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

21.
The number of pairs (x, y) where x, y are integers satisfying the equation 21x + 48y = 5 is
A.
Zero
B.
One
C.
Two
D.
Infinity
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ANSWER :
A. Zero
22.
Let x and y be positive integers such that x is prime and y is composite. Which of the following statements are correct?
1. (y − x) can be an even integer.
2. xy can be an even integer.
3. 0.5(x + y) can be an even integer.
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
23.
Let x and y be positive integers such that x > y. The expressions 3x + 2y and 2x + 3y when divided by 5 leave remainders 2 and 3 respectively. What is the remainder when (x − y) is divided by 5?
A.
4
B.
2
C.
1
D.
0
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ANSWER :
A. 4
24.
In a race A, B and C take part. A beats B by 30 m, B beats C by 20 m and A beats C by 48 m. Which of the following is/are correct?
1. The length of the race is 300 m.
2. The speeds of A, B and C are in the ratio 50 : 45 : 42.
Select the correct answer using the code given below.
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
C. Both 1 and 2
25.
If the roots of the quadratic equation \( x^{2} - 4x - \log_{10} N = 0 \) are all real, then the minimum value of N is
A.
\( \frac{1}{100} \)
B.
\( \frac{1}{1000} \)
C.
\( \frac{1}{10000} \)
D.
10000
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ANSWER :
C. \( \frac{1}{10000} \)
26.
A motor boat, whose speed is 15 km/hour in still water goes 30 km downstream and comes back in a total of 4 hours and 30 minutes. The speed of the stream is
A.
4 km/hour
B.
5 km/hour
C.
6 km/hour
D.
10 km/hour
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ANSWER :
B. 5 km/hour
27.
If 4 men working 4 hours per day for 4 days complete 4 units of work, then how many units of work will be completed by 2 men working for 2 hours per day in 2 days?
A.
2
B.
1
C.
\( \frac{1}{2} \)
D.
\( \frac{1}{8} \)
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ANSWER :
C. \( \frac{1}{2} \)
28.
By increasing the speed of his car by 15 km/hour, a person covers 300 km distance by taking an hour less than before. The original speed of the car was
A.
45 km/hour
B.
50 km/hour
C.
60 km/hour
D.
75 km/hour
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ANSWER :
C. 60 km/hour
29.
If m persons can paint a house in d days, how many days will it take for (m + 2) persons to paint the same house?
A.
md + 2
B.
md − 2
C.
\( \frac{m + 2}{md} \)
D.
\( \frac{md}{m + 2} \)
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ANSWER :
D. \( \frac{md}{m + 2} \)
30.
If a : b = 3 : 5 and b : c = 7 : 8, then 2a : 3b : 7c is equal to
A.
42 : 105 : 280
B.
13 : 21 : 35
C.
6 : 15 : 40
D.
30 : 21 : 35
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ANSWER :
A. 42 : 105 : 280
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