1
IIT-JEE 2006
MCQ (Single Correct Answer)
+6
-1.5
Match the following : $$(3, 0)$$ is the pt. from which three normals are drawn to the parabola $${y^2} = 4x$$ which meet the parabola in the points $$P, Q $$ and $$R$$. Then

Column $${\rm I}$$
(A) Area of $$\Delta PQR$$
(B) Radius of circumcircle of $$\Delta PQR$$
(C) Centroid of $$\Delta PQR$$
(D) Circumcentre of $$\Delta PQR$$

Column $${\rm I}$$$${\rm I}$$
(p) $$2$$
(q) $$5/2$$
(r) $$(5/2, 0)$$
(s) $$(2/3, 0)$$

A
$$\left( A \right) - \left( p \right),\left( B \right) - \left( q \right),\left( C \right) - \left( s \right),\left( D \right) - \left( r \right)$$
B
$$\left( A \right) - \left( p \right),\left( B \right) - \left( q \right),\left( C \right) - \left( r \right),\left( D \right) - \left( s \right)$$
C
$$\left( A \right) - \left( s \right),\left( B \right) - \left( r \right),\left( C \right) - \left( p \right),\left( D \right) - \left( q \right)$$
D
$$\left( A \right) - \left( r \right),\left( B \right) - \left( s \right),\left( C \right) - \left( q \right),\left( D \right) - \left( p \right)$$
2
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
The minimum area of triangle formed by the tangent to the $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and coordinate axes is
A
$$ab$$ sq. units
B
$${{{{a^2} + {b^2}} \over 2}}$$ sq. units
C
$${{{{\left( {a + b} \right)}^2}} \over 2}$$ sq. units
D
$${{{a^2} + ab + {b^2}} \over 3}$$ sq. units
3
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
Tangent to the curve $$y = {x^2} + 6$$ at a point $$(1, 7)$$ touches the circle $${x^2} + {y^2} + 16x + 12y + c = 0$$ at a point $$Q$$. Then the coordinates of $$Q$$ are
A
$$(-6, -11)$$
B
$$(-9, -13)$$
C
$$(-10, -15)$$
D
$$(-6, -7)$$
4
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+2
-0.5
The angle between the tangents drawn from the point $$(1, 4)$$ to the parabola $${y^2} = 4x$$ is
A
$$\pi /6$$
B
$$\pi /4$$
C
$$\pi /3$$
D
$$\pi /2$$
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