CDS Exam (I)- 2017 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2017 - Elementary Mathematics

CDS Exam (I)- 2017 - Elementary Mathematics Defence Questions

1.
What is \( \sqrt{\frac{0.064 \times 6.25}{0.081 \times 4.84}} \) equal to?
A.
\( \frac{10}{99} \)
B.
\( \frac{100}{99} \)
C.
\( \frac{99}{10} \)
D.
\( \frac{99}{100} \)
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ANSWER :
B. \( \frac{100}{99} \)
2.
\( (x + 4) \) is a factor of which one of the following expressions?
A.
\( x^{2} - 7x + 44 \)
B.
\( x^{2} + 7x - 44 \)
C.
\( x^{2} - 7x - 44 \)
D.
\( x^{2} + 7x + 44 \)
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ANSWER :
B. \( x^{2} + 7x - 44 \)
3.
If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( 2x^{2} + 6x + k = 0 \), where \( k < 0 \), then what is the maximum value of \( \frac{\alpha}{\beta} + \frac{\beta}{\alpha} \)?
A.
2
B.
\( -2 \)
C.
9
D.
\( -9 \)
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ANSWER :
B. \( -2 \)
4.
Consider the following statements :
1. If \( a = bc \) with HCF \( (b, c) = 1 \), then HCF \( (c, bd) = \) HCF \( (c, d) \).
2. If \( a = bc \) with HCF \( (b, c) = 1 \), then LCM \( (a, d) = \) LCM \( (c, bd) \).
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 :
A. 1 only
5.
What is the square root of \( \frac{(0.75)^{3}}{1 - 0.75} + \left[0.75 + (0.75)^{2} + 1\right] \)?
A.
1
B.
2
C.
3
D.
4
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ANSWER :
B. 2
6.
What is the number of digits in \( 2^{40} \)? (Given that \( \log_{10} 2 = 0.301 \))
A.
14
B.
13
C.
12
D.
11
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ANSWER :
B. 13
7.
If one root of \( (a^{2} - 5a + 3)x^{2} + (3a - 1)x + 2 = 0 \) is twice the other, then what is the value of 'a'?
A.
\( \frac{2}{3} \)
B.
\( -\frac{2}{3} \)
C.
\( \frac{1}{3} \)
D.
\( -\frac{1}{3} \)
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ANSWER :
A. \( \frac{2}{3} \)
8.
What is the remainder when the number \( (4444)^{4444} \) is divided by 9?
A.
4
B.
6
C.
7
D.
8
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ANSWER :
C. 7
9.
If \( x = \frac{\sqrt{a + b} + \sqrt{a - b}}{\sqrt{a + b} - \sqrt{a - b}} \), then what is \( bx^{2} - 2ax + b \) equal to \( (b \neq 0) \)?
A.
0
B.
1
C.
ab
D.
2ab
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ANSWER :
A. 0
10.
What is the value of \( \frac{(443 + 547)^{2} + (443 - 547)^{2}}{443 \times 443 + 547 \times 547} \)?
A.
0
B.
1
C.
2
D.
3
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ANSWER :
C. 2
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