1
JEE Main 2020 (Online) 8th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\int {{{\cos xdx} \over {{{\sin }^3}x{{\left( {1 + {{\sin }^6}x} \right)}^{2/3}}}}} = f\left( x \right){\left( {1 + {{\sin }^6}x} \right)^{1/\lambda }} + c$$

where c is a constant of integration, then $$\lambda f\left( {{\pi \over 3}} \right)$$ is equal to
A
$${9 \over 8}$$
B
2
C
-2
D
$$-{9 \over 8}$$
2
JEE Main 2020 (Online) 8th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The inverse function of

f(x) = $${{{8^{2x}} - {8^{ - 2x}}} \over {{8^{2x}} + {8^{ - 2x}}}}$$, x $$ \in $$ (-1, 1), is :
A
$${1 \over 4}{\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$
B
$${1 \over 4}\left( {{{\log }_8}e} \right){\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$
C
$${1 \over 4}\left( {{{\log }_8}e} \right){\log _e}\left( {{{1 + x} \over {1 - x}}} \right)$$
D
$${1 \over 4}{\log _e}\left( {{{1 + x} \over {1 - x}}} \right)$$
3
JEE Main 2020 (Online) 8th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The shortest distance between the lines

$${{x - 3} \over 3} = {{y - 8} \over { - 1}} = {{z - 3} \over 1}$$ and

$${{x + 3} \over { - 3}} = {{y + 7} \over 2} = {{z - 6} \over 4}$$ is :
A
3
B
$${7 \over 2}\sqrt {30} $$
C
$$3\sqrt {30} $$
D
$$2\sqrt {30} $$
4
JEE Main 2020 (Online) 8th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let ƒ(x) = xcos–1(–sin|x|), $$x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, then which of the following is true?
A
ƒ' is decreasing in $$\left( { - {\pi \over 2},0} \right)$$ and increasing in $$\left( {0,{\pi \over 2}} \right)$$
B
ƒ '(0) = $${ - {\pi \over 2}}$$
C
ƒ is not differentiable at x = 0
D
ƒ' is increasing in $$\left( { - {\pi \over 2},0} \right)$$ and decreasing in $$\left( {0,{\pi \over 2}} \right)$$
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