CDS Exam (II)- 2015 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2015 - Elementary Mathematics

CDS Exam (II)- 2015 - Elementary Mathematics Defence Questions

31.
Two trains, one is of 121 m in length at the speed of 40 km/hour and the other is of 99 m in length at the speed of 32 km/hour are running in opposite directions. In how much time will they be completely clear from each other from the moment they meet?
A.
10 s
B.
11 s
C.
16 s
D.
21 s
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ANSWER :
B. 11 s
32.
Three athletes run a 4 km race. Their speeds are in the ratio 16 : 15 : 11. When the winner wins the race, then the distance between the athlete in the second position to the athlete in the third position is
A.
1000 m
B.
800 m
C.
750 m
D.
600 m
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ANSWER :
A. 1000 m
33.
The sum of first 47 terms of the series \( \frac{1}{4} + \frac{1}{5} - \frac{1}{6} - \frac{1}{4} - \frac{1}{5} + \frac{1}{6} + \frac{1}{4} + \frac{1}{5} - \frac{1}{6} - \ldots \) is
A.
0
B.
\( -\frac{1}{6} \)
C.
\( \frac{1}{6} \)
D.
\( \frac{9}{20} \)
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ANSWER :
B. \( -\frac{1}{6} \)
34.
Which one of the following is correct?
A.
(x + 2) is a factor of \( x^{4} - 6x^{3} + 12x^{2} - 24x + 32 \)
B.
(x + 2) is a factor of \( x^{4} + 6x^{3} - 12x^{2} + 24x - 32 \)
C.
(x − 2) is a factor of \( x^{4} - 6x^{3} + 12x^{2} - 24x + 32 \)
D.
(x − 2) is a factor of \( x^{4} + 6x^{3} - 12x^{2} + 24x - 32 \)
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ANSWER :
C. (x − 2) is a factor of \( x^{4} - 6x^{3} + 12x^{2} - 24x + 32 \)
35.
20% of a number when added to 20 becomes the number itself, then the number is
A.
20
B.
25
C.
50
D.
80
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ANSWER :
B. 25
36.
Consider the following statements:
1. \( \frac{1 + \tan^{2} \theta}{1 + \cot^{2} \theta} = \left(\frac{1 - \tan \theta}{1 - \cot \theta}\right)^{2} \) is true for all \( 0 < \theta < \frac{\pi}{2} \), \( \theta \neq \frac{\pi}{4} \).
2. \( \cot \theta = \frac{1}{\tan \theta} \) is true for \( \theta = 45^{\circ} \) only.
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
37.
If \( x = a\cos \theta \) and \( y = b\cot \theta \), then \( (ax^{-1} - by^{-1})(ax^{-1} + by^{-1}) \) is equal to
A.
0
B.
1
C.
\( \tan^{2} \theta \)
D.
\( \sin^{2} \theta \)
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ANSWER :
B. 1
38.
\( \frac{\cos \theta}{1 - \sin \theta} \) is equal to [where \( \theta \neq \frac{\pi}{2} \)]
A.
\( \frac{\tan \theta - 1}{\tan \theta + 1} \)
B.
\( \frac{1 + \sin \theta}{\cos \theta} \)
C.
\( \frac{\tan \theta + 1}{\tan \theta - 1} \)
D.
\( \frac{1 + \cos \theta}{\sin \theta} \)
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ANSWER :
B. \( \frac{1 + \sin \theta}{\cos \theta} \)
39.
If \( \tan(x + 40^{\circ})\tan(x + 20^{\circ})\tan(3x)\tan(70^{\circ} - x)\tan(50^{\circ} - x) = 1 \), then the value of x is equal to
A.
\( 30^{\circ} \)
B.
\( 20^{\circ} \)
C.
\( 15^{\circ} \)
D.
\( 10^{\circ} \)
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ANSWER :
C. \( 15^{\circ} \)
40.
If \( \theta \) is an acute angle and \( \sin \theta \cos \theta = 2\cos^{3} \theta - 1.5\cos \theta \), then what is \( \sin \theta \) equal to?
A.
\( \frac{\sqrt{5} - 1}{4} \)
B.
\( \frac{1 - \sqrt{5}}{4} \)
C.
\( \frac{\sqrt{5} + 1}{4} \)
D.
\( -\frac{\sqrt{5} + 1}{4} \)
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ANSWER :
A. \( \frac{\sqrt{5} - 1}{4} \)
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