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

21.
The arithmetic mean of \( n \) numbers is M. If the sum of first \( (n - 1) \) term is \( k \), then what is the \( n \)th number?
A.
M - \( k \)
B.
\( n \)M - \( k \)
C.
\( n \)(M - \( k \))
D.
M - \( nk \)
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ANSWER :
B. \( n \)M - \( k \)
22.
What is the geometric mean of 3, 9, 27, 81, 243, 729, 2187?
A.
81
B.
105
C.
144
D.
243
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ANSWER :
A. 81
23.
A person purchases 1 kg of tea powder from each of the four places A, B, C, D at the rate of ₹1,000 per 1 kg, 2 kg, 4 kg, 5 kg. If, on an average, he purchases \( x \) kg of tea powder per ₹1,000, then what is the approximate value of \( x \)?
A.
1.95
B.
2.00
C.
2.05
D.
2.10
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ANSWER :
C. 2.05
24.
What is the sum of the largest and the smallest 4-digit numbers made by using single digit prime numbers (without repetition)?
A.
7887
B.
7997
C.
8998
D.
9889
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ANSWER :
D. 9889
25.
What is the remainder when \( 3^{255} \) is divided by 28?
A.
1
B.
11
C.
24
D.
27
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ANSWER :
D. 27
26.
What is the value of \( x \) \( (0 \leq x \leq 8) \) if \( (100^{97} + 100^{54} + x + 1) \) leaves a remainder 0 when divided by 9?
A.
8
B.
6
C.
4
D.
1
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ANSWER :
B. 6
27.
In a triangle ABC, D is a point on BC. If \( AB \cdot DC = AC \cdot BD \), \( \angle BAD = \alpha \) and \( \angle CAD = \beta \) then which one of the following is correct?
A.
\( \alpha = \beta \)
B.
\( \alpha = 2\beta \)
C.
\( 2\alpha = \beta \)
D.
\( 2\alpha = 3\beta \)
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ANSWER :
A. \( \alpha = \beta \)
28.
Let N = 12345678AB be a 10-digit number, where A, B are digits. If N is divisible by 9, then which of the following statements is/are correct?
I. (A + B) is divisible by 9.
II. If A is odd, then B is odd.
Select the 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 :
A. I only
29.
If \( x^{3} + \frac{1}{x^{3}} = \frac{65}{8} \) and \( y^{3} + \frac{1}{y^{3}} = \frac{730}{27} \), then which one of the following is a value of \( xy \)?
A.
3
B.
6
C.
8
D.
9
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ANSWER :
B. 6
30.
If \( 11x + 5y \) is a prime number where \( x \), \( y \) are natural numbers, then what is the minimum value of \( (x + y) \)?
A.
3
B.
4
C.
5
D.
6
😑 View Answer Error
ANSWER :
C. 5
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