Let $f(x) = 1 - \sqrt{x^2}$, where the square root is to be taken as positive. Then:

The function $f(x) = x^3 + ax^2 + bx + c$ where $a^2 \leq 3b$ has:

An open tank with a square bottom,to contain $4000 \ cm^3$ of liquid,is to be constructed. The dimensions of the tank,so that the surface area of the tank is minimum,are

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 $f(x)$ be a polynomial of degree $5$ such that $x=\pm 1$ are its critical points. If $\mathop {\lim }\limits_{x \to 0} \left(2+\frac{f(x)}{x^{3}}\right)=4,$ then which one of the following is not true?