If the number of terms in the expansion of $(x - 2y + 3z)^n$ is $45$,then $n=$

If $x$ is so small that $x^3$ and higher powers of $x$ may be neglected,then $\frac{(1 + x)^{3/2} - (1 + \frac{1}{2}x)^3}{(1 - x)^{1/2}}$ may be approximated as

$f(x+h)=0$ represents the transformed equation of the equation $f(x)=x^4+2x^3-19x^2-8x+60=0$. If this transformation removes the term containing $x^3$ from $f(x)=0$,then $h=$

Let $r$ be the remainder when $2021^{2020}$ is divided by $2020^2$. Then $r$ lies between

The coefficient of $x^{4}$ in the expansion of $(1+x+x^{2})^{10}$ is

For $|x| < \frac{1}{5}$,the coefficient of $x^3$ in the expansion of $\frac{1}{(1-5 x)(1-4 x)}$ is