While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $$1 \mathrm{~mm}$$ and circular scale reading is equal to 42 divisions. Pitch of screw gauge is $$1 \mathrm{~mm}$$ and it has 100 divisions on circular scale. The diameter of the wire is $$\frac{x}{50} \mathrm{~mm}$$. The value of $$x$$ is :

Given below are two statements :

Statement I : In an LCR series circuit, current is maximum at resonance.

Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.

In the light of the above statements, choose the correct from the options given below :

$$\sigma$$ 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: