To maximize torque, the magnetic moment (m = nIA) should be maximized. For a given length l, the area A is maximum when the number of turns n = 1, forming the largest possible radius. Hence, the correct answer is ...

The deflection in a galvanometer is inversely proportional to the series resistance. Reducing the deflection from 30 to 20 units means increasing the resistance by a factor of 30/20 = 3/2. Therefore, the new resistance is 3000 × 3/2 = ...

The sensitivity ratio without and with shunt is 60/10 = 6, indicating that the current through the shunt is 5 times the galvanometer current. Using S = Rg/n-1′ we get S = 20/5 = 4Ω. Hence, the correct answer is ...

In a cyclotron, a charged particle speeds up between the dees due to the electric field, while the magnetic field inside the dees keeps it moving in a circular path without changing its speed. Hence, the correct answer is (B).

The time period of a charged particle in a uniform magnetic field is given by T = 2m/qB, which is independent of the speed of the particle. Hence, the correct answer is (A) Speed of the particle.