CDS Exam (I)- 2024- Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2024- Elementary Mathematics

CDS Exam (I)- 2024- Elementary Mathematics Defence Questions

31.
A bottle contains spirit and water in the ratio 1 : 4 and another identical bottle contains spirit and water in the ratio 4 : 1. In what ratio should the mixtures in the two bottles be mixed to get a new mixture in which the ratio of spirit to water is 1 : 3?
A.
5 : 1
B.
6 : 1
C.
10 : 1
D.
11 : 1
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ANSWER :
D. 11 : 1
32.
If \( 3 \sin \theta + 5 \cos \theta = 5 \), then what is the value of \( 5 \sin \theta - 3 \cos \theta \)?
A.
-3
B.
-2
C.
5
D.
8
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ANSWER :
A. -3
33.
Consider the following in respect of the polynomial \( x^{4k} + x^{4k+2} + x^{4k+4} + x^{4k+6} \):
1. The remainder is zero when the polynomial is divided by \( x^{2} + 1 \).
2. The remainder is zero when the polynomial is divided by \( x^{4} + 1 \).
Which of the statements given above is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
C. Both 1 and 2
34.
What is the minimum value of \( \frac{\sin^{2} A + 5 \sin A + 1}{\sin A} \) for \( 0 < A \leq \frac{\pi}{2} \)?
A.
3
B.
5
C.
7
D.
9
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ANSWER :
C. 7
35.
What is \( \frac{3}{1^{2} \times 2^{2}} + \frac{5}{2^{2} \times 3^{2}} + \frac{7}{3^{2} \times 4^{2}} + \ldots \) equal to?
A.
1
B.
4
C.
7
D.
9
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ANSWER :
A. 1
36.
If \( \frac{1}{a + \frac{1}{b + \frac{1}{c + \frac{1}{d + \frac{1}{e}}}}} = \frac{421}{972} \), then what is the value of \( a \times b \times c \times d \times e \)?
A.
720
B.
480
C.
360
D.
60
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ANSWER :
A. 720
37.
A cube whose edge is 14 cm long has on each of its faces a circle of 7 cm radius painted yellow. What is the total area of unpainted surface? (Take \( \pi = \frac{22}{7} \))
A.
126 square cm
B.
189 square cm
C.
252 square cm
D.
315 square cm
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ANSWER :
C. 252 square cm
38.
From a circular metal plate of radius 7 cm and thickness 0.16 mm, a sector is cut off containing an angle \( 150^{\circ} \). The remaining piece is moulded into a spherical bead of radius r. What is the value of r in cm?
A.
0.35
B.
0.7
C.
1.05
D.
1.4
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ANSWER :
B. 0.7
39.
The chord AB of a circle with centre at O is \( 2\sqrt{3} \) times the height of the minor segment. If P is the area of the sector OAB and Q is the area of the minor segment of the circle, then what is the approximate value of \( \frac{P}{Q} \)?
(Take \( \sqrt{3} = 1.7 \) and \( \pi = 3.14 \))
A.
1.4
B.
1.7
C.
2.2
D.
2.6
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ANSWER :
B. 1.7
40.
What is the area of the region between two concentric circles, if the length of a chord of the outer circle touching the inner circle at a particular point of its circumference is 14 cm? (Take \( \pi = \frac{22}{7} \))
A.
154 square cm
B.
144 square cm
C.
132 square cm
D.
Cannot be determined due to insufficient data
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ANSWER :
A. 154 square cm
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