Which of the following transitions in a hydrogen atom emits photons of the highest frequency? ($n=$ principal quantum number)

An electron makes a transition from an excited state to the ground state of a hydrogen-like atom. Out of the following statements,which one is correct?

$A$ hydrogen atom falls from $n^{\text{th}}$ higher energy orbit to the first energy orbit $(n=1)$. The energy released is equal to $12.75 \text{ eV}$. The $n^{\text{th}}$ orbit is:

If an electron in the excited state falls to the ground state,a photon of energy $5 \ eV$ is emitted. The wavelength of the photon is nearly: (in $nm$)

Energy of the electron in $n^{th}$ orbit of hydrogen atom is given by $E_n = - \frac{13.6}{n^2} \ eV$. The amount of energy needed to transfer an electron from the first orbit to the third orbit is........$eV$.

Energy levels $A, B$ and $C$ of a certain atom correspond to increasing values of energy, i.e., $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are the wavelengths of radiations corresponding to transitions $C$ to $B, B$ to $A$ and $C$ to $A$ respectively, which of the following relations is correct?