A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is $$\lambda$$, calculate the change of microscope's resolving power due to oil and choose the correct option.

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

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 :

In a meter bridge experiment, for measuring unknown resistance 'S', the null point is obtained at a distance $$30 \mathrm{~cm}$$ from the left side as shown at point D. If R is $$5.6$$ $$\mathrm{k} \Omega$$, then the value of unknown resistance 'S' will be __________ $$\Omega$$.