CDS Exam (II)- 2016 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2016 - Elementary Mathematics

CDS Exam (II)- 2016 - Elementary Mathematics Defence Questions

31.
If \( 2p + 3q = 12 \) and \( 4p^{2} + 4pq - 3q^{2} = 126 \), then what is the value of \( p + 2q \)?
A.
5
B.
\( \frac{21}{4} \)
C.
\( \frac{25}{4} \)
D.
\( \frac{99}{16} \)
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ANSWER :
D. \( \frac{99}{16} \)
32.
The number of digits in \( 3^{30} \) is \( n \) and it is given that \( \log_{10} 3 = 0.4771 \). What is the value of \( n \)?
A.
13
B.
14
C.
15
D.
16
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ANSWER :
C. 15
33.
What is the unit digit of \( 7^{139} \)?
A.
9
B.
7
C.
6
D.
3
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ANSWER :
D. 3
34.
If \( 4x + 3a = 0 \), then what is the value of \( \frac{x^{2} + ax + a^{2}}{x^{3} - a^{3}} - \frac{x^{2} - ax + a^{2}}{x^{3} + a^{3}} \)?
A.
\( -\frac{4}{7a} \)
B.
\( -\frac{7}{a} \)
C.
\( -\frac{32}{7a} \)
D.
\( \frac{24}{7a} \)
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ANSWER :
C. \( -\frac{32}{7a} \)
35.
Incomes of Mahesh and Kamal are in the ratio 1 : 2 and their expenses are in the ratio 1 : 3. Which one of the following statements is correct?
A.
Mahesh saves more than what Kamal saves
B.
Savings of both of them are equal
C.
Kamal saves more than what Mahesh saves
D.
It is not possible to determine who saves more
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ANSWER :
D. It is not possible to determine who saves more
36.
X and Y entered into partnership with Rs. 700 and Rs. 600 respectively. After 3 months X withdrew \( \frac{2}{7} \) of his stock but after 3 months, he puts back \( \frac{3}{5} \) of what he had withdrawn. The profit at the end of the year is Rs. 726. How much of this should X receive?
A.
Rs. 336
B.
Rs. 366
C.
Rs. 633
D.
Rs. 663
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ANSWER :
B. Rs. 366
37.
A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10 a.m. pipe X was opened. At what time will the tank be filled if pipe Y is opened at 11 a.m.?
A.
12:45 hours
B.
5:00 p.m.
C.
11:45 a.m.
D.
11:50 a.m.
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ANSWER :
C. 11:45 a.m.
38.
A train travelling at 48 km/hour completely crosses another train having half its length and travelling in opposite direction at 42 km/hour in 12 s. It also passes a railway platform in 45 s. What is the length of the platform?
A.
600 m
B.
400 m
C.
300 m
D.
200 m
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ANSWER :
B. 400 m
39.
The speeds of three cars are in the ratio 2 : 3 : 4. What is the ratio between the times taken by these cars to travel the same distance?
A.
4 : 3 : 2
B.
2 : 3 : 4
C.
4 : 3 : 6
D.
6 : 4 : 3
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ANSWER :
D. 6 : 4 : 3
40.
If the mean age of combined group of boys and girls is 18 years and the mean of age of boys is 20 and that of girls is 16, then what is the percentage of boys in the group?
A.
60
B.
50
C.
45
D.
40
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ANSWER :
B. 50
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