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

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2015 - Elementary Mathematics

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

11.
The difference between the squares of two consecutive odd integers is always divisible by
A.
3
B.
7
C.
8
D.
16
ANSWER :
C. 8
12.
The expression \( x^{3}q^{2} - x^{3}p^{4} + 4x^{2}p^{4} - 4x^{2}q^{2} + 3xq^{2} - 3xp^{4} \) is divisible by
A.
\( (x - 1) \) only
B.
\( (x - 3) \) only
C.
both \( (x - 1) \) and \( (x - 3) \)
D.
neither \( (x - 1) \) nor \( (x - 3) \)
ANSWER :
C. both \( (x - 1) \) and \( (x - 3) \)
13.
The difference between compound interest and simple interest at the same rate of interest R percent per annum on an amount of ₹ 15,000 for 2 years is ₹ 96. What is the value of R?
A.
8
B.
10
C.
12
D.
Cannot be determined due to insufficient data
ANSWER :
A. 8
14.
What is the maximum value of m if the number \( N = 35 \times 45 \times 55 \times 60 \times 124 \times 75 \) is divisible by \( 5^{m} \)?
A.
4
B.
5
C.
6
D.
7
ANSWER :
C. 6
15.
A milkman claims to sell milk at its cost price only, but 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.
80%
B.
\( \frac{250}{3} \)%
C.
75%
D.
\( \frac{200}{3} \)%
ANSWER :
B. \( \frac{250}{3} \)%
16.
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest on ₹ 12,000 after 3 years at the same rate of interest?
A.
₹ 2,160
B.
₹ 3,120
C.
₹ 3,972
D.
₹ 6,240
ANSWER :
C. ₹ 3,972
17.
16 litres of a mixture contains milk and water in the ratio 5 : 3. If 4 litres of milk is added to this mixture, the ratio of milk to water in the new mixture would be
A.
2 : 1
B.
7 : 3
C.
4 : 3
D.
8 : 3
ANSWER :
B. 7 : 3
18.
A person could save 10% of his income. But 2 years later, when his income increased by 20%, he could save the same amount only as before. By how much percentage has his expenditure increased?
A.
\( 22\frac{2}{9} \)%
B.
\( 23\frac{1}{3} \)%
C.
\( 24\frac{2}{9} \)%
D.
\( 25\frac{2}{9} \)%
ANSWER :
A. \( 22\frac{2}{9} \)%
19.
In how much time would the simple interest on a principal amount be 0.125 times the principal amount at 10% per annum?
A.
\( 1\frac{1}{4} \) years
B.
\( 1\frac{3}{4} \) years
C.
\( 2\frac{1}{4} \) years
D.
\( 2\frac{3}{4} \) years
ANSWER :
A. \( 1\frac{1}{4} \) years
20.
A man rows downstream 32 km and 14 km upstream, and he takes 6 hours to cover each distance. What is the speed of the current?
A.
0.5 km/hr
B.
1 km/hr
C.
1.5 km/hr
D.
2 km/hr
ANSWER :
C. 1.5 km/hr