Two sides of a triangle are given. If the area of the triangle is maximum,then the angle between the given sides is (in $^{\circ}$)

The condition for the function $f(x) = x^3 + px^2 + qx + r$ $(x \in R)$ to have no extreme value is:

If $x = -1$ and $x = 2$ are the extreme points of the function $y = a \log|x| + bx^2 + x$,then find the values of $a$ and $b$.

The maximum value of ${\left( {\frac{1}{x}} \right)^x}$ is

Two particles $P$ and $Q$ located at the points $P(t, t^3 - 16t - 3)$ and $Q(t + 1, t^3 - 6t - 6)$ are moving in a plane. The minimum distance between the points during their motion is:

$A$ 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: