The total number of degrees of freedom of molecules of hydrogen of volume 1 cc  at NTP is $1.34\times {10}^{(5\times N)}$. Find N.

1 mole of hydrogen at NTP occupies 22.4 litres.
Therefore, number of moles in 1 cc of hydrogen at NTP = $\frac{1}{22.4\times 1000}\left(1\right)=4.46\times {10}^{-5}$ 
Number of molecules of Hydrogen =  $\left(4.46\times {10}^{-5}\right)\left(6.023\times {10}^{23}\right)=26.86\times {10}^{18}$
Each hydrogen molecule has 5 degrees of freedom.
So, total number of degrees of freedom =  $5\times 26.86\times {10}^{18}=1.34\times {10}^{20}$