1
JEE Main 2018 (Offline)
+4
-1
Let $$f\left( x \right) = {x^2} + {1 \over {{x^2}}}$$ and $$g\left( x \right) = x - {1 \over x}$$,
$$x \in R - \left\{ { - 1,0,1} \right\}$$.
If $$h\left( x \right) = {{f\left( x \right)} \over {g\left( x \right)}}$$, then the local minimum value of h(x) is
A
$$2\sqrt 2$$
B
3
C
-3
D
$$-2\sqrt 2$$
2
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is :
A
$$6\sqrt 2 \pi$$
B
$$6\sqrt 3 \pi$$
C
$$8\sqrt 2 \pi$$
D
$$8\sqrt 3 \pi$$
3
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
Out of Syllabus
If $$\beta$$ is one of the angles between the normals to the ellipse, x2 + 3y2 = 9 at the points (3 cos $$\theta$$, $$\sqrt 3 \sin \theta$$) and ($$-$$ 3 sin $$\theta$$, $$\sqrt 3 \,\cos \theta$$); $$\theta \in \left( {0,{\pi \over 2}} \right);$$ then $${{2\,\cot \beta } \over {\sin 2\theta }}$$ is equal to :
A
$${2 \over {\sqrt 3 }}$$
B
$${1 \over {\sqrt 3 }}$$
C
$$\sqrt 2$$
D
$${{\sqrt 3 } \over 4}$$
4
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
Out of Syllabus
A tangent to the curve, y = f(x) at P(x, y) meets x-axis at A and y-axis at B. If AP : BP = 1 : 3 and f(1) = 1, then the curve also passes through the point :
A
$$\left( {{1 \over 3},24} \right)$$
B
$$\left( {{1 \over 2},4} \right)$$
C
$$\left( {2,{1 \over 8}} \right)$$
D
$$\left( {3,{1 \over 28}} \right)$$
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