If the coefficients of a^m and aⁿ in the expansion of (1 + a)^{m + n} are $$\alpha$$ and $$\beta$$, then which one of the following is correct?

What is the number of non-zero terms in the expansion of $${(1 + 2\sqrt 3 x)^{11}} + {(1 - 2\sqrt 3 x)^{11}}$$ (after simplification)?

How many terms are there in the expansion of $${(1 + 2x + {x^2})^5} + {(1 + 4y + 4{y^2})^5}$$ ?

If the middle term in the expansion of $${\left( {{x^2} + {1 \over x}} \right)^{2n}}$$ is $$184756{x^{10}}$$, then what is the value of n?