1
JEE Main 2018 (Offline)
+4
-1
If the curves y2 = 6x, 9x2 + by2 = 16 intersect each other at right angles, then the value of b is :
A
$${9 \over 2}$$
B
6
C
$${7 \over 2}$$
D
4
2
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
$$-2\sqrt 2$$
3
JEE Main 2018 (Offline)
+4
-1
Let S = { t $$\in R:f(x) = \left| {x - \pi } \right|.\left( {{e^{\left| x \right|}} - 1} \right)$$$$\sin \left| x \right|$$ is not differentiable at t}, then the set S is equal to
A
{0, $$\pi$$}
B
$$\phi$$ (an empty set)
C
{0}
D
{$$\pi$$}
4
JEE Main 2018 (Offline)
+4
-1
Let y = y(x) be the solution of the differential equation

$$\sin x{{dy} \over {dx}} + y\cos x = 4x$$, $$x \in \left( {0,\pi } \right)$$.

If $$y\left( {{\pi \over 2}} \right) = 0$$, then $$y\left( {{\pi \over 6}} \right)$$ is equal to
A
$$- {4 \over 9}{\pi ^2}$$
B
$${4 \over {9\sqrt 3 }}{\pi ^2}$$
C
$$- {8 \over {9\sqrt 3 }}{\pi ^2}$$
D
$$- {8 \over 9}{\pi ^2}$$
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