X different wavelength may be observed in the spectrum from a hydrogen sample if the atoms are excited to…

Use the concept of hydrogen like atom spectrum when the atoms are excited to a sixth excited state, to find different wavelengths observed in the spectrum.

The total possible transitions are,

 $\frac{n\left(n-1\right)}{2}=\frac{6\times 5}{2}=15$

Here $n$ is the principal quantum number.