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1

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)
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 2000 Screening

MCQ (Single Correct Answer)
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 $$ {3 \over 2}$$
3

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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 1999

MCQ (Single Correct Answer)
If two distinct chords, drawn from the point (p, q) on the circle $${x^2}\, + \,{y^2} = \,px\, + \,qy\,\,(\,where\,pq\, \ne \,0)$$ are bisected by the x - axis, then
A
$${p^2}\, = \,\,{q^2}$$
B
$$\,{p^2}\, = \,\,8\,{q^2}$$
C
$${p^2}\, < \,\,8\,{q^2}$$
D
$${p^2}\, > \,\,8\,{q^2}$$.

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