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

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CDS Exam (I)- 2026 - Elementary Mathematics

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

41.
If \( \frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4 \), then which one of the following is a value of \( (\tan^{2} \theta + \cot^{2} \theta) \)?
A.
\( \frac{5}{3} \)
B.
\( \frac{10}{3} \)
C.
4
D.
5
😑 View Answer Error
ANSWER :
B. \( \frac{10}{3} \)
42.
For \( 0 < \theta < \frac{\pi}{2} \), consider the following:
I. \( (\tan^{4} \theta + \tan^{6} \theta)(\cot^{4} \theta + \cot^{6} \theta) = \sec^{2} \theta \mathrm{cosec}^{2} \theta \)
II. \( \frac{\tan \theta + \sin \theta}{\tan \theta - \sin \theta} = \cot^{2} \theta (\sec \theta + 1)^{2} \)
Which of the above is/are identities?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
C. Both I and II
43.
If \( 3\sin \theta + 4\cos \theta = 5 \), then what is a value of \( 4\tan \theta + 3\cot \theta \)?
A.
7
B.
8
C.
9
D.
10
😑 View Answer Error
ANSWER :
A. 7
44.
At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be \( \frac{5}{6} \). On walking 70 m towards the tower, the tangent of the angle of elevation of the top of the tower is found to be \( \frac{9}{8} \). What is the height of the tower?
A.
225 m
B.
270 m
C.
300 m
D.
330 m
😑 View Answer Error
ANSWER :
A. 225 m
45.
Two persons are on diametrically opposite sides of a tower. They measure the angles of elevation of the top of the tower as \( 30^{\circ} \) and \( 60^{\circ} \) respectively. If the height of the tower is 100 m, what is the approximate distance between the two persons?
A.
220 m
B.
225 m
C.
230 m
D.
235 m
😑 View Answer Error
ANSWER :
C. 230 m
46.
In a cyclic quadrilateral ABCD, the diagonal AC bisects the angle C. Which of the following statements is/are correct?
I. \( \angle ABD = \angle ADB \)
II. The diagonal BD is parallel to the tangent of the circle at A
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 :
C. Both I and II
47.
Let \( x \) be the length of a diagonal of a face of a cube and \( y \) be the length of a diagonal of the cube. If \( x + y = (5 + 2\sqrt{6}) \) units, then what is the total surface area of the cube?
A.
\( 6(x + y) \)
B.
\( 6xy \)
C.
\( 3(x + y) \)
D.
\( 3xy \)
😑 View Answer Error
ANSWER :
A. \( 6(x + y) \)
48.
ABC is a triangle in which AB = AC and D is any point on BC. Which of the following statements is/are correct?
I. \( AB^{2} - AD^{2} = CD \times BD \)
II. \( BC^{2} + BD^{2} - DC^{2} = 2BD \times BC \)
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 :
C. Both I and II
49.
ABC is a triangle right-angled at B with sides BC = \( a \), CA = \( b \) and AB = \( c \). Let \( p \) be the length of the perpendicular from B to AC. Which of the following statements is/are correct?
I. \( p = \frac{ac}{\sqrt{a^{2} + c^{2}}} \)
II. \( pb = ac \)
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 :
C. Both I and II
50.
ABC is an equilateral triangle. Let PQRS be a square inscribed in it such that P is on AB and Q is on AC. Which of the following is/are correct?
I. AP : PB = 4 : 3
II. \( \sqrt{3}AB = (2 + \sqrt{3})PQ \)
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 :
B. II only
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