1
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
$$h\left( {g\left( 3 \right)} \right) = 36$$
2
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
$${\sin ^2}\left( {{{X + Y} \over 2}} \right) = {3 \over 5}$$
3
JEE Advanced 2016 Paper 1 Offline
+3
-1
The least value of a $$\in R$$ for which $$4a{x^2} + {1 \over x} \ge 1,$$, for all $$x>0$$. is
A
$${1 \over {64}}$$
B
$${1 \over {32}}$$
C
$${1 \over {27}}$$
D
$${1 \over {25}}$$
4
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A solution curve of the differential equation

$$\left( {{x^2} + xy + 4x + 2y + 4} \right){{dy} \over {dx}} - {y^2} = 0,$$ $$x>0,$$ passes through the

point $$(1,3)$$. Then the solution curve
A
intersects $$y=x+2$$ exactly at one point
B
intersects $$y=x+2$$ exactly at two points
C
intersects $$y = {\left( {x + 2} \right)^2}$$
D
does NOT intersect $$\,y = {\left( {x + 3} \right)^2}$$
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