1
IIT-JEE 2006
MCQ (Single Correct Answer)
+5
-1.25
ABCD is a square of side length 2 units. $$C_1$$ is the circle touching all the sides of the square ABCD and $$C_2$$ is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.

A line L' through A is drawn parallel to BD. Point S moves such that its distances from the BD and the vertex A are equal. If locus of S cuts L' at $$T_2$$ and $$T_3$$ and AC at $$T_1$$, then area of $$\Delta \,{T_1}\,{T_2}\,{T_3}$$ is

A
$${1 \over 2}\,sq.\,units$$
B
$${2 \over 3}\,sq.\,units$$
C
1 sq. units
D
2 sq.units
2
IIT-JEE 2006
MCQ (Single Correct Answer)
+5
-1.25
ABCD is a square of side length 2 units. $${C_1}$$ is the circle touching all the sides of the square ABCD and $${C_2}$$ is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.

If P is any point of $${C_1}$$ and Q is another point on $${C_2}$$, then


$${{P{A^2}\, + \,P{B^2}\, + P{C^2}\, + P{D^2}} \over {Q{A^2} + \,Q{B^2}\, + Q{C^2}\, + Q{D^2}}}$$ is equal to
A
0.75
B
1.25
C
1
D
0.5
3
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0.75
The axis of a parabola is along the line $$y = x$$ and the distances of its vertex and focus from origin are $$\sqrt 2 $$ and $$2\sqrt 2 $$ respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is
A
$${\left( {x + y} \right)^2} = \left( {x - y - 2} \right)$$
B
$${\left( {x - y} \right)^2} = \left( {x + y - 2} \right)$$
C
$${\left( {x - y} \right)^2} = 4\left( {x + y - 2} \right)$$
D
$${\left( {x - y} \right)^2} = 8\left( {x + y - 2} \right)$$
4
IIT-JEE 2006
MCQ (More than One Correct Answer)
+5
-1.25
The equations of the common tangents to the parabola $$y = {x^2}$$ and $$y = - {\left( {x - 2} \right)^2}$$ is/are
A
$$y = 4\left( {x - 1} \right)$$
B
$$y=0$$
C
$$y = - 4\left( {x - 1} \right)$$
D
$$y = - 30x - 50$$
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