CDS Exam (II)- 2019 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2019 - Elementary Mathematics

CDS Exam (II)- 2019 - Elementary Mathematics Defence Questions

41.
The areas of three adjacent faces of a cuboid are x, y and z. If V is the volume of the cuboid, then which one of the following is correct?
A.
\( V = xyz \)
B.
\( V^{2} = xyz \)
C.
\( V = x^{2}y^{2}z^{2} \)
D.
\( V^{3} = xyz \)
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ANSWER :
B. \( V^{2} = xyz \)
42.
If \( l \) is the length of the median of an equilateral triangle, then what is its area?
A.
\( \frac{\sqrt{3}l^{2}}{2} \)
B.
\( \frac{\sqrt{3}l^{2}}{3} \)
C.
\( \sqrt{3}l^{2} \)
D.
\( 2l^{2} \)
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ANSWER :
B. \( \frac{\sqrt{3}l^{2}}{3} \)
43.
A piece of wire is in the form of a sector of a circle of radius 20 cm, subtending an angle \( 150^{\circ} \) at the centre. If it is bent in the form of a circle, then what will be its radius?
A.
7 cm
B.
7.5 cm
C.
8 cm
D.
None of the above
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ANSWER :
D. None of the above
44.
Suppose P, Q and R are the mid-points of sides of a triangle of area \( 128 cm^{2} \). If a triangle ABC is drawn by joining the mid-points of sides of triangle PQR, then what is the area of triangle ABC?
A.
\( 4 cm^{2} \)
B.
\( 8 cm^{2} \)
C.
\( 16 cm^{2} \)
D.
\( 32 cm^{2} \)
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ANSWER :
B. \( 8 cm^{2} \)
45.
Let two lines p and q be parallel. Consider two points B and C on the line p and two points D and E on the line q. The line through B and E intersects the line through C and D at A in between the two lines p and q. If AC : AD = 4 : 9, then what is the ratio of area of triangle ABC to that of triangle ADE?
A.
2 : 3
B.
4 : 9
C.
16 : 81
D.
1 : 2
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ANSWER :
C. 16 : 81
46.
An equilateral triangle and a square are constructed using metallic wires of equal length. What is the ratio of area of triangle to that of square?
A.
3 : 4
B.
2 : 3
C.
\( 4\sqrt{3} : 9 \)
D.
\( 2\sqrt{3} : 9 \)
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ANSWER :
C. \( 4\sqrt{3} : 9 \)
47.
All the four sides of a parallelogram are of equal length. The diagonals are in the ratio 1 : 2. If the sum of the lengths of the diagonals is 12 cm, then what is the area of the parallelogram?
A.
\( 9 cm^{2} \)
B.
\( 12 cm^{2} \)
C.
\( 16 cm^{2} \)
D.
\( 25 cm^{2} \)
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ANSWER :
C. \( 16 cm^{2} \)
48.
ABC is a triangle right angled at B. If AB = 5 cm and BC = 10 cm, then what is the length of the perpendicular drawn from the vertex B to the hypotenuse?
A.
4 cm
B.
\( 2\sqrt{5} \) cm
C.
\( \frac{1}{\sqrt{5}} \) cm
D.
8 cm
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ANSWER :
B. \( 2\sqrt{5} \) cm
49.
Two cylinders of equal volume have their heights in the ratio 2 : 3. What is the ratio of their radii?
A.
\( \sqrt{3} : 1 \)
B.
\( \sqrt{3} : \sqrt{2} \)
C.
2 : 3
D.
\( \sqrt{3} : 2 \)
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ANSWER :
B. \( \sqrt{3} : \sqrt{2} \)
50.
The length and breadth of a rectangle are increased by 20% and 10% respectively. What is the percentage increase in the area of the rectangle?
A.
32%
B.
30%
C.
25%
D.
15%
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ANSWER :
A. 32%
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