1
JEE Advanced 2015 Paper 1 Offline
Numerical
+4
-0
Let the curve $$C$$ be the mirror image of the parabola $${y^2} = 4x$$ with respect to the line $$x+y+4=0$$. If $$A$$ and $$B$$ are the points of intersection of $$C$$ with the line $$y=-5$$, then the distance between $$A$$ and $$B$$ is
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2
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
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3
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
$$\left( {1,\sqrt 2 } \right)$$
4
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
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