UPSC question paper – 2001 – 2005-Geometry & Mensuration of india




#1. A big rectangular plot of area 4320 m2 is divided into 3 square shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square shaped plots were formed by fencing parallel to the longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot? [2005]

#2. Consider the volumes of the following: [2002] 1. A parallelopiped of length 5 cm, breadth 3 cm and height 4 cm 2. A cube of each side 4 cm 3. A cylinder of radius 3 cm and length 3 cm. 4. A sphere of radius 3 cm. The volumes of these in the decreasing order is

#3. The length of the longest pole that can be placed in a room 12 m long, 9 m wide and 8 m high, is [2002]

#4. In the above figure, ABCD is a cyclic quadrilateral, AB = BC and ÐBAC = 70°, then ÐADC is [2001]

#5. A circle of 1 m radius is drawn inside a square as shown in figure given above. What is the area of the shaded portion (in m2 ) ? [2001]


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