At some instant, a radioactive sample S₁ having an activity 5 $$\mu $$Ci has twice the number of nuclei as another sample S₂ which has an activity of 10 $$\mu $$Ci. The half lives of S₁ and S₂ are :

A carrier wave of peak voltage 14 V is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of 80% will be :

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :

In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 k$$\Omega $$ are used. The figure of merit of the galvanometer is 60 $$\mu A/$$division. In the absence of shunt resistance, the galvanometer produces a deflection of $$\theta $$ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $$\theta /2,$$ is closest to :