CDS Exam (II)- 2014 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2014 - Elementary Mathematics

CDS Exam (II)- 2014 - Elementary Mathematics Defence Questions

21.
If \( a_{n} = 3 - 4n \), then what is \( a_{1} + a_{2} + a_{3} + \ldots + a_{n} \) equal to?
A.
\( -n(4n - 3) \)
B.
\( -n(2n - 1) \)
C.
\( -n^{2} \)
D.
\( -n(2n + 1) \)
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ANSWER :
B. \( -n(2n - 1) \)
22.
A train travels at a speed of 40 km/hr and another train at a speed of 20 m/s. What is the ratio of speed of the first train to that of the second train?
A.
2 : 1
B.
5 : 9
C.
5 : 3
D.
9 : 5
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ANSWER :
B. 5 : 9
23.
\( (x + y) : (x - y) = 3 : 5 \) and xy = positive imply that
A.
x and y are both positive
B.
x and y are both negative
C.
one of them is positive and one of them is negative
D.
no real solutions for x and y exist
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ANSWER :
D. no real solutions for x and y exist
24.
How many pairs of X and Y are possible in the number 763X4Y2, if the number is divisible by 9?
A.
8
B.
9
C.
10
D.
11
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ANSWER :
D. 11
25.
What is the remainder when \( 4^{1012} \) is divided by 7?
A.
1
B.
2
C.
3
D.
4
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ANSWER :
D. 4
26.
What is the highest common factor of \( 2x^{3} + x^{2} - x - 2 \) and \( 3x^{3} - 2x^{2} + x - 2 \)?
A.
\( x - 1 \)
B.
\( x + 1 \)
C.
\( 2x + 1 \)
D.
\( 2x - 1 \)
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ANSWER :
A. \( x - 1 \)
27.
What is the remainder when \( (1235 \times 4523 \times 2451) \) is divided by 12?
A.
1
B.
3
C.
5
D.
7
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ANSWER :
B. 3
28.
What is the remainder when \( (17^{23} + 23^{23} + 29^{23}) \) is divided by 23?
A.
0
B.
1
C.
2
D.
3
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ANSWER :
A. 0
29.
p, q and r are prime numbers such that \( p < q < r < 13 \). In how many cases would \( (p + q + r) \) also be a prime number?
A.
1
B.
2
C.
3
D.
None of the above
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ANSWER :
B. 2
30.
The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF is 1456. If one of the numbers is 160, then what is the other number?
A.
120
B.
136
C.
144
D.
184
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ANSWER :
C. 144
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