When the excited electron of a $H$ atom from $n=5$ drops to the ground state,the maximum number of emission lines observed are $.......$

Match the equations given in List-$I$ with their names in List-$II$.

List-$I$	List-$II$
$(1)$ $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$	$(A)$ De Broglie equation
$(2)$ $mvr \ge \frac{nh}{2\pi}$	$(B)$ Uncertainty principle
$(3)$ $\lambda = \frac{h}{\sqrt{2m(KE)}}$	$(C)$ Frequency equation of $H$-spectrum
$(4)$ $\nu = 3.29 \times 10^{15} \left( \frac{1}{n_i^2} - \frac{1}{n_f^2} \right)$	$(D)$ Angular momentum is quantized

Which of the following violates the Aufbau principle and Hund's rule?

Consider the following:
$I$. The electron spin quantum number describes the orientation of the spin of the nucleus with respect to the magnetic field.
$II$. The orbitals represented by the quantum numbers $n=3, l=2, m=+2$ and $n=3, l=2, m=-2$ have the same energy.
$III$. The energy of a photon is directly proportional to wavelength but inversely proportional to wave number.
$IV$. Lyman series of lines appear in ultra-violet region.
The correct statements are:

Which of the following arrangements of electrons is most likely to be stable?

The shape of the probability distribution curve for the $2s$ orbital is .........