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

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

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

11.
A lamp is kept on a vertical pole. The height of the top of the lamp above the ground is \( \frac{5\sqrt{3}}{2} \) m. The perpendicular distances of the bottom of the pole from two adjacent walls meeting perpendicularly are 0.7 m and 2.4 m. What is the distance of the top of the lamp from the corner point of the walls on the ground?
A.
3 m
B.
5 m
C.
6 m
D.
7 m
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ANSWER :
B. 5 m
12.
C is the centre of a circle of radius 20 cm. AB is a chord of length 32 cm. E is a point on AB such that CE = 13 cm. What is \( AE \times EB \) equal to?
A.
231 square cm
B.
256 square cm
C.
272 square cm
D.
297 square cm
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ANSWER :
A. 231 square cm
13.
The inside of a bowl is part of a sphere. When water is put into the bowl to a depth d, the water surface becomes a circle of radius 2d. What is the radius of the sphere?
A.
2.5d
B.
2.75d
C.
3d
D.
3.25d
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ANSWER :
A. 2.5d
14.
In a triangle ABC, AB = 2 cm, BC = 4 cm and AC = 3 cm. The bisector of angle A meets BC at D and the bisector of angle B meets AD at E. What is AE : ED equal to?
A.
5 : 4
B.
5 : 3
C.
4 : 3
D.
3 : 2
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ANSWER :
A. 5 : 4
15.
In a triangle ABC, the bisector of angle A cuts BC at D. If AB + AC = 10 cm and BD : DC = 3 : 1, then what is the length of AC?
A.
2.5 cm
B.
6 cm
C.
7.5 cm
D.
8 cm
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ANSWER :
A. 2.5 cm
16.
In a triangle ABC, AB + BC = 7.1 cm,
BC + CA = 12.1 cm and CA + AB = 7.2 cm.
What is the area of the triangle?
A.
3 square cm
B.
32 square cm
C.
33 square cm
D.
3.3 square cm
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ANSWER :
D. 3.3 square cm
17.
The adjacent sides of a parallelogram are 10 cm and 8 cm and the angle between them is \( 150^{\circ} \). What is the area of the parallelogram?
A.
\( 40\sqrt{3} \) square cm
B.
40 square cm
C.
\( 20\sqrt{3} \) square cm
D.
20 square cm
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ANSWER :
B. 40 square cm
18.
The measure of an angle formed by the bisectors of the angles A and C of the triangle ABC is \( 130^{\circ} \). What is the measure of the angle B?
A.
\( 65^{\circ} \)
B.
\( 75^{\circ} \)
C.
\( 80^{\circ} \)
D.
\( 85^{\circ} \)
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ANSWER :
C. \( 80^{\circ} \)
19.
What is
\( \log_{10} 2000 + \log_{10} 400 + 4 \log_{10} 25 + 5 \log_{10} 20 \)
equal to?
A.
10
B.
16
C.
18
D.
20
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ANSWER :
C. 18
20.
If \( \frac{\log_{10}(100001 - 4^{x})}{5 - x} = 1 \), then what is x equal to?
A.
0
B.
1
C.
10
D.
100
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ANSWER :
A. 0
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