A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be:

In amplitude modulation, sinusoidal carrier frequency used is denoted by $${\omega _c}$$ and the signal frequency is denoted by $${\omega _m}$$. The bandwidth ($$\Delta {\omega _m}$$) of the signal is such that $$\Delta {\omega _m}$$ < < $$\omega _c$$. Which of the following frequencies is not contained in the modulated wave?

The following observations were taken for determining surface tension T of water by capillary method:
diameter of capillary, D = 1.25 $$\times$$ 10^-2 m
rise of water, h = 1.45 $$\times$$ 10^-2m
Using g = 9.80 m/s² and the simplified relation T = $${{rhg} \over 2} \times {10^3}N/m$$, the possible error in surface tension is closest to :