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

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

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

11.
How many real roots does the equation \( \sqrt{x + 9} = x - 3 \) have?
A.
Only one
B.
Only two
C.
Only three
D.
None
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ANSWER :
A. Only one
12.
If \( x = 97 + 56\sqrt{3} \), then what is the value of \( \sqrt[4]{x} + \frac{1}{\sqrt[4]{x}} \)?
A.
7
B.
6
C.
5
D.
4
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ANSWER :
D. 4
13.
Let L be the LCM and H be the HCF of two given numbers. L and H are in the ratio 6 : 1. If the sum of the two numbers is 45, then what is the product of the numbers?
A.
243
B.
486
C.
504
D.
Cannot be determined due to insufficient data
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ANSWER :
B. 486
14.
A man walks at an average speed of 3 km/hr from his home and reaches office 40 minutes early. If he walks at an average speed of 2 km/hr, he would reach office 40 minutes late. What is the distance between his home and office?
A.
6 km
B.
8 km
C.
10 km
D.
12 km
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ANSWER :
B. 8 km
15.
If \( 3^{x - 1} + 3^{3 - x} = 6 \), then what is \( 2^{x - 1} + 2^{3 - x} \) equal to?
A.
4
B.
3
C.
2
D.
1
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ANSWER :
A. 4
16.
If \( x\left(a - b + \frac{ab}{a - b}\right) = y\left(a + b - \frac{ab}{a + b}\right) \) and \( x + y = 2a^{3} \), then what is \( x - y \) equal to?
A.
\( -2b^{3} \)
B.
\( -2ab^{3} \)
C.
\( 2b^{3} \)
D.
\( 2ab^{3} \)
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ANSWER :
A. \( -2b^{3} \)
17.
Which one of the following is a factor of \( 3\sqrt{3}x^{3} + 2\sqrt{2}y^{3} - 18xy + 6\sqrt{6} \)?
A.
\( \sqrt{3}x + \sqrt{2}y - \sqrt{3} \)
B.
\( \sqrt{3}x + \sqrt{2}y - \sqrt{6} \)
C.
\( 3x^{2} + 2y^{2} - \sqrt{18}x - \sqrt{12}y - \sqrt{6}xy + 6 \)
D.
\( 3x^{2} + 2y^{2} + \sqrt{18}x + \sqrt{12}y - \sqrt{6}xy + 6 \)
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ANSWER :
C. \( 3x^{2} + 2y^{2} - \sqrt{18}x - \sqrt{12}y - \sqrt{6}xy + 6 \)
18.
What is number of digits in the expansion of \( 125^{100} \)? (Given \( \log_{10} 2 = 0.301 \))
A.
69
B.
70
C.
209
D.
210
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ANSWER :
D. 210
19.
What is the HCF of
\( acx^{3} + bcx^{2} + adx^{2} + acdx + bdx + bcd \) and
\( adx^{3} + acx^{2} + bdx^{2} + bcx + acdx + bcd \)
if HCF \( (c, d) = 1, c \neq d \)?
A.
\( bx + c \)
B.
\( cx + d \)
C.
\( ax + d \)
D.
\( ax + b \)
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ANSWER :
D. \( ax + b \)
20.
If \( x^{n} - py^{n} + qz^{n} \) is divisible by \( x^{2} + abyz - bzx - axy \), then what is \( \frac{p}{a^{n}} - \frac{q}{b^{n}} \) equal to?
A.
-1
B.
0
C.
1
D.
2
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ANSWER :
C. 1
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