$$\sigma$$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :

An element $$\Delta l=\Delta x\hat{i}$$ is placed at the origin and carries a large current $$I=10 \mathrm{~A}$$. The magnetic field on the $$y$$-axis at a distance of $$0.5 \mathrm{~m}$$ from the elements $$\Delta x$$ of $$1 \mathrm{~cm}$$ length is:

A small ball of mass $$m$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_0$$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

A train starting from rest first accelerates uniformly up to a speed of $$80 \mathrm{~km} / \mathrm{h}$$ for time $$t$$, then it moves with a constant speed for time $$3 t$$. The average speed of the train for this duration of journey will be (in $$\mathrm{km} / \mathrm{h}$$) :