On the interval $[0,1]$,the function $f(x) = x^{25}(1-x)^{75}$ takes its maximum value at the point

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

The displacement $x$ of a particle at time $t$ is given by $x = t^4 - kt^3$. If the velocity of the particle is maximum at $t = 2$,then $k = $ ..........

For a positive real number $x$,when its reciprocal is added to it,the sum attains a minimum value. What is the value of $x$?

The displacement $S$ of a particle measured from a fixed point $O$ on a line is given by $S = t^3 - 16t^2 + 64t - 16$. Then the time at which displacement of the particle is maximum is