In the expansion of $$\left(1+3 x+3 x^2+x^3\right)^{2 n}$$, the term which has greatest binomial coefficient, is

If $$U_{n+1}=3 U_n-2 U_{n-1}$$ and $$U_0=2, U_1=3$$, then $$U_n$$ is equal to

If $$4^n+15n+P$$ is divisible by 9 for all $$n\in N$$, then the least negative integral value of P is

The total number of terms in the expansion of $${(x + y)^{100}} + {(x - y)^{100}}$$ is