$A$ nucleus ${}_{n}^{m}X$ emits one $\alpha$ particle and two ${\beta^-}$ particles. The resulting nucleus is

$A$ conducting rod of length $2l$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. $A$ uniform magnetic field $\vec B$ exists parallel to the axis of rotation. The $e.m.f.$ induced between the two ends of the rod is

The two thigh bones (femurs),each of cross-sectional area $10 \,cm^2$,support the upper part of a person of mass $50 \,kg$. The average pressure sustained by the femurs is ........... $N/m^2$.

$A$ mixture of $2\, \text{moles}$ of helium gas (atomic mass $= 4\, \text{amu}$) and $1\, \text{mole}$ of argon gas (atomic mass $= 40\, \text{amu}$) is kept at $300\, \text{K}$ in a container. The ratio of the $r.m.s.$ speeds $\left( \frac{v_{\text{rms}}(\text{helium})}{v_{\text{rms}}(\text{argon})} \right)$ is

Which one of the following elements reduces $NaOH$ to $Na$?

Cultivation of $Bt$ Cotton has been much in the news. The prefix "$Bt$" means