In an experiment four quantities $$a,b,c$$ and $$d$$ are measured with percentage error $$1\% ,2\% ,3\% $$ and $$4\% $$ respectively. Quantity $$P$$ is calculated as follows
$$P = \frac{{{a^3}{b^2}}}{{cd}}\% $$ error in $$P$$ is
A quantity $$X$$ is given by $${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}}$$ where $${ \in _0}$$ is the permittivity of the free space, $$L$$ is a length, $$\Delta V$$ is a potential difference and $$\Delta t$$ is a time interval. The dimensional formula for $$X$$ is the same as that of-
Pressure depends on distance as, $$P = \frac{\alpha }{\beta }exp\left( { - \frac{{\alpha z}}{{k\theta }}} \right),$$ where $$\alpha ,$$ $$\beta $$ are constants, $$z$$ is distance, $$k$$ is Boltzman’s constant and $$\theta $$ is temperature. The dimension of $$\beta $$ are-