The coefficient of $x^{37}$ in the expansion of $(1-x)^{30} \, (1 + x + x^2)^{29}$ is :

The expression $[x + (x^3-1)^{1/2}]^5 + [x - (x^3-1)^{1/2}]^5$ is a polynomial of degree :

The coefficient of $x^8$ in the expansion of $(1 -x^4)^4 (1 + x)^5$ is :-

If the second, third and fourth terms in the expansion of $(x+y)^{\mathrm{n}}$ are $135$,$30$ and $\frac{10}{3}$, respectively, then $6\left(n^3+x^2+y\right)$ is equal to .............

The coefficient of  $x^2$ in the expansion of the product $(2 -x^2)$. $((1 + 2x + 3x^2)^6 +(1 -4x^2)^6)$  is

The coefficient of ${x^4}$ in the expansion of ${(1 + x + {x^2} + {x^3})^n}$ is