GATE EC 2015 Question Paper (31-Jan-2015) (Shift 2)

A unity negative feedback system has an open loop transfer function,

$\mathrm{G}\left(\mathrm{s}\right)=\frac{\mathrm{K}}{\mathrm{s}\left(\mathrm{s}+10\right)}$

The gain K for which the system to have damping ratio of $0.25$ is_________.

A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB, the number of levels in the quantizer is ________.

The signal $\cos \left(10\pi \mathrm{t}+\frac{\pi }{4}\right)$ is ideally sampled at a sampling frequency of $15\mathrm{Hz}$. the sampled signal is passed through a filter with impulse response

$\left(\frac{\sin \left(\pi \mathrm{t}\right)}{\pi \mathrm{t}}\right)\cos \left(40\pi \mathrm{t}-\frac{\pi }{2}\right).$ The filter output is

In a source free region in vacuum, if the electrostatic potential, $\varphi =2{\mathrm{x}}^2+{\mathrm{y}}^2+\mathrm{c}{\mathrm{z}}^2$, the value of constant c must be____________.

The electric field of a uniform plane electromagnetic wave is

$\vec{\mathrm{E}}=\left({\vec{\mathrm{a}}}_{\mathrm{x}}+\mathrm{j}4{\vec{\mathrm{a}}}_{\mathrm{y}}\right)\exp \left[\mathrm{j}\left(2\pi \times {10}^7\mathrm{t}-0.2\mathrm{z}\right)\right]$

The polarization of the wave is