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

$A$ wheel with ten metallic spokes,each $0.50 \ m$ long,is rotated with a speed of $120 \ rev/min$ in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is $0.4 \ G$,the induced $e.m.f.$ between the axle and the rim of the wheel is equal to:

$A$ capacitor of capacity $0.1 \mu F$ connected in series to a resistor of $10 M \Omega$ is charged to a certain potential and then made to discharge through the resistor. The time in which the potential will take to fall to half its original value is (Given,$\log _{10} 2=0.3010$ ) (in $~s$)

The area bounded by the parabola $y=x^2$ and the line $y=x$ is

Boron in green plants assists in

Under the influence of a uniform magnetic field,a charged particle is moving in a circle of radius $R$ with constant speed $v$. The time period of the motion