1
IIT-JEE 2001 Screening
+2
-0.5
Let A B be a chord of the circle $${x^2} + {y^2} = {r^2}$$ subtending a right angle at the centre. Then the locus of the centriod of the triangle PAB as P moves on the circle is
A
a parabola
B
a circle
C
an ellipse
D
a pair of straight lines
2
IIT-JEE 2001 Screening
+2
-0.5
Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals
A
$$\sqrt {PQ.\,RS}$$
B
(PQ + RS) / 2
C
2 PQ. RS/(PQ + RS)
D
$$\sqrt {\left( {P{Q^2} + \,R{S^2}} \right)} \,\,/2$$
3
IIT-JEE 2000 Screening
+2
-0.5
The triangle PQR is inscribed in the circle $${x^2}\, + \,\,{y^2} = \,25$$. If Q and R have co-ordinates (3, 4) and ( - 4, 3) respectively, then $$\angle \,Q\,P\,R$$ is equal to
A
$${\pi \over 2}$$
B
$${\pi \over 3}$$
C
$${\pi \over 4}$$
D
$${\pi \over 6}$$
4
IIT-JEE 2000 Screening
+2
-0.5
If the circles $${x^2}\, + \,{y^2}\, + \,\,2x\, + \,2\,k\,y\,\, + \,6\,\, = \,\,0,\,\,{x^2}\, + \,\,{y^2}\, + \,2ky\, + \,k\, = \,0$$ intersect orthogonally, then k is
A
2 or $$- {3 \over 2}$$
B
- 2 or $$- {3 \over 2}$$
C
2 or $${3 \over 2}$$
D
- 2 or $${3 \over 2}$$
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