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

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CDS Exam (I)- 2018 - Elementary Mathematics

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

1.
\( 5^{17} + 5^{18} + 5^{19} + 5^{20} \) is divisible by
A.
7
B.
9
C.
11
D.
13
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ANSWER :
D. 13
2.
If a + b = 2c, then what is the value of \( \frac{a}{a-c} + \frac{b}{b-c} \)?
A.
−1
B.
0
C.
1
D.
2
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ANSWER :
D. 2
3.
If \( x = y^{a} \), \( y = z^{b} \) and \( z = x^{c} \) where \( x \neq 1 \), \( y \neq 1 \), \( z \neq 1 \), then what is the value of abc?
A.
−1
B.
1
C.
0
D.
3
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ANSWER :
B. 1
4.
If 2b = a + c and \( y^{2} = xz \), then what is \( x^{b-c} y^{c-a} z^{a-b} \) equal to?
A.
3
B.
2
C.
1
D.
−1
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ANSWER :
C. 1
5.
Which one of the following is correct?
A.
Decimal expansion of a rational number is terminating.
B.
Decimal expansion of a rational number is non-terminating.
C.
Decimal expansion of an irrational number is terminating.
D.
Decimal expansion of an irrational number is non-terminating and non-repeating.
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ANSWER :
D. Decimal expansion of an irrational number is non-terminating and non-repeating.
6.
If the roots of the equation \( px^{2} + x + r = 0 \) are reciprocal to each other, then which one of the following is correct?
A.
p = 2r
B.
p = r
C.
2p = r
D.
p = 4r
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ANSWER :
B. p = r
7.
If 65x − 33y = 97 and 33x − 65y = 1, then what is xy equal to?
A.
2
B.
3
C.
−2
D.
−3
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ANSWER :
A. 2
8.
If \( \frac{b}{y} + \frac{z}{c} = 1 \) and \( \frac{c}{z} + \frac{x}{a} = 1 \), then what is \( \frac{ab + xy}{bx} \) equal to?
A.
1
B.
2
C.
0
D.
−1
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ANSWER :
A. 1
9.
If \( \frac{a^{2}-1}{a} = 5 \), then what is the value of \( \frac{a^{6}-1}{a^{3}} \)?
A.
125
B.
−125
C.
140
D.
−140
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ANSWER :
C. 140
10.
If x + y + z = 0, then what is \( (y+z-x)^{3} + (z+x-y)^{3} + (x+y-z)^{3} \) equal to?
A.
\( (x+y+z)^{3} \)
B.
3(x + y)(y + z)(z + x)
C.
24xyz
D.
−24xyz
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ANSWER :
D. −24xyz
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