An electron (mass $$\mathrm{m}$$) with an initial velocity $$\vec{v}=v_{0} \hat{i}\left(v_{0}>0\right)$$ is moving in an electric field $$\vec{E}=-E_{0} \hat{i}\left(E_{0}>0\right)$$ where $$E_{0}$$ is constant. If at $$\mathrm{t}=0$$ de Broglie wavelength is $$\lambda_{0}=\frac{h}{m v_{0}}$$, then its de Broglie wavelength after time t is given by

What is the half-life period of a radioactive material if its activity drops to $$1 / 16^{\text {th }}$$ of its initial value in 30 years?

A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below.

The logic gate circuit is :

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to