Where is the International Rice Research Institute $(IRRI)$ located?

$A$ light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 \, cm$,the frequency of the tuning fork is .... $Hz$

$A$ horizontal force of $10\,N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and wall is $0.2$. The weight of the block is ........ $N$.

$\begin{aligned} & f(x, y)=2(x-y)^2-x^4-y^4 \\ & \left|\left(f_{x x} f_{y y}-f_{x y}^2\right)\right|_{(0,0)} \end{aligned}$

As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion:

An ideal transformer has $100$ turns in the primary and $250$ turns in the secondary. The peak value of the $AC$ voltage in the primary is $28\ V$. The $r.m.s.$ secondary voltage is nearest to $....V$.