An insulating thin rod of length $$l$$ has a linear charge density $$\rho \left( x \right)$$ = $${\rho _0}{x \over l}$$ on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is -

A uniform metallic wire has a resistance of 18 $$\Omega $$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is -

A plano convex lens of refractive index $$\mu $$₁ and focal length ƒ₁ is kept in contact with another plano concave lens of refractive index $$\mu $$₂ and focal length ƒ₂. If the radius of curvature of their spherical faces is R each and ƒ₁ = 2ƒ₂, then $$\mu $$₁ and $$\mu $$₂ are related as -

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10^–12 m, the minimum electron energy required is close to -