1
JEE Main 2021 (Online) 27th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
A box open from top is made from a rectangular sheet of dimension a $$\times$$ b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to :
A
$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over {12}}$$
B
$${{a + b - \sqrt {{a^2} + {b^2} + ab} } \over 6}$$
C
$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over 6}$$
D
$${{a + b + \sqrt {{a^2} + {b^2} + ab} } \over 6}$$
2
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+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
$${{10} \over {3 + 2\sqrt 3 }}$$
3
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+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
4
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+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 $$\left( { - {\pi \over 6},0} \right)$$
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