If the sum of the coefficients of all even powers of

$\operatorname{Let}\left(1+x+x^{2}+\ldots+x^{2 n}\right)\left(1-x+x^{2}-x^{3}+\ldots+x^{2 n}\right)$

$=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}+a_{4} x^{4}+\ldots+a_{4 n} x^{4 n}$

So, 

$a_{0}+a_{1}+a_{2}+\ldots+a_{4 n}=2 n+1$ ..............(1)

$a_{0}-a_{1}+a_{2}-a_{3} \ldots+a_{4 n}=2 n+1$ ...........(2)

$\Rightarrow \mathrm{a}_{0}+\mathrm{a}_{2}+\mathrm{a}_{4}+\ldots+\mathrm{a}_{4 \mathrm{n}}=2 \mathrm{n}+1$

$\Rightarrow 2 \mathrm{n}+1=61 \quad \Rightarrow \mathrm{n}=30$