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) 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, $${{1 \over 2}}$$]
3
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
The maximum value of

$$f(x) = \left| {\matrix{ {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\cos 2x} \cr {1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\cos 2x} \cr {{{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \cr } } \right|,x \in R$$ is :
A
$$\sqrt 5$$
B
$${3 \over 4}$$
C
5
D
$$\sqrt 7$$
4
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Out of Syllabus
Let slope of the tangent line to a curve at any point P(x, y) be given by $${{x{y^2} + y} \over x}$$. If the curve intersects the line x + 2y = 4 at x = $$-$$2, then the value of y, for which the point (3, y) lies on the curve, is :
A
$$- {{18} \over {19}}$$
B
$$- {{4} \over {3}}$$
C
$${{18} \over {35}}$$
D
$$- {{18} \over {11}}$$
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