If $$\omega $$ $$\left( { \ne 1} \right)$$ be a cube root of unity and $${\left( {1 + {\omega ^2}} \right)^n} = {\left( {1 + {\omega ^4}} \right)^n},$$ then the least positive value of n is

Pressure depends on distance as, $$P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$$, where $$\alpha $$, $$\beta $$ are constants, z in distance, k is Boltzman's constant and $$\theta $$ is temperature. The dimention of $$\beta $$ are

A wire of length $$l = 6 \pm 0.06$$ cm and $$r = 0.5 \pm 0.005$$ cm and mass $$m = 0.3 \pm 0.003$$ gm. Maximum percentage error in density is

A particle starts sliding down a frictionless inclined plane. If S_n is the distance traveled by it from time t = n - 1 sec to t = n sec, the ratio S_n / S_n+1 is