JEE Main 2021 (Online) 27th August Evening Shift | Application of Derivatives Question 106 | Mathematics

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 :

$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over {12}}$$

$${{a + b - \sqrt {{a^2} + {b^2} + ab} } \over 6}$$

$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over 6}$$

$${{a + b + \sqrt {{a^2} + {b^2} + ab} } \over 6}$$

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-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 :

$${5 \over {2 + \sqrt 3 }}$$

$${{10} \over {2 + 3\sqrt 3 }}$$

$${5 \over {3 + \sqrt 3 }}$$

$${{10} \over {3 + 2\sqrt 3 }}$$

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-1

The local maximum value of the function $$f(x) = {\left( {{2 \over x}} \right)^{{x^2}}}$$, x > 0, is

$${\left( {2\sqrt e } \right)^{{1 \over e}}}$$

$${\left( {{4 \over {\sqrt e }}} \right)^{{e \over 4}}}$$

$${(e)^{{2 \over e}}}$$

JEE Main 2021 (Online) 25th July Morning Shift