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

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CDS Exam (II)- 2015 - Elementary Mathematics

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

41.
Consider the following statements:
1. \( \sin 66^{\circ} \) is less than \( \cos 66^{\circ} \).
2. \( \sin 26^{\circ} \) is less than \( \cos 26^{\circ} \).
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 :
B. 2 only
42.
If a and b are positive, then the relation \( \sin \theta = \frac{2a + 3b}{3b} \) is
A.
not possible
B.
possible only if a = b
C.
possible if a > b
D.
possible if a < b
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ANSWER :
A. not possible
43.
An aeroplane flying at a height of 3000 m passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from some point on the ground are \( 60^{\circ} \) and \( 45^{\circ} \) respectively. Then the vertical distance between the two planes is
A.
\( 1000(\sqrt{3} - 1) \) m
B.
\( 1000\sqrt{3} \) m
C.
\( 1000(3 - \sqrt{3}) \) m
D.
\( 3000\sqrt{3} \) m
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ANSWER :
C. \( 1000(3 - \sqrt{3}) \) m
44.
A pole is standing erect on the ground which is horizontal. The tip of the pole is tied tight with a rope of length \( \sqrt{12} \) m to a point on the ground. If the rope is making \( 30^{\circ} \) with the horizontal, then the height of the pole is
A.
\( 2\sqrt{3} \) m
B.
\( 3\sqrt{2} \) m
C.
3 m
D.
\( \sqrt{3} \) m
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ANSWER :
D. \( \sqrt{3} \) m
45.
If \( \tan \theta + \sec \theta = 2 \), then \( \tan \theta \) is equal to
A.
\( \frac{3}{4} \)
B.
\( \frac{5}{4} \)
C.
\( \frac{3}{2} \)
D.
\( \frac{5}{2} \)
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ANSWER :
A. \( \frac{3}{4} \)
46.
A's salary was increased by 40% and then decreased by 20%. On the whole A's salary is increased by
A.
60%
B.
40%
C.
20%
D.
12%
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ANSWER :
D. 12%
47.
A number consists of two digits, whose sum is 7. If the digits are reversed, the number is increased by 27. The product of digits of the number is
A.
6
B.
8
C.
10
D.
12
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ANSWER :
C. 10
48.
In a race of 100 m, A beats B by 4 m and A beats C by 2 m. By how many metres (approximately) would C beat B in another 100 m race assuming C and B run with their respective speeds as in the earlier race?
A.
2
B.
2.04
C.
2.08
D.
3.20
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ANSWER :
B. 2.04
49.
In an election 10% of the voters on the voter list did not cast their vote and 60 voters cast their ballot papers blank. There were only two candidates. The winner was supported by 47% of total voters in the voter list and he got 308 votes more than his rival. The number of voters on the voter list is
A.
3600
B.
6200
C.
6028
D.
6400
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ANSWER :
B. 6200
50.
Consider all positive two digit numbers each of which when divided by 7 leaves a remainder 3. What is their sum?
A.
661
B.
666
C.
676
D.
777
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ANSWER :
C. 676
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