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

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2016 - Elementary Mathematics

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

21.
The cost of 2.5 kg rice is Rs. 125. The cost of 9 kg rice is equal to that of 4 kg pulses. The cost of 14 kg pulses is equal to that of 1.5 kg tea. The cost of 2 kg tea is equal to that of 5 kg nuts. What is the cost of 11 kg nuts?
A.
Rs. 2310
B.
Rs. 3190
C.
Rs. 4070
D.
Rs. 4620
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ANSWER :
D. Rs. 4620
22.
Which one of the following is correct in respect of the number 1729?
A.
It cannot be written as the sum of the cubes of two positive integers
B.
It can be written as the sum of the cubes of two positive integers in one way only
C.
It can be written as the sum of the cubes of two positive integers in two ways only
D.
It can be written as the sum of the cubes of two positive integers in three ways only
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ANSWER :
C. It can be written as the sum of the cubes of two positive integers in two ways only
23.
A shopkeeper increases the cost price of an item by 20% and offers a discount of 10% on this marked price. What is his percentage gain?
A.
15%
B.
12%
C.
10%
D.
8%
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ANSWER :
D. 8%
24.
There are two numbers \( p \) and \( q \) such that their HCF is 1. Which of the following statements are correct?
1. Both \( p \) and \( q \) may be prime.
2. One number may be prime and the other composite.
3. Both the numbers may be composite.
Select the correct answer using the code given below.
A.
1 and 2 only
B.
2 and 3 only
C.
1 and 3 only
D.
1, 2 and 3
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ANSWER :
D. 1, 2 and 3
25.
What is \( \sqrt{1 + \frac{1}{1^{2}} + \frac{1}{2^{2}}} + \sqrt{1 + \frac{1}{2^{2}} + \frac{1}{3^{2}}} + \ldots + \sqrt{1 + \frac{1}{2007^{2}} + \frac{1}{2008^{2}}} \) equal to?
A.
\( 2008 - \frac{1}{2008} \)
B.
\( 2007 - \frac{1}{2007} \)
C.
\( 2007 - \frac{1}{2008} \)
D.
\( 2008 - \frac{1}{2009} \)
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ANSWER :
A. \( 2008 - \frac{1}{2008} \)
26.
A person can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. What is the speed of the current?
A.
2 km/hour
B.
2.5 km/hour
C.
3 km/hour
D.
4 km/hour
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ANSWER :
D. 4 km/hour
27.
Consider the following statements in respect of positive odd integers \( x \) and \( y \):
1. \( x^{2} + y^{2} \) is even integer.
2. \( x^{2} + y^{2} \) is divisible by 4.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
A. 1 only
28.
What are the roots of the equation \( 2^{x+2} \cdot 27^{\frac{x}{x-1}} = 9 \)?
A.
\( 2, 1 - \log\left(\frac{3}{2}\right) \)
B.
\( 2, 1 - \log\left(\frac{2}{3}\right) \)
C.
\( -2, 1 - \left(\frac{\log 3}{\log 2}\right) \)
D.
\( -2, 1 - \left(\frac{\log 2}{\log 3}\right) \)
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ANSWER :
C. \( -2, 1 - \left(\frac{\log 3}{\log 2}\right) \)
29.
There are twelve friends A, B, C, D, E, F, G, H, I, J, K and L who invested money in some business in the ratio of 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 10 : 11 : 12 and the duration for which they invested the money is in the ratio of 12 : 11 : 10 : 9 : 8 : 7 : 6 : 5 : 4 : 3 : 2 : 1 respectively. Who will get the maximum profit at the end of the year?
A.
F only
B.
G only
C.
Both F and G
D.
Neither F nor G
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ANSWER :
C. Both F and G
30.
\( 2^{122} + 4^{62} + 8^{42} + 4^{64} + 2^{130} \) is divisible by which one of the following integers?
A.
3
B.
5
C.
7
D.
11
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ANSWER :
D. 11
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