Residue Formula

Q. The residue of $f\left(z\right)=\frac{z^3}{(z-1{)}^4(z-2\left)\right(z-3)}$ at $z=3$ is

1. $-8$
2. $\frac{101}{16}$
3. $0$
4. $\frac{27}{16}$

Q. The residuses of a complex function $X\left(z\right)=\frac{1-2z}{z(z-1)(z-2)}$ at its poles are

1. $\frac{1}{2},-\frac{1}{2}$ and $1$
2. $\frac{1}{2},-\frac{1}{2}$ and $-1$
3. $\frac{1}{2},1$ and $-\frac{3}{2}$
4. $\frac{1}{2},-1$ and $\frac{3}{2}$

Q. The sum of residues of $f\left(z\right)=\frac{2z}{(z-1{)}^2(z-2)}$ at its singular point is

1. $-8$
2. $-4$
3. $0$
4. $4$

Q.

For $f\left(z\right)=\frac{sin\left(z\right)}{z^2}$, the residue of the pole $z=0$ is

1. 1

Q. Consider the following complex function:
$f\left(z\right)=\frac{9}{(z-1)(z+1{)}^2}$
Which of the following is one of hte residues of the above function?

1. $-1$
2. $\frac{9}{16}$
3. $2$
4. $-\frac{9}{4}$