$$500$$ students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate course enrolment as follows: chemistry $$(329)$$, physics $$(186)$$, Mathematics $$(295)$$, chemistry and physics $$(83)$$, chemistry and Mathematics $$(217)$$, and physic and Mathematics $$(63)$$, How many students are taking all $$3$$ subjects?

The general solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} - 5y = 0\,\,\,$$ in terms of arbitrary constants $${K_1}$$ and $${K_2}$$ is

The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are

An integral $${\rm I}$$ over a counter clock wise circle $$C$$ is given by $${\rm I} = \oint\limits_c {{{{z^2} - 1} \over {{z^2} + 1}}} \,\,{e^z}\,dz$$
If $$C$$ is defined as $$\left| z \right| = 3,$$ then the value of $${\rm I}$$ is