1
JEE Advanced 2015 Paper 1 Offline
Numerical
+4
-0
If the normals of the parabola $${y^2} = 4x$$ drawn at the end points of its latus rectum are tangents to the circle $${\left( {x - 3} \right)^2} + {\left( {y + 2} \right)^2} = {r^2}$$, then the value of $${r^2}$$ is
Your input ____
2
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$P$$ and $$Q$$ be distinct points on the parabola $${y^2} = 2x$$ such that a circle with $$PQ$$ as diameter passes through the vertex $$O$$ of the parabola. If $$P$$ lies in the first quadrant and the area of the triangle $$\Delta OPQ$$ is $${3\sqrt 2 ,}$$ then which of the following is (are) the coordinates of $$P$$?
A
$$\left( {4,2\sqrt 2 } \right)$$
B
$$\left( {9,3\sqrt 2 } \right)$$
C
$$\left( {{1 \over 4},{1 \over {\sqrt 2 }}} \right)$$
D
$$\left( {1,\sqrt 2 } \right)$$
3
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Let X and Y be two arbitrary, 3 $$\times$$ 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 $$\times$$ 3, non-zero, symmetric matrix. Then which of the following matrices is(are) skew symmetric?

A
Y3Z4 $$-$$ Z4Y3
B
X44 + Y44
C
X4Z3 $$-$$ Z3X4
D
X23 + Y23
4
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Which of the following values of $$\alpha$$ satisfy the equation

$$\left| {\matrix{ {{{(1 - \alpha )}^2}} & {{{(1 + 2\alpha )}^2}} & {{{(1 + 3\alpha )}^2}} \cr {{{(2 + \alpha )}^2}} & {{{(2 + 2\alpha )}^2}} & {{{(2 + 3\alpha )}^2}} \cr {{{(3 + \alpha )}^2}} & {{{(3 + 2\alpha )}^2}} & {{{(3 + 3\alpha )}^2}} \cr } } \right| = - 648\alpha $$ ?

A
$$-$$4
B
9
C
$$-$$9
D
4
JEE Advanced Papers
EXAM MAP