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 maximum value of $y=x(\log x)^2$ is

Let a function $f(x) = \begin{cases} -\ln(3x - [3x]) & ; 3x \neq n, n \in N \\ \ln(\operatorname{sgn}(3x)) & ; 3x = n, n \in N \end{cases}$,where $[.]$ and $\operatorname{sgn}(x)$ denote the greatest integer function and signum function respectively. Then the number of points where $f(x)$ is minimum in $x \in (0, 5)$ is:

The maximum area of a right-angled triangle with hypotenuse $h$ is

Find the maximum and minimum values of $f,$ if any,of the function given by $f(x)=|x|, x \in R.$

If $x=-2$ and $x=4$ are the extreme points of $y=x^3-\alpha x^2-\beta x+5$,then