GATE Questions & Answers of Taylor’s series

What is the Weightage of Taylor’s series in GATE Exam?

Total 5 Questions have been asked from Taylor’s series topic of Complex Analysis subject in previous GATE papers. Average marks 1.60.

The Taylor series expansion of  3 sin x +  2 cos x is

The Taylor series expansion of $\frac{\mathrm{sin}x}{x-\mathrm{\pi }}$ at $x=\pi$ is given by

Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x=0?

In the Taylor series expansion of exp(x) + sin(x) about the point x=$\pi$, the coefficient of (x-$\pi$)2 is