There are $9$ balls to be placed in $9$ boxes. If $5$ of the balls cannot fit into $3$ specific small boxes,find the number of ways of arranging one ball in each of the boxes.

Extraction of zinc from zinc blende is achieved by

If $(1, 3), (2, 5),$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are:

The work function of a certain metal is $3.31 \times 10^{-19} \, J$. The maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength $5000 \, \text{Å}$ is: (Given: $h = 6.62 \times 10^{-34} \, J \cdot s$, $c = 3 \times 10^8 \, m/s$, $e = 1.6 \times 10^{-19} \, C$) (in $\text{eV}$)

Observe the following statements:
$I$. If $dy + 2xy dx = 2e^{-x^2} dx$, then $ye^{x^2} = 2x + c$.
$II$. If $ye^{-x^2} - 2x = c$, then $dx = (2e^{-x^2} - 2xy) dy$.
Which of the following is a correct statement?

The radius of the smallest electron orbit in a hydrogen-like ion is $(0.51 \times 10^{-10} / 4) \text{ m}$. This ion is: