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

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CDS Exam (I)- 2014 - Elementary Mathematics

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

11.
15 men complete a work in 16 days. If 24 men are employed, then the time required to complete that work will be
A.
7 days
B.
8 days
C.
10 days
D.
12 days
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ANSWER :
C. 10 days
12.
A train takes 9 seconds to cross a pole. If the speed of the train is 48 km/hr, the length of the train is
A.
150 m
B.
120 m
C.
90 m
D.
80 m
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ANSWER :
B. 120 m
13.
Ravi's brother is 3 years elder to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, the ages of Ravi's father and mother respectively when his brother was born were
A.
32 years and 23 years
B.
32 years and 29 years
C.
35 years and 29 years
D.
35 years and 33 years
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ANSWER :
A. 32 years and 23 years
14.
In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains −9 and −1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was
A.
\( x^{2} + 10x + 9 = 0 \)
B.
\( x^{2} - 10x + 16 = 0 \)
C.
\( x^{2} - 10x + 9 = 0 \)
D.
None of the above
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ANSWER :
C. \( x^{2} - 10x + 9 = 0 \)
15.
If \( m \) and \( n \) are the roots of the equation \( ax^{2} + bx + c = 0 \), then the equation whose roots are \( \frac{m^{2} + 1}{m} \) and \( \frac{n^{2} + 1}{n} \) is
A.
\( acx^{2} + (ab + bc)x + b^{2} + (a - c)^{2} = 0 \)
B.
\( acx^{2} + (ab - bc)x + b^{2} + (a - c)^{2} = 0 \)
C.
\( acx^{2} + (ab - bc)x + b^{2} - (a - c)^{2} = 0 \)
D.
\( acx^{2} + (ab + bc)x + b^{2} - (a - c)^{2} = 0 \)
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ANSWER :
A. \( acx^{2} + (ab + bc)x + b^{2} + (a - c)^{2} = 0 \)
16.
The value of \( x^{2} - 4x + 11 \) can never be less than
A.
7
B.
8
C.
11
D.
22
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ANSWER :
A. 7
17.
If \( \left(x^{2} + \frac{1}{x^{2}}\right) = \frac{17}{4} \), then what is \( \left(x^{3} - \frac{1}{x^{3}}\right) \) equal to?
A.
\( \frac{75}{16} \)
B.
\( \frac{63}{8} \)
C.
\( \frac{95}{8} \)
D.
None of the above
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ANSWER :
B. \( \frac{63}{8} \)
18.
If \( 3x^{4} - 2x^{3} + 3x^{2} - 2x + 3 \) is divided by \( (3x + 2) \), then the remainder is
A.
0
B.
\( \frac{185}{27} \)
C.
\( \frac{181}{25} \)
D.
\( \frac{3}{4} \)
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ANSWER :
B. \( \frac{185}{27} \)
19.
What should be added to the expression \( x(x + a)(x + 2a)(x + 3a) \) so that the sum may be a perfect square?
A.
\( 9a^{2} \)
B.
\( 4a^{2} \)
C.
\( a^{4} \)
D.
None of the above
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ANSWER :
C. \( a^{4} \)
20.
If the roots of the equation \( Ax^{2} + Bx + C = 0 \) are −1 and 1, then which one of the following is correct?
A.
A and C are both zero
B.
A and B are both positive
C.
A and C are both negative
D.
A and C are of opposite sign
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ANSWER :
D. A and C are of opposite sign
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