The population $$p$$ $$(t)$$ at time $$t$$ of a certain mouse species satisfies the differential equation $${{dp\left( t \right)} \over {dt}} = 0.5\,p\left( t \right) - 450.\,\,$$ If $$p(0)=850,$$ then the time at which the population becomes zero is :

If $$g\left( x \right) = \int\limits_0^x {\cos 4t\,dt,} $$ then $$g\left( {x + \pi } \right)$$ equals

The area between the parabolas $${x^2} = {y \over 4}$$ and $${x^2} = 9y$$ and the straight line $$y=2$$ is :

If the $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\,\ln \,\left| {\sin x - 2\cos x} \right| + k,} $$ then $$a$$ is
equal to :