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

If $$\overrightarrow A = xy\,\widehat a{}_x + {x^2}\widehat a{}_y\,\,$$ then $$\,\,\oint {\overrightarrow A .d\overrightarrow r \,\,} $$ over the path shown in the figure is

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

A function $$n(x)$$ satisfies the differential equation $${{{d^2}n\left( x \right)} \over {d{x^2}}} - {{n\left( x \right)} \over {{L^2}}} = 0$$ where $$L$$ is a constant. The boundary conditions are $$n(0)=k$$ and $$n\left( \propto \right) = 0.$$ The solution to this equation is