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

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CDS Exam (II)- 2014 - Elementary Mathematics

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

41.
If m and n are the roots of the equation \( x^{2} + ax + b = 0 \), and \( m^{2} \) and \( n^{2} \) are the roots of the equation \( x^{2} - cx + d = 0 \), then which of the following is/are correct?
1. \( 2b - a^{2} = c \)
2. \( b^{2} = d \)
Select the correct answer using the code given below.
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
B. 2 only
42.
If \( N^{2} - 33 \), \( N^{2} - 31 \) and \( N^{2} - 29 \) are prime numbers, then what is the number of possible values of N, where N is an integer?
A.
1
B.
2
C.
6
D.
None of the above
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ANSWER :
B. 2
43.
There are 48 cricket balls, 72 hockey balls and 84 tennis balls, and they have to be arranged in several rows in such a way that every row contains the same number of balls of one type. What is the minimum number of rows required for this to happen?
A.
12
B.
16
C.
17
D.
19
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ANSWER :
C. 17
44.
The HCF of two natural numbers m and n is 24 and their product is 552. How many sets of values of m and n are possible?
A.
1
B.
2
C.
4
D.
No set of m and n is possible satisfying the given conditions
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ANSWER :
D. No set of m and n is possible satisfying the given conditions
45.
If m and n \( (m > n) \) are the roots of the equation \( 7(x + 2a)^{2} + 3a^{2} = 5a(7x + 23a) \) where \( a > 0 \), then what is \( 3m - n \) equal to?
A.
12a
B.
14a
C.
15a
D.
18a
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ANSWER :
C. 15a
46.
A person selling an article for ₹ 96 finds that his loss percent is one-fourth of the amount of rupees that he paid for the article. What can be the cost price?
A.
₹ 160 only
B.
₹ 240 only
C.
₹ 160 or ₹ 240
D.
Neither ₹ 160 nor ₹ 240
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ANSWER :
C. ₹ 160 or ₹ 240
47.
If \( (x + k) \) is the common factor of \( x^{2} + ax + b \) and \( x^{2} + cx + d \), then what is k equal to?
A.
\( \frac{d - b}{c - a} \)
B.
\( \frac{d - b}{a - c} \)
C.
\( \frac{a + b}{c + a} \)
D.
\( \frac{d - b}{c + a} \)
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ANSWER :
A. \( \frac{d - b}{c - a} \)
48.
What is the remainder when \( x^{5} - 5x^{2} + 125 \) is divided by \( x + 5 \)?
A.
0
B.
125
C.
−3125
D.
3125
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ANSWER :
C. −3125
49.
What is the lowest common multiple of \( ab(x^{2} + 1) + x(a^{2} + b^{2}) \) and \( ab(x^{2} - 1) + x(a^{2} - b^{2}) \)?
A.
\( (a^{2}x^{2} - b^{2})(a + bx) \)
B.
\( (a^{2}x^{2} - b^{2})(a + bx)^{2} \)
C.
\( (a^{2}x^{2} - b^{2})(a - bx) \)
D.
\( (a^{2}x^{2} - b^{2})(a - bx)^{2} \)
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ANSWER :
A. \( (a^{2}x^{2} - b^{2})(a + bx) \)
50.
A certain number of two digits is three times the sum of its digits. If 45 is added to the number, the digits will be reversed. What is the sum of the squares of the two digits of the number?
A.
41
B.
45
C.
53
D.
64
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ANSWER :
C. 53
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