CDS Exam (I)- 2021 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2021 - Elementary Mathematics

CDS Exam (I)- 2021 - Elementary Mathematics Defence Questions

21.
For how many real values of \( k \) is \( 6kx^{2} + 12kx - 24x + 16 \) a perfect square for every integer \( x \)?
A.
Zero
B.
One
C.
Two
D.
Four
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ANSWER :
C. Two
22.
If \( x + \frac{1}{x} = \frac{5}{2} \), then what is \( x^{4} - \frac{1}{x^{4}} \) equal to?
A.
\( \frac{195}{16} \)
B.
\( \frac{255}{16} \)
C.
\( \frac{625}{16} \)
D.
0
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ANSWER :
B. \( \frac{255}{16} \)
23.
If the equation \( 4x^{2} - 2kx + 3k = 0 \) has equal roots, then what are the values of \( k \)?
A.
4, 12
B.
4, 8
C.
0, 12
D.
0, 8
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ANSWER :
C. 0, 12
24.
If the sum as well as the product of the roots of the equation \( px^{2} - 6x + q = 0 \) is 6, then what is \( (p + q) \) equal to?
A.
8
B.
7
C.
6
D.
5
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ANSWER :
B. 7
25.
\( 4x^{3} + 12x^{2} - x - 3 \) is divisible by
A.
\( (2x + 1) \) only
B.
\( (2x - 1) \) only
C.
Both \( (2x + 1) \) and \( (2x - 1) \)
D.
Neither \( (2x + 1) \) nor \( (2x - 1) \)
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ANSWER :
C. Both \( (2x + 1) \) and \( (2x - 1) \)
26.
Which one of the following fractions will have minimum change in its value if 3 is added to both the numerator and the denominator of all the fractions?
A.
\( \frac{2}{3} \)
B.
\( \frac{3}{4} \)
C.
\( \frac{4}{5} \)
D.
\( \frac{5}{6} \)
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ANSWER :
D. \( \frac{5}{6} \)
27.
Let the average score of a class of boys and girls in an examination be \( p \). The ratio of boys and girls in the class is 3 : 1. If the average score of the boys is \( (p + 1) \), then what is the average score of the girls?
A.
\( (p - 1) \)
B.
\( (p - 2) \)
C.
\( (p - 3) \)
D.
\( p \)
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ANSWER :
C. \( (p - 3) \)
28.
The incomes of A, B and C are in the ratio 7 : 9 : 12 and their expenditures are in the ratio 8 : 9 : 15. If A's saving is one-fourth of his income, then the ratio of savings of A, B and C is
A.
56 : 99 : 69
B.
99 : 56 : 69
C.
69 : 56 : 99
D.
99 : 69 : 56
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ANSWER :
A. 56 : 99 : 69
29.
A train 200 m long passes a platform 100 m long in 10 seconds. What is the speed of the train?
A.
40 m/s
B.
30 m/s
C.
25 m/s
D.
20 m/s
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ANSWER :
B. 30 m/s
30.
If
\( \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \ldots + \frac{1}{n(n + 1)} = \frac{99}{100} \)
then what is the value of \( n \)?
A.
98
B.
99
C.
100
D.
101
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ANSWER :
B. 99
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