frac{1}{\mathrm{cosec} \theta - \cot \theta} \) equal to?
A.
-p
B.
\( -\frac{1}{p} \)
C.
p
D.
\( \frac{1}{p} \)
😑 View Answer Error
ANSWER :
C. p
43.
If \( 8\sin \theta - \cos \theta = 4 \), where \( \frac{\pi}{6} < \theta < \frac{\pi}{3} \), then what is \( \sin \theta \) equal to?
A.
\( \frac{3}{5} \)
B.
\( \frac{5}{13} \)
C.
\( \frac{4}{5} \)
D.
\( \frac{12}{13} \)
😑 View Answer Error
ANSWER :
A. \( \frac{3}{5} \)
44.
A person walking along a straight road observes that at two consecutive kilometer-stones the angles of elevation of a hill in front of him are \( 30^{\circ} \) and \( 60^{\circ} \) respectively. What is the height of the hill?
A.
\( 3\sqrt{3} \) km
B.
\( 2\sqrt{3} \) km
C.
\( \sqrt{3} \) km
D.
\( \frac{\sqrt{3}}{2} \) km
😑 View Answer Error
ANSWER :
D. \( \frac{\sqrt{3}}{2} \) km
45.
A tower subtends an angle \( \alpha \) at a point P on the same level as the foot of the tower. Q is a point vertically above P and PQ = h. If the angle of depression of the foot of the tower measured from Q is \( \beta \), then what is the height of the tower?
A.
\( h\tan \alpha \tan \beta \)
B.
\( h\cot \alpha \tan \beta \)
C.
\( h\tan \alpha \cot \beta \)
D.
\( h\cot \alpha \cot \beta \)
😑 View Answer Error
ANSWER :
C. \( h\tan \alpha \cot \beta \)
46.
If \( 5\sin \theta + 12\cos \theta = 13 \), where \( 0 < \theta < \frac{\pi}{2} \), then what is \( \tan \theta + \cot \theta \) equal to?
A.
\( \frac{194}{65} \)
B.
\( \frac{169}{60} \)
C.
\( \frac{313}{156} \)
D.
\( \frac{371}{120} \)
😑 View Answer Error
ANSWER :
B. \( \frac{169}{60} \)
47.
What is the ratio of the greatest value of \( \sin^{2} x + 2 \) (where \( 0 \leq x \leq \frac{\pi}{2} \)) to its least value?
A.
3
B.
\( \frac{3}{2} \)
C.
2
D.
\( \frac{1}{2} \)
😑 View Answer Error
ANSWER :
B. \( \frac{3}{2} \)
48.
If \( A + B + C = \pi \) \( (A, B, C > 0) \) and the angle C is obtuse, then which of the following is/are correct?
I. \( \sin A \cdot \sin B < 1 \)
II. \( \tan A \cdot \tan B > 1 \)
Select the answer using the code given below:
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
A. I only
49.
If \( (\cos 35^{\circ} + \cos 55^{\circ}) = p \), then what is \( \sin 35^{\circ} \cdot \cos 35^{\circ} \) equal to?
A.
\( \frac{(1 - p^{2})}{2} \)
B.
\( \frac{(p^{2} - 1)}{2} \)
C.
\( \frac{(1 + p^{2})}{2} \)
D.
\( \frac{(p - 1)}{2} \)
😑 View Answer Error
ANSWER :
B. \( \frac{(p^{2} - 1)}{2} \)
50.
If \( p = \sec \theta + \tan \theta \) and \( q = \mathrm{cosec} \theta - \cot \theta \), then what is (p - q - pq) equal to?
A.
-1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
C. 1
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