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

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CDS Exam (II)- 2025 - Elementary Mathematics

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

11.
What is the remainder when
\( (17^{25} + 19^{25}) \)
is divided by 18?
A.
0
B.
1
C.
3
D.
9
😑 View Answer Error
ANSWER :
A. 0
12.
The HCF of \( x \) and \( y \) is \( H \). Consider the following statements in respect of the HCF of \( p = \frac{x^{3} + y^{3}}{x^{2} - xy + y^{2}} \) and \( q = \frac{x^{3} - y^{3}}{x^{2} + xy + y^{2}} \):
I. The HCF of \( p \) and \( q \) can be \( H \).
II. The HCF of \( p \) and \( q \) can be \( 2H \).
Which of the statements given above is/are correct?
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
13.
If \( x^{4} = x^{2} + 1 \), where \( x > 0 \), then what is \( 2x^{4} \) equal to?
A.
\( 2 + \sqrt{3} \)
B.
\( 3 + \sqrt{5} \)
C.
\( 5 - 2\sqrt{3} \)
D.
\( 3 - \sqrt{5} \)
😑 View Answer Error
ANSWER :
B. \( 3 + \sqrt{5} \)
14.
If \( \frac{p + q}{q + r} = \frac{r + s}{s + p} \); \( (q + r) \neq 0 \), \( (s + p) \neq 0 \), then which one of the following is correct?
A.
\( p + q + r + s = 0 \)
B.
\( p = r \)
C.
Either \( p + q + r + s = 0 \) or \( p = r \)
D.
None of the above
😑 View Answer Error
ANSWER :
C. Either \( p + q + r + s = 0 \) or \( p = r \)
15.
If \( n \) is natural number less than 7, then what is the number of values of \( n \) for which \( (12n + 2) \) and \( (8n + 1) \) are relatively prime?
A.
6
B.
5
C.
4
D.
3
😑 View Answer Error
ANSWER :
A. 6
16.
What is the HCF of \( x^{3} + y^{3} + 3xy - 1 \) and \( (x + y)^{4} - 1 \)?
A.
\( x + y \)
B.
\( x + y + 1 \)
C.
\( x + y - 1 \)
D.
1
😑 View Answer Error
ANSWER :
C. \( x + y - 1 \)
17.
Let \( x = n(n + 1)(n + 2) \), where \( n \) is an even natural number. Which of the following statements is/are correct?
I. \( x \) is always divisible by 48.
II. \( x^{2} \) is always divisible by 144.
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
18.
What is the LCM of \( x^{4} + x^{2}y^{2} + y^{4} \), \( x^{3}y + y^{4} \) and \( x^{4}y^{2} - x^{3}y^{3} \)?
A.
\( x^{3}y^{3}(x^{6} - y^{6}) \)
B.
\( x^{3}y^{2}(x^{6} - y^{6}) \)
C.
\( x^{3}y(x^{6} - y^{6}) \)
D.
\( xy(x^{6} - y^{6}) \)
😑 View Answer Error
ANSWER :
B. \( x^{3}y^{2}(x^{6} - y^{6}) \)
19.
Let XYZ be a 3-digit number. Let D be the difference between XYZ and ZYX. What is the remainder when D is divided by 99?
A.
0
B.
1
C.
7
D.
9
😑 View Answer Error
ANSWER :
A. 0
20.
Let \( p \) and \( q \) be two natural numbers such that \( (p + q)^{p + q} \) is divisible by 512. What is the least value of \( (p + q) \)?
A.
4
B.
6
C.
8
D.
12
😑 View Answer Error
ANSWER :
C. 8
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