Geometry Previous Year Questions (CAT)  Set 0007

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

Question 1
(CAT 2001)

Answer: Option 2

Question 2
ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.
Then D is
(a) 3 km east and 1 km north of A
(b) 3 km east and √3 km north of A
(c) √3 km east and 1 km south of A
(d) √3 km west and 3 km north of A (CAT 1993)

Answer: Option B

Question 3
There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimetres then the area (in square centimetres) of the triangle ABC would be
(CAT 2003 Leaked)

Answer: Option 3

Question 4
A vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the lengths OP and AB respectively. Suppose ∠APB = 60°, then the relationship between h and b can be expressed as
(1) 2b^{2 }= h^{2 }
(2) 2h^{2 }= b^{2}
(3) 3b^{2 }= 2h^{2 }
(4) 3h^{2 }= 2b^{2 } (CAT 2003 Leaked)
A vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the lengths OP and AB respectively. Suppose ∠APB = 60°, then the relationship between h and b can be expressed as
(1) 2b^{2 }= h^{2 }
(2) 2h^{2 }= b^{2}
(3) 3b^{2 }= 2h^{2 }
(4) 3h^{2 }= 2b^{2 } (CAT 2003 Leaked)

Answer: Option 2

Question 5
In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B ) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to
(1) 1 : 1
(2) 3 : 2
(3) 4 : 1
(4) 3 : 8
(CAT 2003 Leaked)

Answer: Option 4