List of top Engineering Mathematics Questions on Line integrals and Green's theorem asked in GATE XE

Let \(C\) be the positively oriented boundary of the domain bounded by the curves \(y=2x^{2}\) and \(y^{2}=4x\). Then the value of the line integral \[ \oint_{C} (2y^{2}+2xy+4y)\,dx + (x^{2}+4xy+8x)\,dy \] is equal to:

Which one of the following functions is differentiable at $z=0$ but NOT differentiable at any other point in the complex plane $\mathbb{C}$?