CDS Exam (I)- 2022 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2022 - Elementary Mathematics

CDS Exam (I)- 2022 - Elementary Mathematics Defence Questions

21.
\( 27^{5} + 3^{13} \) is divisible by
A.
8
B.
10
C.
12
D.
21
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ANSWER :
B. 10
22.
Let \( p = 2^{2n+2} + m \) and \( q = 2^{4n} - m \) (where n is even natural number). What should be the least value of m such that p as well as q is divisible by 5?
A.
-1
B.
1
C.
4
D.
6
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ANSWER :
B. 1
23.
If squaring a positive real number x is same as adding 12, then what is x equal to?
A.
2
B.
3
C.
4
D.
5
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ANSWER :
C. 4
24.
What is
\( \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \ldots + \frac{1}{\sqrt{2020} + \sqrt{2021}} \)
equal to?
A.
\( \sqrt{2020} + 1 \)
B.
\( \sqrt{2021} + 1 \)
C.
\( \sqrt{2020} + \sqrt{2021} - 1 \)
D.
\( \sqrt{2021} - 1 \)
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ANSWER :
D. \( \sqrt{2021} - 1 \)
25.
If
\( x + \frac{1}{x} = \frac{5}{2} \)
then what is the value of the following?
\( \frac{5x}{7x^{2} - 3x + 7} \)
A.
\( \frac{3}{7} \)
B.
\( \frac{5}{12} \)
C.
\( \frac{3}{14} \)
D.
\( \frac{10}{29} \)
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ANSWER :
D. \( \frac{10}{29} \)
26.
If
\( a + b = 2 \), \( \frac{1}{a} + \frac{1}{b} = 2 \)
then what is the value of \( a^{3} + b^{3} \)?
A.
2
B.
4
C.
6
D.
8
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ANSWER :
A. 2
27.
8 men or 12 women can do a piece of work in 24 days. In how many days can the work be done by 8 men and 12 women?
A.
12 days
B.
18 days
C.
24 days
D.
Cannot be determined due to insufficient data
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ANSWER :
A. 12 days
28.
A car takes p minutes to travel a distance of 350 km with an average speed of u km/hr. Another car takes q minutes to travel the same distance with an average speed of v km/hr. If u - v = 5 and q - p = 140, then what is the value of u?
A.
35
B.
30
C.
25
D.
20
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ANSWER :
B. 30
29.
How many minutes are there in x weeks and x days?
A.
11520x
B.
5760x
C.
480x
D.
192x
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ANSWER :
A. 11520x
30.
The arithmetic mean and the geometric mean of two positive numbers p and q \( (p > q) \) are A and G respectively. Which one of the following is correct?
A.
\( A > G \)
B.
\( G > A \)
C.
\( A = G \)
D.
\( A^{2} = G \)
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ANSWER :
A. \( A > G \)
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