An urn contains $$5$$ red and $$7$$ green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is

The value of the integral $${1 \over {2\pi j}}\int\limits_c {{{{z^2} + 1} \over {{z^2} - 1}}} dz$$
where $$z$$ is a complex number and $$C$$ is a unit circle with center at $$1+0j$$ in the complex plane is ____.

In the neighborhood of $$z=1,$$ the function $$f(z)$$ has a power series expansion of the form
$$f\left( z \right) = 1 + \left( {1 - z} \right) + {\left( {1 - z} \right)^2} + ..................$$
Then $$f(z)$$ is