1
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is :
A
$${5 \over {2 + \sqrt 3 }}$$
B
$${{10} \over {2 + 3\sqrt 3 }}$$
C
$${5 \over {3 + \sqrt 3 }}$$
D
$${{10} \over {3 + 2\sqrt 3 }}$$
2
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
The local maximum value of the function $$f(x) = {\left( {{2 \over x}} \right)^{{x^2}}}$$, x > 0, is
A
$${\left( {2\sqrt e } \right)^{{1 \over e}}}$$
B
$${\left( {{4 \over {\sqrt e }}} \right)^{{e \over 4}}}$$
C
$${(e)^{{2 \over e}}}$$
D
1
3
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Let $$f(x) = 3{\sin ^4}x + 10{\sin ^3}x + 6{\sin ^2}x - 3$$, $$x \in \left[ { - {\pi \over 6},{\pi \over 2}} \right]$$. Then, f is :
A
increasing in $$\left( { - {\pi \over 6},{\pi \over 2}} \right)$$
B
decreasing in $$\left( {0,{\pi \over 2}} \right)$$
C
increasing in $$\left( { - {\pi \over 6},0} \right)$$
D
decreasing in $$\left( { - {\pi \over 6},0} \right)$$
4
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let f : R $$\to$$ R be defined as

$$f(x) = \left\{ {\matrix{ { - {4 \over 3}{x^3} + 2{x^2} + 3x,} & {x > 0} \cr {3x{e^x},} & {x \le 0} \cr } } \right.$$. Then f is increasing function in the interval
A
$$\left( { - {1 \over 2},2} \right)$$
B
(0,2)
C
$$\left( { - 1,{3 \over 2}} \right)$$
D
($$-$$3, $$-$$1)
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