Which of the following is the correct order of size of the given species?

If $y=a \cos (\log x)+b \sin (\log x)$,where $a, b$ are parameters,then $x^2 y^{\prime \prime}+x y^{\prime}$ is equal to

The coordinates of the point $P$ on the curve $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$,where the tangent is inclined at an angle $\frac{\pi}{4}$ to the $x$-axis,are

If the equation of one tangent to the circle with centre at $(2, -1)$ from the origin is $3x + y = 0$,then the equation of the other tangent through the origin is

The set $\{x \in R : [x - |x|] = 5\}$ is equal to

The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together is