1
IIT-JEE 2007
Subjective
+6
-0
Match the statements in Column $$I$$ with the properties in Column $$II$$ and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the $$ORS$$.

Column $$I$$
(A) Two intersecting circles
(B) Two mutually external circles
(C) Two circles, one strictly inside the other
(D) Two branches vof a hyperbola

Column $$II$$
(p) have a common tangent
(q) have a common normal
(r) do not have a common tangent
(s) do not have a common normal

2
IIT-JEE 2007
+4
-1
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent to the circle at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$R$$ and tangents to the parabola at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$S$$.

The ratio of the areas of the triangles $$PQS$$ and $$PQR$$ is

A
$$1:\sqrt 2$$
B
$$1:2$$
C
$$1:4$$
D
$$1:8$$
3
IIT-JEE 2007
+4
-1
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent to the circle at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$R$$ and tangents to the parabola at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$S$$.

The radius of the incircle of the triangle $$PQR$$ is

A
$$4$$
B
$$3$$
C
$${8 \over 3}$$
D
$$2$$
4
IIT-JEE 2007
+4
-1
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent to the circle at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$R$$ and tangents to the parabola at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$S$$.

The radius of the circumcircle of the triangle $$PRS$$ is

A
$$5$$
B
$$3\sqrt 3$$
C
$$3\sqrt 2$$
D
$$2\sqrt 3$$
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