1
IIT-JEE 2009 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
In a triangle $$ABC$$ with fixed base $$BC$$, the vertex $$A$$ moves such that $$\cos \,B + \cos \,C = 4{\sin ^2}{A \over 2}.$$\$

If $$a, b$$ and $$c$$ denote the lengths of the sides of the triangle opposite to the angles $$A, B$$ and $$C$$, respectively, then

A
$$b+c=4a$$
B
$$b+c=2a$$
C
locus of point $$A$$ is an ellipse
D
locus of point $$A$$ is a pair of straight lines
2
IIT-JEE 2008 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$P\left( {{x_1},{y_1}} \right)$$ and $$Q\left( {{x_2},{y_2}} \right),{y_1} < 0,{y_2} < 0,$$ be the end points of the latus rectum of the ellipse $${x^2} + 4{y^2} = 4.$$ The equations of parabolas with latus rectum $$PQ$$ are :
A
$${x^2} + 2\sqrt 3y = 3 + \sqrt 3$$
B
$${x^2} - 2\sqrt 3y = 3 + \sqrt 3$$
C
$${x^2} + 2\sqrt 3y = 3 - \sqrt 3$$
D
$${x^2} - 2\sqrt 3 y = 3 - \sqrt 3$$
3
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
On the ellipse $$4{x^2} + 9{y^2} = 1,$$ the points at which the tangents are parallel to the line $$8x = 9y$$ are
A
$$\left( {{2 \over 5},{1 \over 5}} \right)$$
B
$$\left( -{{2 \over 5},{1 \over 5}} \right)$$
C
$$\left( -{{2 \over 5},-{1 \over 5}} \right)$$
D
$$\left( {{2 \over 5},-{1 \over 5}} \right)$$
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