The eigen values of a skew-symmetric matrix are

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