CDS Exam (I)- 2023 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2023 - Elementary Mathematics

CDS Exam (I)- 2023 - Elementary Mathematics Defence Questions

21.
If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2} - 7x + 1 = 0 \), then what is the value of \( \alpha^{4} + \beta^{4} \)?
A.
2207
B.
2247
C.
2317
D.
2337
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ANSWER :
A. 2207
22.
Consider the following statements in respect of all factors of 360:
1. The number of factors is 24.
2. The sum of all factors is 1170.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
C. Both 1 and 2
23.
Consider a 6-digit number of the form XYXYXY. The number is divisible by:
A.
3 and 7 only
B.
7 and 13 only
C.
3, 13 and 37 only
D.
3, 7, 13 and 37
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ANSWER :
D. 3, 7, 13 and 37
24.
What is the HCF of \( 3^{29} - 9 \) and \( 3^{38} - 9 \)?
A.
\( 3^{9} - 1 \)
B.
\( 3^{11} - 1 \)
C.
\( 3^{11} - 3 \)
D.
\( 3^{11} - 9 \)
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ANSWER :
D. \( 3^{11} - 9 \)
25.
If \( x = \sqrt{4\sqrt{4\sqrt{4\sqrt{4 \ldots}}}} \), then what is the value of x?
A.
2
B.
4
C.
8
D.
16
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ANSWER :
B. 4
26.
Let m and n be natural numbers. What is the minimum value of (m + n) such that 33m + 22n is divisible by 121?
A.
3
B.
4
C.
5
D.
10
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ANSWER :
B. 4
27.
The product of two numbers is 2160 and their HCF is 12. If the sum of the squares of the two numbers is 4896, then what is the mean of the two numbers?
A.
24
B.
36
C.
48
D.
96
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ANSWER :
C. 48
28.
The age of Q exceeds the age of P by 3 years. The age of R is twice the age of P and the age of Q is twice the age of S. Further, the age difference of R and S is 30 years. What is the sum of the ages of P and Q?
A.
35 years
B.
38 years
C.
39 years
D.
45 years
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ANSWER :
D. 45 years
29.
If a, b and c are the sides of a triangle ABC, then \( \sqrt{a} + \sqrt{b} - \sqrt{c} \) is always:
A.
Negative
B.
Positive
C.
Zero
D.
Non-positive
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ANSWER :
B. Positive
30.
There are four bells which ring at an interval of 15 minutes, 25 minutes, 35 minutes and 45 minutes respectively. If all of them ring at 9 A.M., how many more times will they ring together in the next 72 hours?
A.
0
B.
1
C.
2
D.
3
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ANSWER :
C. 2
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