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

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

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

41.
The mean weight of 150 students in a class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. What is the ratio of number of boys to number of girls?
A.
1 : 2
B.
1 : 1
C.
2 : 1
D.
2 : 3
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ANSWER :
A. 1 : 2
42.
Two towers A and B of height 23 m and 11 m, respectively, stand 9 m apart. A straight rod is joined to the two tops of the towers. A monkey sitting on the top of A, climbs the rod to reach the top of B. If the monkey takes 5 minutes to reach the other end, what is the average speed of the monkey?
A.
10 m/min
B.
5 m/min
C.
10 cm/s
D.
5 cm/s
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ANSWER :
D. 5 cm/s
43.
A spherical wooden ball of radius \( r \) is to be divided into eight identical parts by cutting by planes passing through the same diameter. What is the surface area of each final piece?
A.
\( \frac{\pi r^{2}}{3} \)
B.
\( \frac{3\pi r^{2}}{2} \)
C.
\( \frac{2\pi r^{2}}{3} \)
D.
\( \frac{4\pi r^{2}}{3} \)
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ANSWER :
B. \( \frac{3\pi r^{2}}{2} \)
44.
A trolley with two wheels one metre apart is moved clockwise on the circular track around a ground with radius 50 m (described by right wheel). If the size of each wheel is of 1 foot radius and the right wheel turns 1,000 times, how many times will the other wheel turn?
A.
1,010
B.
1,015
C.
1,020
D.
1,025
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ANSWER :
C. 1,020
45.
What is the remainder when \( 70 \times 71 \times 72 \times 73 \times 74 \times 75 \times 76 \times 77 \times 78 \times 79 \) is divided by 1000?
A.
3
B.
2
C.
1
D.
0
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ANSWER :
D. 0
46.
A vertical pole of length 80 m is situated on the horizontal plane. The base of the pole is at P. There are two points A and B such that P, A, B are on the same straight line. Let the angles of elevation of top of the pole from A and B be \( \alpha \) and \( \beta \) \( (\alpha > \beta) \) respectively. If PA = 64 m and AB = 36 m, then what is \( (\alpha + \beta) \) equal to?
A.
\( 60^{\circ} \)
B.
\( 90^{\circ} \)
C.
\( 120^{\circ} \)
D.
\( 135^{\circ} \)
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ANSWER :
B. \( 90^{\circ} \)
47.
Let \( k \) be a positive integer. What is the quotient when \( x^{8k+3} + x^{8k+6} + x^{8k+9} + x^{8k+12} \) is divided by \( (1 + x^{3})(1 + x^{6}) \)?
A.
\( x^{8k} \)
B.
\( x^{8k+1} \)
C.
\( x^{8k+2} \)
D.
\( x^{8k+3} \)
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ANSWER :
D. \( x^{8k+3} \)
48.
A square is drawn inside a square of side 14 cm in such a way that the corners of the inner square coincide with the mid points of the sides of the outer square. What is the area lying between the two squares?
A.
98 square cm
B.
56 square cm
C.
49 square cm
D.
24.5 square cm
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ANSWER :
A. 98 square cm
49.
The base of a right-angled triangle is \( \frac{4}{3} \) times the height of triangle. If the area of the triangle is 54 square cm, then what is the perimeter of the triangle?
A.
30 cm
B.
32 cm
C.
36 cm
D.
40 cm
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ANSWER :
C. 36 cm
50.
What is the area of a triangle having sides 4, 4 and 6 units?
A.
\( 3\sqrt{7} \) square unit
B.
8 square unit
C.
7 square unit
D.
\( 7\sqrt{3} \) square unit
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ANSWER :
A. \( 3\sqrt{7} \) square unit
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