Geometry Previous Year Questions (CAT)  Set 0004

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

Question 1
(CAT 2004)

Answer: Option 2

Question 2
(CAT 2004)

Answer: Option 2

Question 3
Let C be a circle with centre P_{0} and AB be a diameter of C. Suppose P_{1} is the midpoint of the line segment P_{0}B, P_{2} is the midpoint of the line segment P_{1}B and so on. Let C_{1}, C_{2}, C_{3}, ... be circles with diameters P_{0}P_{1}, P_{1}P_{2}, P_{2}P_{3} ... respectively. Suppose the circles C_{1}, C_{2}, C_{3}, ... are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is:
(1) 8 : 9
(2) 9 : 10
(3) 10 : 11
(4) 11 : 12Â Â (CAT 2004)

Answer: Option 4

Question 4
If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be _______
Â (CAT 2004)

Answer: Option 1

Question 5

Answer: Option 4

Question 6
A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?
(1) 16.665
(2) 16.565
(3) 15.465
(4) 14.365Â Â (CAT 2003 Retest)

Answer: Option 4

Question 7
A square tin sheet of side 12 inches is converted into a box with open top in the following steps –
the sheet is placed horizontally. Then, equal sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box?
(1) 3
(2) 4
(3) 1
(4) 2 (CAT 2003 Retest)

Answer: Option 4

Question 8
(CAT 2003 Retest)

Answer: Option 1 Option 2 Option 3

Question 9
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(CAT 2003 Retest)

Answer: Option 1 Option 3 Option 2

Question 10
(CAT 2003 Retest)