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

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CDS Exam (I)- 2025 - Elementary Mathematics

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

41.
What is \( \sqrt{17 - 4\sqrt{15}} + \sqrt{8 - 2\sqrt{15}} \) equal to?
A.
\( \sqrt{3} \)
B.
\( 2\sqrt{3} \)
C.
\( 2(\sqrt{5} - \sqrt{3}) \)
D.
\( 2(\sqrt{5} + \sqrt{3}) \)
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ANSWER :
A. \( \sqrt{3} \)
42.
What is the maximum value of the sum of the numbers 36, 33, 30, 27, 24, ...?
A.
240
B.
237
C.
234
D.
231
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ANSWER :
C. 234
43.
There are two natural numbers m and n \( (m > n) \). When m is divided by 12, it leaves a remainder 4. When n is divided by 12, it leaves a remainder 6. Which of the following statements is/are correct?
I. The remainder when (m + n) is divided by 12 is 10.
II. The remainder when (m - n) is divided by 12 is 10.
Select the correct answer using the code given below:
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
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ANSWER :
C. Both I and II
44.
If (x + y) : (y + z) : (z + x) = 3 : 5 : 6 and x + y + z = 14, then what is \( x^{2} + y^{2} + z^{2} \) equal to?
A.
81
B.
84
C.
87
D.
90
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ANSWER :
B. 84
45.
The ratio of sum of two numbers to their difference is 5 : 1. What is the ratio of the sum of their squares to the difference of their squares?
A.
13 : 5
B.
25 : 1
C.
9 : 4
D.
16 : 1
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ANSWER :
A. 13 : 5
46.
Travelling at \( \frac{3}{5} \)th of his usual speed, a man is late by 20 minutes. What is the usual time if he travels with his usual speed?
A.
25 minutes
B.
30 minutes
C.
32 minutes
D.
35 minutes
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ANSWER :
B. 30 minutes
47.
What is the remainder when \( 2^{p} - 1 \) is divided by p, where \( p > 5 \) is a prime number?
A.
1
B.
2
C.
3
D.
4
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ANSWER :
A. 1
48.
What is the number of factors of \( 24^{3} - 16^{3} - 8^{3} \)?
A.
33
B.
30
C.
28
D.
24
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ANSWER :
A. 33
49.
What is the least number of complete years in which a sum of money put out at 20% compound interest (compounded annually) will be more than doubled?
A.
2
B.
3
C.
4
D.
5
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ANSWER :
C. 4
50.
A train of certain length takes time t to pass completely through a station of length x. The same train with same speed takes time 2t to pass completely through another station of length y. What is the time taken by the train to pass completely through a station of length (x + y)?
A.
(2yt + xt) / (y - x)
B.
(yt + xt) / (y - x)
C.
(3yt - xt) / (2y - x)
D.
(2yt - xt) / (y - x)
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ANSWER :
D. (2yt - xt) / (y - x)
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