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

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CDS Exam (II)- 2021 - Elementary Mathematics

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

21.
If \( 96 - 64a^{3} + \frac{8}{a^{6}} - \frac{48}{a^{3}} - t^{3} = 0 \), then what is \( a^{2}t + 4a^{3} \) equal to?
A.
0
B.
1
C.
2
D.
3
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ANSWER :
C. 2
22.
If \( A + B = \frac{x^{2} - 8}{x + 2} \) and \( A - B = \frac{-x^{2} + 2x + 4}{x + 2} \), then what is \( B \) equal to?
A.
\( \frac{x^{2} - 4}{x^{2} + 4x + 4} \)
B.
\( \frac{x^{2} - 4}{x^{2} - 4x + 4} \)
C.
\( \frac{2x^{2} - 7x + 3}{2x - 1} \)
D.
\( \frac{2x^{2} + 7x - 3}{2x - 1} \)
😑 View Answer Error
ANSWER :
C. \( \frac{2x^{2} - 7x + 3}{2x - 1} \)
23.
What is
\( \frac{x^{4}}{(x^{2} - y^{2})(x^{2} - z^{2})} + \frac{y^{4}}{(y^{2} - x^{2})(y^{2} - z^{2})} + \frac{z^{4}}{(z^{2} - x^{2})(z^{2} - y^{2})} \) equal to?
A.
-1
B.
0
C.
1
D.
\( x^{2} + y^{2} + z^{2} \)
😑 View Answer Error
ANSWER :
D. \( x^{2} + y^{2} + z^{2} \)
24.
If \( (2ab - b^{2}) : (6a^{2} - ab) = 1 : 6 \), then what is \( (a + b) : (a - b) \) equal to?
A.
3 only
B.
5 only
C.
-3 or 3
D.
-5 or 5
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ANSWER :
D. -5 or 5
25.
If \( \frac{x}{b + c - a} = \frac{y}{b - c - a} = \frac{z}{a + b - c} = k \), then what is
\( x^{2} + y^{2} + z^{2} - 2xy - 2yz + 2zx \) equal to?
A.
\( k^{2}(a^{2} + b^{2} + c^{2}) \)
B.
\( k^{2}(a^{2} - b^{2} + c^{2}) \)
C.
\( k^{2}(a + b + c)^{2} \)
D.
\( k^{2}(a - b + c)^{2} \)
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ANSWER :
C. \( k^{2}(a + b + c)^{2} \)
26.
If three positive numbers are in the ratio 2 : 3 : 5 and the sum of their squares is 1368, then what is sum of the numbers?
A.
30
B.
45
C.
60
D.
75
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ANSWER :
C. 60
27.
Consider the following inequalities:
1. \( \frac{a^{2} - b^{2}}{a^{2} + b^{2}} > \frac{a - b}{a + b} \) where \( a > b > 0 \)
2. \( \frac{a^{3} + b^{3}}{a^{2} + b^{2}} > \frac{a^{2} + b^{2}}{a + b} \) only when \( a > b > 0 \)
Which of the above is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
A. 1 only
28.
Let work done by \( (3n - 1) \) men in \( (2n + 1) \) days be \( x \) and work done by \( (3n + 1) \) men in \( (4n - 3) \) days be \( y \). If \( x : y = 6 : 11 \), then what is the value of \( n \)?
A.
6
B.
7
C.
8
D.
9
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ANSWER :
B. 7
29.
If \( \frac{ay - bx}{c} = \frac{cx - az}{b} = \frac{bz - cy}{a} \), then which of the following is/are correct?
1. \( \frac{x}{a} = \frac{y}{b} \)
2. \( \frac{x + y + z}{a + b + c} = \frac{z}{c} \)
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 :
C. Both 1 and 2
30.
A person wishes to fence \( 375 m^{2} \) rectangular garden. He has 65 m of barbed wire and is able to fence only three sides of the garden. What is the perimeter of the garden?
A.
80 m
B.
84 m
C.
90 m
D.
100 m
😑 View Answer Error
ANSWER :
A. 80 m
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