PYQs Based Test - 24 : Taylor and Laurent's Series

In the Laurent series expression of $f\left(z\right)=\frac{1}{\left(z-1\right)\left(z-2\right)}$ valid for 0 < |z - 1|< 1, the co-efficient of $\frac{1}{\left(z-1\right)}$ is

Statement (I): f(z) = sinz can be expanded at $\mathrm{z}=\pi /4$ by using Laurent series

Statement (I): $f\left(z\right)=\frac{1}{z+4}$ can be expanded by Taylor’s series in a valid region, 1 < |z| < 3

Which of the statements are true

Using McLaurin’s series expansion, the value of log (sec x) is

If the principal part of the Laurent’s series vanishes, then the Laurent’s series reduces to

Expansion of $f\left(z\right)=\frac{1}{\left(2z+1\right)\left(z-3\right)}$ in a valid region $|z|>3$