MENSURATION (QUANTITATIVE APTITUDE) EPFO UPSC

Total Questions: 30

21. If the length of each of two equal sides of an isosceles triangle is 10 cm. and the adjacent angle is 45°, then the area of the triangle is

Correct Answer: (b) 25√2 square cm.
Solution:

22. Two circles with centres A and B and radius 2 units touch each other externally at 'C'. A third circle with centre 'C' and radius '2' units meets other two at D and E. Then the area of the quadrilateral ABED is

Correct Answer: (b) 3√3 sq. units
Solution:

23. ABCD is a parallelogram in which diagonals AC and BD intersect at O. If E, F, G and H are the mid-points of AO, DO, CO and BO respectively, then the ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD is

Correct Answer: (c) 1 : 2
Solution:

24. The length of a room floor exceeds its breadth by 20m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 5 m. The area of the floor (in square meters) is:

Correct Answer: (c) 300
Solution:

25. Three solid iron cubes of edges 4 cm, 5 cm and 6 cm are melted together to make a new cube. 62 cm3 of the melted material is lost due to improper handing. The area (in cm2) of the whole surface of the newly formed cube is

Correct Answer: (a) 294
Solution:

26. A cylindrical can whose base is horizontal and is of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed inside, water just covers the sphere. The sphere fits in the can exactly. The depth of water in the can before the sphere was put, is

Correct Answer: (c) 7/3 cm
Solution:

27. Answer the following question [(π= 22/7)]

Correct Answer: (a) 1078 cubic cm
Solution:

28. A conical cup is filled with ice-cream. The ice-cream forms a hemispherical shape on its open top. The height of the hemispherical part is 7 cm. The radius of the hemispherical part equals the height of the cone. Then the volume of the ice-cream is [(Take π= 22/7)]

Correct Answer: (d) 2/9 Part
Solution:

29. A spherical ball of radius 1 cm is dropped into a conical vessel of radius 3 cm and slant height 6 cm. The volume of water (in cm³), that can just immerse the ball, is

Correct Answer: (a) 5π/3
Solution:

30. Assume that a drop of water is spherical and its diameter is one tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32000 drops of water fill the glass completely, then the height of the glass (in cm.) is

Correct Answer: (b) 4
Solution: