The function $f(x) = 2x^3 - 3x^2 - 12x + 4, x \in R$ has

The perimeter of a triangle is $10 \text{ cm}$. If one of its sides is $4 \text{ cm}$,then the remaining sides of the triangle,when the area of the triangle is maximum,are

The function $f(x) = 2x^3 - 21x^2 + 36x + 7$ has a local maximum at $x = $ ........

$A$ wire of length $20 \ m$ is to be cut into two pieces. $A$ piece of length $\ell_1$ is bent to make a square of area $A_1$ and the other piece of length $\ell_2$ is made into a circle of area $A_2$. If $2A_1 + 3A_2$ is minimum,then $(\pi \ell_1) : \ell_2$ is equal to:

An open-topped box is to be constructed by removing equal squares from each corner of a $3 \text{ m}$ by $8 \text{ m}$ rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

An enemy fighter jet is flying along the curve given by $y = x^2 + 2$. $A$ soldier is placed at $(3, 2)$ and wants to shoot down the jet when it is nearest to him. The nearest distance is: