If $$S = \int\limits_1^\infty {{x^{ - 3}}dx} $$ then $$S$$ has the value

for the scalar field $$u = {{{x^2}} \over 2} + {{{y^2}} \over 3},\,\,$$ the magnitude of the gradient at the point $$(1,3)$$ is

A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

If $$P$$ and $$Q$$ are two random events, then which of the following is true?