Let $f(z)=\frac{\sin z}{z^2}- \frac{\cos z}{z}$ then
$f$ has a pole of order $2$ at $0$,
$f$ has a simple pole at $0$,
$\int_{|z|=1}f(z)=0$ anticlockwise,
residue of $f$ at $0$ is $-2\pi i$,
I am not able to figure out which of the statement is correct or false. I think only 4 is correct by residue theorem.