The magnetic force acting on a charged particle of charge $-2\mathrm{\mu C}$ in a magnetic field of $2\mathrm{T}$ acting in $\mathrm{y}-$direction.When the particle velocity is $\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}\right)\times {10}^6 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

How much younger an astronaut will appear to earth if he returns after one year having move with velocity equal to $0.5 C$?

A particle with a lifetime of $2\times {10}^{-6} \sec$ moves through the lab with a speed of $0.9 \mathrm{C}$. It's lifetime, as measured by an observer in the lab is