Geometry Previous Year Questions (CAT)  Set 0002

Previous years`s CAT questions: Geometry
Post your solutions as reply to respective questions below.

Question 1
Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is
(1) 4
(2) 5
(3) 6
(4) 7 (CAT 2005)

Answer: Option 3

Question 2
In the XY plane, the area of the region bounded by the graph of x + y + x – y = 4 is
(1) 8
(2) 12
(3) 16
(4) 20 (CAT 2005)

Answer: Option 3

Question 3
A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is
(1) 10
(2) 12
(3) 14
(4) 16 (CAT 2005)

Answer: Option 2

Question 4
A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son’s head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in metres) is the son standing from his father?
1. 0.9
2. 0.75
3. 0.6
4. 0.45 (CAT 2004)

Answer: Option 4

Question 5
In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have a common tangent that touches them at points Rand S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in theratio 4 : 3. It is also known that the length of PO is 28 cm.
(CAT 2004)

Answer: Option 2 Option 2 Option 3

Question 6
A rectangular sheet of paper, when halved by folding it at the midpoint of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?
1. 4√2
2. 2√2
3. √2
4. None of the above (CAT 2004)

Answer: Option 2

Question 7
A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower?
1) 5(√3 + 1)
2) 6(√3 + √2)
3) 7(√3 – 1)
4) 4. 8(√3 – 2) (CAT 2003)

Answer: Option 1

Question 8
Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/h. They continue walking for 4 hours along their respective roads and reach points B and C on R1 and R2, respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram’s and Shyam’s return to the point A is:
1) (10√19 + 26)/3
2) (2√19 + 10)/3
3) (√19 + 26)/3
4) (√19 + 10)/3 (CAT 2003)

Answer: Option 2

Question 9
In order to cover less distance, a boy – rather than going along the longer and the shorter lengths of the rectangular path, goes by the diagonal. The boy finds that he saved a distance equal to half the longer side. The ratio of the length and breadth is
1) 1/2
2) 2/3
3) 3/4
4) 7/15 (CAT 2002)

Answer: Option 3

Question 10
A certain city has a circular wall around it, and this wall has four gates pointing north,south,east and west. A house stands outside the city, three kms north of the north gate, and it can just be seen from a point nine kms east of the south gate. What is the diameter of the wall that surrounds the city?
1. 6 km
2. 9 km
3. 12 km
4. None of these (CAT 2001)