The maximum area of a rectangle with a perimeter of $176 \ cm$ is .......... $sq. \ cm$.

The lengths of the sides of a triangle are $10+x^2$,$10+x^2$ and $20-2x^2$. If for $x=k$,the area of the triangle is maximum,then $3k^2$ is equal to

An extreme value of $f(x)=\frac{4}{\sin x}+\frac{1}{1-\sin x}$ in $(0, \pi / 2)$ is

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

Let $P(x) = x^4 + ax^3 + bx^2 + cx + d$ be such that $x = 0$ is the only real root of $P'(x) = 0$. If $P(-1) < P(1)$,then in the interval $[-1, 1]$:

Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$, then $p^{\prime}(0)$ is equal to