GATE EC 2010 Question Paper (14-Feb-2010) (Shift 1)

If $e^y=x^{\frac{1}{x}}$, then y has a

A fair coin is tossed independently four times. The probability of the event “the number of times heads show up is more than the number of times tails show up" is

If $\vec{A}=xy{\hat{a}}_x+x^2{\hat{a}}_y,$ then ${\oint }_C\vec{A}.d\vec{l}$ over the path shown in the figure is

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

Consider a differential equation $\frac{dy(x)}{dx}-y(x)=x$ with the initial condition y(0) = 0. Using Euler's first order method with a step size of 0.1. The value of y(0.3) is