In an a.c. circuit, voltage and current are given by:

$$V=100 \sin (100 t) V$$ and $$I=100 \sin \left(100 t+\frac{\pi}{3}\right) \mathrm{mA}$$ respectively.

The average power dissipated in one cycle is:

A particle is moving in a straight line. The variation of position '$$x$$' as a function of time '$$t$$' is given as $$x=\left(t^3-6 t^2+20 t+15\right) m$$. The velocity of the body when its acceleration becomes zero is :

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $$10 \mathrm{~m}$$. If it dissipates $$10 \%$$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is:

[Use, $$\mathrm{g}: 10 \mathrm{~ms}^{-2}$$]

$$N$$ moles of a polyatomic gas $$(f=6)$$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $$N$$ is :