UPSC Previous Year question paper – 1996-2000- Geometry & Mensuration of india



UPSC previous year question paper of subject Geometry & Mensuration of india from the year 1996-2000 with answers.



#1. A rectangular piece of iron sheet measuring 50 cm by 100 cm is rolled into cylinder of height 50 cm. If the cost of painting the cylinder is Rs 50 per square metre, then what will be the cost of painting the outer surface of the cylinder? [2000]

#2. In the given figure, all line segments of the shaded portion are of same length and at right angles to each other. The same can be out of a board of side 10 cm. What is the area of the shaded portion? [2000]

#3. A rectangular water tank measures 15m × 6m at top and is 10m deep. It is full of water. If water is drawn out lowering the level by 1 meter, how much of water has been drawn out? [2000]

#4. What is the maximum number of pieces of 5 cm × 5 cm × 10 cm of cake that can be cut from a big cake of 5cm × 30 cm × 30 cm size? [2000]

#5. A goat is tied to two poles P and Q with ropes that are 15 meters long. P and Q are 20 metres apart as shown in the given diagram: [2000] Which one of the following shaded portions indicates the total area over which the goat can graze?

#6. Which one of the following has a greater perimeter than the rest?[2000]

#7. In the given figure Ð OQP = 30 and Ð ORP=20., then Ð QOR is equal to [2000]

#8. The area of an ellipse is twice that of a circle. The major diameter of the ellipse is twice that of the minor diameter. The radius of the circle is [1999]

#9. At a given time, two players are standing on a play-field. The cartesian coordinates of their locations are (20, 60) and (–40, –20) units. What is the distance between the players? [1999]

#10. If the angle of triangle are in the ratio of 4 : 3 : 2, then the triangle [1999]

#11. A man is standing on the 6m long pole whose length of shadow is 8m. If the length of his shadow is 2.4m, what is the height of the man ? [1999]

#12. The surface area of spherical dome-shaped roof of a cylindrical water tank shown in the figure is [1999]

#13. A square pond has 2 m sides and is 1m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, then what would be the volume of earth to be removed? [1998]

#14. LMNOP is a semicircle with centre at R and diametre LP. LSR and RQP are also semi circles with centres at T and U respectively and diameters LR = RP = 1 4 LP. The ratio of perimeter of LMNOP and LSRQP is [1998]

#15. The length, breadth and height of a room are l, b and h respectively. The perimeter of the ceiling expressed as a percentage of the total area of the four walls, is [1997]

#16. If the numbers representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be [1997]

#17. A rectangular plot of lawn shown in the figure has dimensions 'x' and 'y' and is surrounded by a gravel pathway of width 2 m. What is the total area of the Gravel Pathway? [1997]

#18. In the following figure [1997] P is 300 km eastward of O and Q is 400 km north of O. R is exactly in the middle of Q and P. The distance between Q and R is

#19. Consider the following figures: Which one of the following conclusions can be drawn from these figures?

#20. The following figure contains three squares with areas of 100, 16 and 49 sq. units respectively laying side by side as shown. By how much should the area of the middle square be reduced in order that the total length PQ of the resulting three squares is 19? [1996]

#21. A rectangle has perimeter of 50 metres. If its length is 13 metres more than its breadth, then its area is: [1996]

#22. Consider the figure given below: PQRS is a square of side 1 unit and Q, S are the centres of the two circles. The area of the shaded portion is [1995]

#23. A rectangular sump of dimension 6m × 5m × 4m is to be built by using bricks to make the outer dimension 6.2 m × 5.2 m × 4.2 m. Approximately how many bricks of size 20 cm × 10 cm × 5 cm are required to build the sump for storing water? [1995]

#24. In the Cartesian plane four points P, Q, R, S have co-ordinates (1, 1), (4, 2), (4, 4) and (1, 4) respectively, The area of the quadrilateral PQRS is [1995]


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