1
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let RS be the diameter of the circle $${x^2}\, + \,{y^2} = 1$$, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point (s)
A
$$\left( {{1 \over 3}\,,{1 \over {\sqrt 3 }}} \right)$$
B
$$\left( {{1 \over 4}\,,{1 \over 2}} \right)$$
C
$$\left( {{1 \over 3}\,, - {1 \over {\sqrt 3 }}} \right)$$
D
$$\left( {{1 \over 4}\,,-{1 \over 2}} \right)$$
2
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
The circle $${C_1}:{x^2} + {y^2} = 3,$$ with centre at $$O$$, intersects the parabola $${x^2} = 2y$$ at the point $$P$$ in the first quadrant, Let the tangent to the circle $${C_1}$$, at $$P$$ touches other two circles $${C_2}$$ and $${C_3}$$ at $${R_2}$$ and $${R_3}$$, respectively. Suppose $${C_2}$$ and $${C_3}$$ have equal radil $${2\sqrt 3 }$$ and centres $${Q_2}$$ and $${Q_3}$$, respectively. If $${Q_2}$$ and $${Q_3}$$ lie on the $$y$$-axis, then
A
$${Q_2}{Q_3} = 12$$
B
$${R_2}{R_3} = 4\sqrt 6$$
C
area of the triangle $$O{R_2}{R_3}$$ is $$6\sqrt 2$$
D
area of the triangle $$P{Q_2}{Q_3}$$ is $$4\sqrt 2$$
3
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$f:\mathbb{R} \to \mathbb{R},\,g:\mathbb{R} \to \mathbb{R}$$ and $$h:\mathbb{R} \to \mathbb{R}$$ be differentiable functions such that $$f\left( x \right)= {x^3} + 3x + 2,$$ $$g\left( {f\left( x \right)} \right) = x$$ and $$h\left( {g\left( {g\left( x \right)} \right)} \right) = x$$ for all $$x \in R$$. Then
A
$$g'\left( 2 \right) = {1 \over {15}}$$
B
$$h'\left( 1 \right) = 666$$
C
$$h\left( 0 \right) = 16$$
D
$$h\left( {g\left( 3 \right)} \right) = 36$$
4
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
In a triangle $$\Delta$$$$XYZ$$, let $$x, y, z$$ be the lengths of sides opposite to the angles $$X, Y, Z$$ respectively, and $$2s = x + y + z$$.
If $${{s - x} \over 4} = {{s - y} \over 3} = {{s - z} \over 2}$$ and area of incircle of the triangle $$XYZ$$ is $${{8\pi } \over 3}$$, then
A
area of the triangle $$XYZ$$ is $$6\sqrt 6$$
B
the radius of circumcircle of the triangle $$XYZ$$ is $${{35} \over 6}\sqrt 6$$
C
$$\sin {X \over 2}\sin {Y \over 2}\sin {Z \over 2} = {4 \over {35}}$$
D
$${\sin ^2}\left( {{{X + Y} \over 2}} \right) = {3 \over 5}$$
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