CDS Exam (II)- 2018 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2018 - Elementary Mathematics

CDS Exam (II)- 2018 - Elementary Mathematics Defence Questions

1.
The highest four-digit number which is divisible by each of the numbers 16, 36, 45, 48 is
A.
9180
B.
9360
C.
9630
D.
9840
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ANSWER :
B. 9360
2.
If \( x^{a} = y \), \( y^{b} = z \) and \( z^{c} = x \), then the value of abc is
A.
1
B.
2
C.
-1
D.
0
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ANSWER :
A. 1
3.
If \( x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}} \), then the value of the expression \( x^{3} - 6x^{2} + 6x \) will be
A.
2
B.
1
C.
0
D.
-2
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ANSWER :
A. 2
4.
How many five-digit numbers of the form XXYXX is/are divisible by 33?
A.
1
B.
3
C.
5
D.
Infinite
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ANSWER :
B. 3
5.
A five-digit number XY235 is divisible by 3 where X and Y are digits satisfying \( X + Y \leq 5 \). What is the number of possible pairs of values of (X, Y)?
A.
5
B.
6
C.
7
D.
9
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ANSWER :
C. 7
6.
If \( x^{2} - 6x - 27 > 0 \), then which one of the following is correct?
A.
\( -3 < x < 9 \)
B.
\( x < 9 \) or \( x > -3 \)
C.
\( x > 9 \) or \( x < -3 \)
D.
\( x < -3 \) only
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ANSWER :
C. \( x > 9 \) or \( x < -3 \)
7.
The number of divisors of the number 38808, exclusive of the divisors 1 and itself, is
A.
74
B.
72
C.
70
D.
68
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ANSWER :
C. 70
8.
HCF and LCM of two polynomials are \( (x + 3) \) and \( (x^{3} - 9x^{2} - x + 105) \) respectively. If one of the two polynomials is \( x^{2} - 4x - 21 \), then the other is
A.
\( x^{2} + 2x - 21 \)
B.
\( x^{2} + 2x + 15 \)
C.
\( x^{2} - 2x - 15 \)
D.
\( x^{2} - x - 15 \)
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ANSWER :
C. \( x^{2} - 2x - 15 \)
9.
If \( \alpha \) and \( \beta \) are two real numbers such that \( \alpha + \beta = -\frac{q}{p} \) and \( \alpha\beta = \frac{r}{p} \), where \( 1 < p < q < r \), then which one of the following is the greatest?
A.
\( \frac{1}{\alpha + \beta} \)
B.
\( \frac{1}{\alpha} + \frac{1}{\beta} \)
C.
\( \frac{1}{\alpha\beta} \)
D.
\( \frac{\alpha\beta}{\alpha + \beta} \)
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ANSWER :
C. \( \frac{1}{\alpha\beta} \)
10.
Two workers 'A' and 'B' working together completed a job in 5 days. Had 'A' worked twice as efficiently as he actually did and 'B' worked one-third as efficiently as he actually did, the work would have completed in 3 days. In how many days could 'A' alone complete the job?
A.
\( 3\frac{1}{2} \) days
B.
\( 4\frac{1}{6} \) days
C.
\( 5\frac{1}{5} \) days
D.
\( 6\frac{1}{4} \) days
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ANSWER :
D. \( 6\frac{1}{4} \) days
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