CDS Exam (I)- 2016 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2016 - Elementary Mathematics

CDS Exam (I)- 2016 - Elementary Mathematics Defence Questions

1.
If the roots of the equation \( kx^{2} + mx + m = 0 \) are in the ratio \( p : q \), then \( \sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} + \sqrt{\frac{m}{k}} \) is equal to
A.
0
B.
1
C.
2
D.
3
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ANSWER :
A. 0
2.
If \( \sqrt{3x^{2} - 7x - 30} - \sqrt{2x^{2} - 7x - 5} = x - 5 \) has \( \alpha \) and \( \beta \) as its roots, then the value of \( \alpha\beta \) is
A.
30
B.
-5
C.
0
D.
5
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ANSWER :
A. 30
3.
If \( \frac{p}{x} + \frac{q}{y} = m \) and \( \frac{q}{x} + \frac{p}{y} = n \), then what is \( \frac{x}{y} \) equal to?
A.
\( \frac{np + mq}{mp + nq} \)
B.
\( \frac{np + mq}{mp - nq} \)
C.
\( \frac{np - mq}{mp - nq} \)
D.
\( \frac{np - mq}{mp + nq} \)
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ANSWER :
C. \( \frac{np - mq}{mp - nq} \)
4.
If \( a^{2} - by - cz = 0 \), \( ax - b^{2} + cz = 0 \) and \( ax + by - c^{2} = 0 \), then the value of \( \frac{x}{a + x} + \frac{y}{b + y} + \frac{z}{c + z} \) will be
A.
\( a + b + c \)
B.
3
C.
1
D.
0
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ANSWER :
C. 1
5.
If the equations \( x^{2} - px + q = 0 \) and \( x^{2} + qx - p = 0 \) have a common root, then which one of the following is correct?
A.
\( p - q = 0 \)
B.
\( p + q - 2 = 0 \)
C.
\( p + q - 1 = 0 \)
D.
\( p - q - 1 = 0 \)
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ANSWER :
D. \( p - q - 1 = 0 \)
6.
If \( x = 2^{\frac{1}{3}} + 2^{-\frac{1}{3}} \), then the value of \( 2x^{3} - 6x - 5 \) is equal to
A.
0
B.
1
C.
2
D.
3
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ANSWER :
A. 0
7.
The sum and difference of two expressions are \( 5x^{2} - x - 4 \) and \( x^{2} + 9x - 10 \) respectively. The HCF of the two expressions will be
A.
\( (x + 1) \)
B.
\( (x - 1) \)
C.
\( (3x + 7) \)
D.
\( (2x - 3) \)
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ANSWER :
B. \( (x - 1) \)
8.
If \( (s - a) + (s - b) + (s - c) = s \), then the value of \( \frac{(s - a)^{2} + (s - b)^{2} + (s - c)^{2} + s^{2}}{a^{2} + b^{2} + c^{2}} \) will be
A.
3
B.
1
C.
0
D.
-1
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ANSWER :
B. 1
9.
If the polynomial \( x^{6} + px^{5} + qx^{4} - x^{2} - x - 3 \) is divisible by \( (x^{4} - 1) \), then the value of \( p^{2} + q^{2} \) is
A.
1
B.
9
C.
10
D.
13
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ANSWER :
C. 10
10.
Let p and q be non-zero integers. Consider the polynomial \( A(x) = x^{2} + px + q \)
It is given that \( (x - m) \) and \( (x - km) \) are simple factors of \( A(x) \), where m is a non-zero integer and k is a positive integer, \( k > 2 \). Which one of the following is correct?
A.
\( (k + 1)^{2}p^{2} = kq \)
B.
\( (k + 1)^{2}q = kp^{2} \)
C.
\( k^{2}q = (k + 1)p^{2} \)
D.
\( k^{2}p^{2} = (k + 1)^{2}q \)
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ANSWER :
B. \( (k + 1)^{2}q = kp^{2} \)
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