CDS Exam (I)- 2019 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2019 - Elementary Mathematics

CDS Exam (I)- 2019 - Elementary Mathematics Defence Questions

41.
What is the value of \( \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\ldots}}}} \)?
A.
1
B.
2
C.
3
D.
4
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ANSWER :
B. 2
42.
In an examination, 52% candidates failed in English and 42% failed in Mathematics. If 17% failed in both the subjects, then what percent passed in both the subjects?
A.
77
B.
58
C.
48
D.
23
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ANSWER :
D. 23
43.
A man who recently died left a sum of ₹3,90,000 to be divided among his wife, five sons and four daughters. He directed that each son should receive 3 times as much as each daughter receives and that each daughter should receive twice as much as their mother receives. What was the wife's share?
A.
₹14,000
B.
₹12,000
C.
₹10,000
D.
₹9,000
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ANSWER :
C. ₹10,000
44.
What is the least number of complete years in which a sum of money put out at 40% annual compound interest will be more than trebled?
A.
3
B.
4
C.
5
D.
6
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ANSWER :
B. 4
45.
A person divided a sum of ₹17,200 into three parts and invested at 5%, 6% and 9% per annum simple interest. At the end of two years, he got the same interest on each part of money. What is the money invested at 9%?
A.
₹3,200
B.
₹4,000
C.
₹4,800
D.
₹5,000
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ANSWER :
B. ₹4,000
46.
What is \( \frac{(x-y)^{3} + (y-z)^{3} + (z-x)^{3}}{3(x-y)(y-z)(z-x)} \) equal to?
A.
1
B.
0
C.
\( \frac{1}{3} \)
D.
3
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ANSWER :
A. 1
47.
If \( a^{x} = b^{y} = c^{z} \) and \( b^{2} = ac \), then what is \( \frac{1}{x} + \frac{1}{z} \) equal to?
A.
\( \frac{1}{y} \)
B.
\( \frac{3}{2y} \)
C.
\( \frac{2}{y} \)
D.
\( \frac{y}{2} \)
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ANSWER :
C. \( \frac{2}{y} \)
48.
If p and q are the roots of the equation \( x^{2} - 15x + r = 0 \) and p − q = 1, then what is the value of r?
A.
55
B.
56
C.
60
D.
64
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ANSWER :
B. 56
49.
For the inequation \( x^{2} - 7x + 12 > 0 \), which one of the following is correct?
A.
\( 3 < x < 4 \)
B.
\( -\infty < x < 3 \) only
C.
\( 4 < x < \infty \) only
D.
\( -\infty < x < 3 \) or \( 4 < x < \infty \)
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ANSWER :
D. \( -\infty < x < 3 \) or \( 4 < x < \infty \)
50.
The expression \( 5^{2n} - 2^{3n} \) has a factor
A.
3
B.
7
C.
17
D.
None of the above
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ANSWER :
C. 17
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