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1
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Consider the function f : R $$\to$$ R defined by

$$f(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \right)} \right)|x|,x \ne 0 \hfill \cr 0,\,\,x = 0 \hfill \cr} \right.$$. Then f is :
A
not monotonic on ($$-$$$$\infty$$, 0) and (0, $$\infty$$)
B
monotonic on (0, $$\infty$$) only
C
monotonic on ($$-$$$$\infty$$, 0) only
D
monotonic on ($$-$$$$\infty$$, 0) $$\cup$$ (0, $$\infty$$)
2
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
The inverse of $$y = {5^{\log x}}$$ is :
A
$$x = {5^{\log y}}$$
B
$$x = {y^{{1 \over {\log 5}}}}$$
C
$$x = {5^{{1 \over {\log y}}}}$$
D
$$x = {y^{\log 5}}$$
3
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

A
Q and R
B
None of these
C
P and R
D
P and Q
4
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Let f be a real valued function, defined on R $$-$$ {$$-$$1, 1} and given by

f(x) = 3 loge $$\left| {{{x - 1} \over {x + 1}}} \right| - {2 \over {x - 1}}$$.

Then in which of the following intervals, function f(x) is increasing?
A
($$-$$$$\infty$$, $$-$$1) $$\cup$$ $$\left( {[{1 \over 2},\infty ) - \{ 1\} } \right)$$
B
($$-$$$$\infty$$, $$\infty$$) $$-$$ {$$-$$1, 1)
C
($$-$$$$\infty$$, $${{1 \over 2}}$$] $$-$$ {$$-$$1}
D
($$-$$1, $${{1 \over 2}}$$]
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