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

11.
The expression
\( \frac{(x^{3} - 1)(x^{2} - 9x + 14)}{(x^{2} + x + 1)(x^{2} - 8x + 7)} \)
simplifies to
A.
\( (x - 1) \)
B.
\( (x - 2) \)
C.
\( (x - 7) \)
D.
\( (x + 2) \)
😑 View Answer Error
ANSWER :
B. \( (x - 2) \)
12.
What should be added to \( \frac{1}{(x - 2)(x - 4)} \) to get \( \frac{2x - 5}{(x^{2} - 5x + 6)(x - 4)} \)?
A.
\( \frac{1}{(x^{2} - 7x + 12)} \)
B.
\( \frac{1}{(x^{2} + 7x + 12)} \)
C.
\( \frac{1}{(x^{2} - 7x - 12)} \)
D.
\( \frac{1}{(x^{2} + 7x - 12)} \)
😑 View Answer Error
ANSWER :
A. \( \frac{1}{(x^{2} - 7x + 12)} \)
13.
If \( \frac{x}{a} + \frac{y}{b} = a + b \) and \( \frac{x}{a^{2}} + \frac{y}{b^{2}} = 2 \), then what is \( \frac{x}{a^{2}} - \frac{y}{b^{2}} \) equal to?
A.
-2
B.
-1
C.
0
D.
1
😑 View Answer Error
ANSWER :
C. 0
14.
If \( (x - k) \) is the HCF of \( x^{2} + ax + b \) and \( x^{2} + cx + d \), then what is the value of \( k \)?
A.
\( \frac{d - b}{c - a} \)
B.
\( \frac{d - b}{a - c} \)
C.
\( \frac{d + b}{c + a} \)
D.
\( \frac{d - b}{c + a} \)
😑 View Answer Error
ANSWER :
B. \( \frac{d - b}{a - c} \)
15.
Consider the following statements:
1. If \( x \) is directly proportional to \( z \) and \( y \) is directly proportional to \( z \), then \( (x^{2} - y^{2}) \) is directly proportional to \( z^{2} \).
2. If \( x \) is inversely proportional to \( z \) and \( y \) is inversely proportional to \( z \), then \( (xy) \) is inversely proportional to \( z^{2} \).
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
C. Both 1 and 2
16.
What is the HCF of \( x^{3} - 19x + 30 \) and \( x^{2} - 5x + 6 \)?
A.
\( (x + 2)(x - 3) \)
B.
\( (x - 2)(x + 3) \)
C.
\( (x + 2)(x - 1) \)
D.
\( (x - 3)(x - 2) \)
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ANSWER :
D. \( (x - 3)(x - 2) \)
17.
What is
\( \frac{8x}{1 - x^{4}} - \frac{4x}{x^{2} + 1} + \frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} \)
equal to?
A.
0
B.
1
C.
2
D.
4
😑 View Answer Error
ANSWER :
A. 0
18.
For what integral value of \( x \) is
\( \frac{12}{7 - \frac{6}{7 - \frac{3}{5 - x}}} = x \)?
A.
4
B.
3
C.
2
D.
1
😑 View Answer Error
ANSWER :
C. 2
19.
If \( x(x - 1)(x - 2)(x - 3) + 1 = k^{2} \), then which one of the following is a possible expression for \( k \)?
A.
\( x^{2} - 3x + 1 \)
B.
\( x^{2} - 3x - 1 \)
C.
\( x^{2} + 3x - 1 \)
D.
\( x^{2} - 2x - 1 \)
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ANSWER :
A. \( x^{2} - 3x + 1 \)
20.
What is
\( \frac{1}{bc(a - b)(a - c)} + \frac{1}{ca(b - c)(b - a)} + \frac{1}{ab(c - a)(c - b)} \)
equal to?
A.
\( a + b + c \)
B.
3
C.
\( ab + bc + ca \)
D.
0
😑 View Answer Error
ANSWER :
D. 0
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