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

21.
What is \( \frac{(a + b)^{2}}{(c - a)(c + a + b)} + \frac{(a + b)c}{c^{2} + bc - a^{2} - ab} - \frac{(a + 2b + c)}{2(c - a)} \), \( a \neq b \), \( b \neq c \), \( c \neq a \) equal to?
A.
-1/2
B.
0
C.
1/2
D.
1
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ANSWER :
A. -1/2
22.
If \( a^{b} = b^{a} \), then what is \( \frac{a \times \left(\frac{a}{b}\right)^{\frac{a}{b}}}{a^{\left(\frac{a}{b}\right)}} \) equal to?
A.
1
B.
\( ab \)
C.
\( b \)
D.
\( a^{b} \)
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ANSWER :
A. 1
23.
If \( x = 2 + 2^{1/2} + 2^{3/2} \), then what is \( x^{2} - 4x - 10 \) equal to?
A.
0
B.
1
C.
4
D.
6
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ANSWER :
C. 4
24.
If \( \frac{\sqrt{p + x} + \sqrt{p - x}}{\sqrt{p + x} - \sqrt{p - x}} = p \), then what is \( x \) equal to?
A.
\( \frac{p}{p^{2} + 1} \)
B.
\( \frac{2p}{p^{2} + 1} \)
C.
\( \frac{p^{2}}{p^{2} + 1} \)
D.
\( \frac{2p^{2}}{p^{2} + 1} \)
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ANSWER :
D. \( \frac{2p^{2}}{p^{2} + 1} \)
25.
If \( \left(\frac{a - b}{2}\right)x^{2} - \left(\frac{a + b}{2}\right)x + b = 0 \), then what are the roots of this equation?
A.
\( 1, \frac{b}{a - b} \)
B.
\( 1, \frac{2b}{a - b} \)
C.
\( \frac{1}{2}, \frac{b}{a + b} \)
D.
\( \frac{1}{2}, \frac{2b}{a + b} \)
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ANSWER :
B. \( 1, \frac{2b}{a - b} \)
26.
If \( x - \frac{1}{x} = 2 \), \( x > 0 \); then what is \( x^{2} - \frac{1}{x^{2}} \) equal to?
A.
6
B.
\( 4\sqrt{2} \)
C.
4
D.
\( 2\sqrt{2} \)
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ANSWER :
B. \( 4\sqrt{2} \)
27.
If \( (a - b)^{2} + (b - c)^{2} + (c - a)^{2} = 6 \) and \( a^{2} + b^{2} + c^{2} = 29 \), then what is \( (a + b + c) \) equal to?
A.
\( \pm 9 \)
B.
\( \pm 8 \)
C.
\( \pm 6 \)
D.
\( \pm 3 \)
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ANSWER :
A. \( \pm 9 \)
28.
If \( p = \frac{\sqrt{5} - 2}{\sqrt{5} + 2} \) and \( q = \frac{\sqrt{5} + 2}{\sqrt{5} - 2} \), then what is \( \left(\frac{p}{q} + \frac{q}{p}\right) \) equal to?
A.
18
B.
\( 8\sqrt{5} \)
C.
322
D.
\( 72\sqrt{5} \)
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ANSWER :
C. 322
29.
What is the digit at hundreds place of the number \( (25)^{10} \)?
A.
1
B.
2
C.
5
D.
6
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ANSWER :
D. 6
30.
A number N is such that when divided by 4, 6, 7 or 9, it leaves 3 as remainder. What is the smallest 4-digit number that satisfies this property?
A.
1003
B.
1005
C.
1007
D.
1011
😑 View Answer Error
ANSWER :
D. 1011
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