In the given circuit the AC source has $$\omega$$ = 100 rad s^-1. Considering the inductor and capacitor to be ideal, what will be the current I flowing through the circuit?

If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is :

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $${{24} \over \pi } \times {10^2}$$ Nm^-2. What is the minimum radius of the wire ? (Take g = 10 ms^-2)

Two waves are simultaneously passing through a string and their equations are :

y₁ = A₁ sin k(x $$-$$ vt), y₂ = A₂ sin k(x $$-$$ vt + x₀). Given amplitudes A₁ = 12 mm and A₂ = 5 mm, x₀ = 3.5 cm and wave number k = 6.28 cm^$$-$$1. The amplitude of resulting wave will be ................ mm.