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

11.
If \( x^{6} + \frac{1}{x^{6}} = k\left(x^{2} + \frac{1}{x^{2}}\right) \), then k is equal to
A.
\( \left(x^{4} - 1 + \frac{1}{x^{4}}\right) \)
B.
\( \left(x^{2} - 1 + \frac{1}{x^{2}}\right) \)
C.
\( \left(x^{4} + 1 + \frac{1}{x^{4}}\right) \)
D.
\( \left(x^{4} - 1 - \frac{1}{x^{4}}\right) \)
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ANSWER :
A. \( \left(x^{4} - 1 + \frac{1}{x^{4}}\right) \)
12.
If the sum of the squares of three consecutive natural numbers is 110, then the sum of their cubes is
A.
625
B.
654
C.
684
D.
725
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ANSWER :
C. 684
13.
The product of two integers p and q, where p > 60 and q > 60, is 7168 and their HCF is 16. The sum of these two integers is
A.
256
B.
184
C.
176
D.
164
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ANSWER :
C. 176
14.
If \( \log_{10} 2 = 0.3010 \) and \( \log_{10} 3 = 0.4771 \), then the value of \( \log_{100} (0.72) \) is equal to
A.
0.9286
B.
\( \bar{1}.9286 \)
C.
\( \bar{1}.8572 \)
D.
1.8572
😑 View Answer Error
ANSWER :
B. \( \bar{1}.9286 \)
15.
If \( a^{x} = b^{y} = c^{z} \) and abc = 1, then the value of \( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \) will be equal to
A.
-1
B.
0
C.
1
D.
3
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ANSWER :
B. 0
16.
If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^{2} + bx + c = 0 \), then the value of \( \frac{1}{a\alpha + b} + \frac{1}{a\beta + b} \) is
A.
\( \frac{a}{bc} \)
B.
\( \frac{b}{ac} \)
C.
\( \frac{c}{ab} \)
D.
\( \frac{1}{abc} \)
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ANSWER :
B. \( \frac{b}{ac} \)
17.
Consider the following statements in respect of three 3-digit numbers XYZ, YZX and ZXY:
1. The sum of the numbers is not divisible by (X + Y + Z).
2. The sum of the numbers is divisible by 111.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
B. 2 only
18.
The number of all pairs (m, n), where m and n are positive integers, such that \( \frac{1}{m} + \frac{1}{n} - \frac{1}{mn} = \frac{2}{5} \) is
A.
6
B.
5
C.
4
D.
2
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ANSWER :
C. 4
19.
If \( a = xy^{p-1} \), \( b = yz^{q-1} \), \( c = zx^{r-1} \), then \( a^{q-r} b^{r-p} c^{p-q} \) is equal to
A.
abc
B.
xyz
C.
0
D.
None of the above
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ANSWER :
D. None of the above
20.
The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their interior angles is \( 9^{\circ} \). Consider the following statements:
1. One of them is a pentagon and the other is a rectangle.
2. One of them is a decagon and the other is an octagon.
3. The sum of their exterior angles is \( 720^{\circ} \).
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
1 and 3
D.
2 and 3
😑 View Answer Error
ANSWER :
D. 2 and 3
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