CDS Exam (I)- 2018 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2018 - Elementary Mathematics

CDS Exam (I)- 2018 - Elementary Mathematics Defence Questions

11.
If (x + 3) is a factor of \( x^{3} + 3x^{2} + 4x + k \), then what is the value of k?
A.
12
B.
24
C.
36
D.
72
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ANSWER :
A. 12
12.
The smallest integer with 4 digits which is a perfect square is
A.
1000
B.
1024
C.
1089
D.
None of the above
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ANSWER :
B. 1024
13.
Which one of the following is a zero of the polynomial \( 3x^{3} + 4x^{2} - 7 \)?
A.
0
B.
1
C.
2
D.
−1
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ANSWER :
B. 1
14.
There are two numbers which are greater than 21 and their LCM and HCF are 3003 and 21 respectively. What is the sum of these numbers?
A.
504
B.
508
C.
514
D.
528
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ANSWER :
A. 504
15.
If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^{2} + bx + c = 0 \), then what is the value of the expression \( (\alpha + 1)(\beta + 1) \)?
A.
\( \frac{a+b+c}{a} \)
B.
\( \frac{b+c-a}{a} \)
C.
\( \frac{a-b+c}{a} \)
D.
\( \frac{a+b-c}{a} \)
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ANSWER :
C. \( \frac{a-b+c}{a} \)
16.
The remainder when \( 3x^{3} + kx^{2} + 5x - 6 \) is divided by (x + 1) is −7. What is the value of k?
A.
−14
B.
14
C.
−7
D.
7
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ANSWER :
D. 7
17.
If f(x) and g(x) are polynomials of degree p and q respectively, then the degree of \( \{f(x) \pm g(x)\} \) (if it is non-zero) is
A.
Greater than min(p, q)
B.
Greater than max(p, q)
C.
Less than or equal to max(p, q)
D.
Equal to min(p, q)
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ANSWER :
C. Less than or equal to max(p, q)
18.
What is the value of \( \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}} - \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} \)?
A.
\( -2\sqrt{15} \)
B.
\( 2\sqrt{15} \)
C.
\( \sqrt{15} \)
D.
\( -\sqrt{15} \)
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ANSWER :
A. \( -2\sqrt{15} \)
19.
What is the value of \( \frac{1}{1 + x^{b-a} + x^{c-a}} + \frac{1}{1 + x^{a-b} + x^{c-b}} + \frac{1}{1 + x^{a-c} + x^{b-c}} \) where \( x \neq 0 \)?
A.
−1
B.
0
C.
1
D.
3
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ANSWER :
C. 1
20.
The sum of a number and its square is 20. Then the number is
A.
−5 or 4
B.
2 or 3
C.
−5 only
D.
5 or −4
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ANSWER :
A. −5 or 4
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