The coefficient of $x^{4}$ is the expansion of $\left(1+\mathrm{x}+\mathrm{x}^{2}\right)^{10}$ is

- [JEE MAIN 2020]

- A
$615$

- B
$625$

- C
$595$

- D
$575$

If the sum of the coefficients in the expansion of ${(x + y)^n}$ is $1024$, then the value of the greatest coefficient in the expansion is

If $a^3 + b^6 = 2$, then the maximum value of the term independent of $x$ in the expansion of $(ax^{\frac{1}{3}}+bx^{\frac{-1}{6}})^9$ is, where $(a > 0, b > 0)$

If the sum of the coefficients in the expansion of $(x - 2y + 3 z)^n,$ $n \in N$ is $128$ then the greatest coefficie nt in the exp ansion of $(1 + x)^n$ is

The coefficient of ${x^5}$ in the expansion of ${({x^2} - x - 2)^5}$ is

The sum of all those terms which are rational numbers in the expansion of $\left(2^{1 / 3}+3^{1 / 4}\right)^{12}$ is:

- [JEE MAIN 2021]