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

1.
What are distinct prime factors of the number 26381?
A.
29, 17, 37
B.
31, 17, 47
C.
19, 37, 13
D.
23, 31, 37
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ANSWER :
D. 23, 31, 37
2.
Which one of the following is a factor of the polynomial
\( (x - 1)(x - 2)(x - 4) - 90 \)?
A.
\( x + 14 \)
B.
\( x - 14 \)
C.
\( x - 6 \)
D.
\( x - 7 \)
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ANSWER :
D. \( x - 7 \)
3.
What is the square root of \( 23 - 4\sqrt{15} \)?
A.
\( \sqrt{6} - 3\sqrt{2} \)
B.
\( 7 - 3\sqrt{5} \)
C.
\( \sqrt{3} - 2\sqrt{5} \)
D.
\( \sqrt{5} - 4\sqrt{3} \)
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ANSWER :
C. \( \sqrt{3} - 2\sqrt{5} \)
4.
What is the remainder after dividing the number \( 37^{1000} \) by 9?
A.
1
B.
3
C.
7
D.
9
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ANSWER :
A. 1
5.
The sum of LCM and HCF of two numbers is 6248 and the difference between LCM and HCF is 6232. If one of the numbers is 104, then what is the other number?
A.
420
B.
480
C.
484
D.
506
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ANSWER :
B. 480
6.
20 men are supposed to complete a work in 10 days. After working for 5 days, they realise that only one-fourth of the work is done. How many more men they need to employ to finish the work on time?
A.
40
B.
30
C.
20
D.
15
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ANSWER :
A. 40
7.
If \( x \) is a negative real number, then which of the following are not correct?
1. There is some natural number \( k \) such that \( kx > 0 \)
2. \( x^{2} + x > 0 \) always
3. \( 2x < x < -x \)
4. \( x^{2} \) is always a rational number
Select the correct answer using the code given below:
A.
1, 2 and 3
B.
1, 2 and 4
C.
1, 3 and 4
D.
2, 3 and 4
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ANSWER :
B. 1, 2 and 4
8.
What is the sum of the linear factors (in \( x \) and \( y \)) of the expression
\( 2x^{2} + xy - 3y^{2} \)?
A.
\( 2x - 3y \)
B.
\( 3x - 2y \)
C.
\( 3x + 2y \)
D.
\( 2x + 3y \)
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ANSWER :
C. \( 3x + 2y \)
9.
Which one of the following equations does not have real roots?
A.
\( 2x^{2} + 16x + 3 = 0 \)
B.
\( 2x^{2} + 10x - 1 = 0 \)
C.
\( x^{2} - 8x + 1 = 0 \)
D.
\( 4x^{2} + 9x + 6 = 0 \)
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ANSWER :
D. \( 4x^{2} + 9x + 6 = 0 \)
10.
The sum and the product of the roots of a quadratic equation are 7 and 12 respectively. If the bigger root is halved and the smaller root is doubled, then what is the resulting quadratic equation?
A.
\( x^{2} - 6x + 12 = 0 \)
B.
\( x^{2} - 8x + 12 = 0 \)
C.
\( x^{2} + 8x + 12 = 0 \)
D.
\( x^{2} - 10x + 12 = 0 \)
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ANSWER :
B. \( x^{2} - 8x + 12 = 0 \)
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