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

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CDS Exam (I)- 2014 - Elementary Mathematics

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

1.
What is the number of positive integral solutions of the equations HCF \( (a, b) = 5 \) and \( a + b = 65 \)?
A.
None
B.
Infinitely many
C.
Less than 65
D.
Exactly one
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ANSWER :
C. Less than 65
2.
The difference of two consecutive cubes
A.
is always a perfect square
B.
is never divisible by 2
C.
is always even
D.
None of the above
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ANSWER :
B. is never divisible by 2
3.
Let \( a, b \) be positive integers. What is HCF \( \left(\frac{a}{HCF(a, b)}, \frac{b}{HCF(a, b)}\right) \) equal to?
A.
\( a \)
B.
\( b \)
C.
1
D.
\( \frac{a}{HCF(a, b)} \)
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ANSWER :
C. 1
4.
The product of four consecutive natural numbers plus one is
A.
a non-square
B.
always sum of two square numbers
C.
a square
D.
None of the above
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ANSWER :
C. a square
5.
For any integers 'a' and 'b' with HCF \( (a, b) = 1 \), what is HCF \( (a + b, a - b) \) equal to?
A.
It is always 1
B.
It is always 2
C.
Either 1 or 2
D.
None of the above
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ANSWER :
C. Either 1 or 2
6.
The expression \( 2x^{3} + x^{2} - 2x - 1 \) is divisible by
A.
\( x + 2 \)
B.
\( 2x + 1 \)
C.
\( x - 2 \)
D.
\( 2x - 1 \)
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ANSWER :
B. \( 2x + 1 \)
7.
A positive number, when increased by 10, equals 200 times its reciprocal. What is that number?
A.
100
B.
10
C.
20
D.
200
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ANSWER :
B. 10
8.
\( x^{3} + 6x^{2} + 11x + 6 \) is divisible by
A.
\( (x + 1) \) only
B.
\( (x + 2) \) only
C.
\( (x + 3) \) only
D.
All of the above
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ANSWER :
D. All of the above
9.
The present age of Ravi's father is four times Ravi's present age. Five years back he was seven times as old as Ravi was at that time. What is the present age of Ravi's father?
A.
84 years
B.
70 years
C.
40 years
D.
35 years
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ANSWER :
C. 40 years
10.
The average age of male employees in a firm is 52 years and that of female employees is 42 years. The mean age of all employees is 50 years. The percentage of male and female employees are respectively
A.
80% and 20%
B.
20% and 80%
C.
50% and 50%
D.
52% and 48%
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ANSWER :
A. 80% and 20%
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