CDS Exam (II)- 2015 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2015 - Elementary Mathematics

CDS Exam (II)- 2015 - Elementary Mathematics Defence Questions

1.
The number of values of x satisfying \( x + \frac{100}{x} > 50 \), where x is a natural number less than or equal to 100, is
A.
51
B.
53
C.
55
D.
57
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ANSWER :
C. 55
2.
What is the sum of digits of the least multiple of 13, which when divided by 6, 8 and 12 leaves 5, 7 and 11 respectively as the remainders?
A.
5
B.
6
C.
7
D.
8
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ANSWER :
D. 8
3.
A milkman claims to sell milk at its cost price only. Still he is making a profit of 20% since he has mixed some amount of water in the milk. What is the percentage of milk in the mixture?
A.
\( \frac{200}{3} \)%
B.
75%
C.
80%
D.
\( \frac{250}{3} \)%
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ANSWER :
D. \( \frac{250}{3} \)%
4.
What is \( \sqrt{4 + \sqrt{4 - \sqrt{4 + \sqrt{4 - \ldots}}}} \) equal to?
A.
3
B.
\( \frac{\sqrt{13} - 1}{2} \)
C.
\( \frac{\sqrt{13} + 1}{2} \)
D.
0
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ANSWER :
C. \( \frac{\sqrt{13} + 1}{2} \)
5.
The largest natural number which divides every natural number of the form \( (n^{3} - n)(n - 2) \), where n is a natural number greater than 2, is
A.
6
B.
12
C.
24
D.
48
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ANSWER :
C. 24
6.
The average of m numbers is \( n^{2} \) and the average of n numbers is \( m^{2} \). The average of (m + n) numbers is
A.
mn
B.
\( m^{2} + n^{2} \)
C.
\( mn(m^{2} + n^{2}) \)
D.
\( mn(m^{2} + n^{2} - mn) \)
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ANSWER :
A. mn
7.
The digit in the units place of the resulting number of the expression \( (234)^{100} + (234)^{101} \) is
A.
6
B.
4
C.
2
D.
0
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ANSWER :
D. 0
8.
If \( x = \sqrt{3} + \sqrt{2} \), then the value of \( x^{3} + x + \frac{1}{x} + \frac{1}{x^{3}} \) is
A.
\( 10\sqrt{3} \)
B.
\( 20\sqrt{3} \)
C.
\( 10\sqrt{2} \)
D.
\( 20\sqrt{2} \)
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ANSWER :
B. \( 20\sqrt{3} \)
9.
The value of \( \frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10} + \ldots + \frac{1}{16 \times 19} \) is
A.
\( \frac{1}{19} \)
B.
\( \frac{6}{19} \)
C.
\( \frac{8}{19} \)
D.
\( \frac{9}{19} \)
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ANSWER :
B. \( \frac{6}{19} \)
10.
Two trains are moving in the same direction at 1.5 km/minute and 60 km/hour respectively. A man in the faster train observes that it takes 27 seconds to cross the slower train. The length of the slower train is
A.
225 m
B.
230 m
C.
240 m
D.
250 m
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ANSWER :
A. 225 m
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