Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to -

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 -