CDS Exam (II)- 2020 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2020 - Elementary Mathematics

CDS Exam (II)- 2020 - Elementary Mathematics Defence Questions

31.
What is the HCF of the polynomials \( x^{6} - 3x^{4} + 3x^{2} - 1 \) and \( x^{3} + 3x^{2} + 3x + 1 \)?
A.
(x + 1)
B.
\( (x + 1)^{2} \)
C.
\( x^{2} + 1 \)
D.
\( (x + 1)^{3} \)
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ANSWER :
D. \( (x + 1)^{3} \)
32.
The HCF and the LCM of two polynomials are 3x + 1 and \( 30x^{3} + 7x^{2} - 10x - 3 \) respectively. If one polynomial is \( 6x^{2} + 5x + 1 \), then what is the other polynomial?
A.
\( 15x^{2} + 4x + 3 \)
B.
\( 15x^{2} + 4x - 3 \)
C.
\( 15x^{2} - 4x + 3 \)
D.
\( 15x^{2} - 4x - 3 \)
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ANSWER :
D. \( 15x^{2} - 4x - 3 \)
33.
If (p + 2)(2q - 1) = 2pq - 10 and (p - 2)(2q - 1) = 2pq - 10, then what is pq equal to?
A.
-10
B.
-5
C.
5
D.
10
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ANSWER :
C. 5
34.
What is the value of
\( \frac{a^{2} + ac}{a^{2}c - c^{3}} - \frac{a^{2} - c^{2}}{a^{2}c + 2ac^{2} + c^{3}} - \frac{2c}{a^{2} - c^{2}} + \frac{3}{a + c} \)?
A.
0
B.
1
C.
\( \frac{ac}{a^{2} + c^{2}} \)
D.
\( \frac{6}{a + c} \)
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ANSWER :
D. \( \frac{6}{a + c} \)
35.
What is the square root of \( 4x^{4} + 8x^{3} - 4x + 1 \)?
A.
\( 2x^{2} - 2x - 1 \)
B.
\( 2x^{2} - x - 1 \)
C.
\( 2x^{2} + 2x + 1 \)
D.
\( 2x^{2} + 2x - 1 \)
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ANSWER :
D. \( 2x^{2} + 2x - 1 \)
36.
The sum of the digits of a two digit number is 13 and the difference between the number and that formed by reversing the digits is 27. What is the product of the digits of the number?
A.
35
B.
40
C.
45
D.
54
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ANSWER :
B. 40
37.
If \( \frac{x}{b + c} = \frac{y}{c + a} = \frac{z}{b - a} \), then which one of the following is correct?
A.
x + y + z = 0
B.
x - y - z = 0
C.
x + y - z = 0
D.
x + 2y + 3z = 0
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ANSWER :
B. x - y - z = 0
38.
X, Y and Z travel from the same place with uniform speeds 4 km/hr, 5 km/hr and 6 km/hr respectively. Y starts 2 hours after X. How long after Y must Z start in order that they overtake X at the same instant?
A.
\( \frac{3}{2} \) hours
B.
\( \frac{4}{3} \) hours
C.
\( \frac{9}{8} \) hours
D.
\( \frac{11}{8} \) hours
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ANSWER :
B. \( \frac{4}{3} \) hours
39.
\( 1 - x - x^{n} + x^{n+1} \), where n is a natural number, is divisible by
A.
\( (1 + x)^{2} \)
B.
\( (1 - x)^{2} \)
C.
\( 1 - 2x - x^{2} \)
D.
\( 1 + 2x - x^{2} \)
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ANSWER :
B. \( (1 - x)^{2} \)
40.
A person sold an article for ₹ 75 which cost him ₹ x. He finds that he realised x% profit on his outlay. What is x equal to?
A.
20%
B.
25%
C.
50%
D.
100%
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ANSWER :
C. 50%
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