What transition in He+ ion shall have the same wave number as the first line in balmar series of H atom A 7 5 B 5 3 C 6 4 D 4 2?

[…] my teacher told me to continue using a trial and error method […]

But nobody told you to do it manually once you have understood how to adjust the Rydberg constant for $\ce{He+}$ and use the formula to get the energies for the given transistions, in order to compare them with the $\ce{H_{\alpha}}$ line (656.3 nm):

import scipy.constants transitions = ((7,5), (5,3), (6,4), (4,2)) def get_he_line_nm(n_upper, n_lower): '''calculate the energy for a line in a He+ spectrum and return it in nanometer''' energy = 4 * scipy.constants.Rydberg * (pow(n_lower, -2) - pow(n_upper, -2)) return 1.0/(scipy.constants.nano * energy) # energy in nm for upper, lower in transitions: wavelength = get_he_line_nm(upper, lower) print('{0} -> {1} : {2:7.2f} nm'.format(upper, lower, wavelength))

will give the output

7 -> 5 : 1162.81 nm 5 -> 3 : 320.37 nm 6 -> 4 : 656.11 nm 4 -> 2 : 121.50 nm