GATE EC 2015 Question Paper (31-Jan-2015) (Shift 1)

In the system shown in figure (a), $\mathrm{m}\left(\mathrm{t}\right)$ is a low-pass signal with bandwidth W Hz. The frequency response of the band-pass filter $\mathrm{H}\left(\mathrm{f}\right)$ is shown in figure (b). If it is desired that the output signal $\mathrm{z}\left(\mathrm{t}\right)=10\mathrm{x}\left(\mathrm{t}\right)$, the maximum value of W (in Hz) should be strictly less than _______.

A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as

${\mathrm{f}}_{\left(\mathrm{R}/0\right)}\left(\mathrm{x}\right)=\{\frac{1}{4},-3\le \mathrm{x}\le 1\mathrm{and}{\mathrm{f}}_{\left(\mathrm{R}/1\right)}\left(\mathrm{x}\right)=\{\frac{1}{6},-1\le \mathrm{x}\le 5$

The minimum decision error probability is

The longitudinal component of the magnetic field inside an air – filled rectangular wave guide made of a perfect electric conductor is given by the following expression

${\mathrm{H}}_{\mathrm{z}}\left(\mathrm{x},\mathrm{y},\mathrm{z},\mathrm{t}\right)=0.1\cos \left(25\pi \mathrm{x}\right)\cos \left(30.3\pi \mathrm{y}\right)\cos \left(12\mathrm{x}\times {10}^9\mathrm{t}-\beta \mathrm{z}\right)\left(\frac{\mathrm{A}}{\mathrm{m}}\right)$

The cross – sectional dimensions if the wave guide are given as $\mathrm{a}=0.08\mathrm{m}$ and $\mathrm{b}=0.033\mathrm{m}$. The mode of propagation inside the waveguide is

The electric field intensity of a plane wave traveling in free space is given by the following expression

$\mathrm{E}\left(\mathrm{x},\mathrm{t}\right)={\mathrm{a}}_{\mathrm{y}}24\pi \cos \left(\omega \mathrm{t}-{\mathrm{k}}_0\mathrm{x}\right)\left(\frac{\mathrm{V}}{\mathrm{m}}\right)$

In this field, consider a square area 10 cm x 10 cm on plane x + y = 1. The total time – averaged power (in mW) passing through the square area is_____________

Consider a uniform plane wave with amplitude $\left({\mathrm{E}}_0\right)$ of $10\frac{\mathrm{V}}{\mathrm{m}}$ and $1.1\mathrm{GHz}$ frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $\left({ϵ}_{\mathrm{r}}\right)$ and permeability $\left({\mu }_{\mathrm{r}}\right)$ as shown in the figure



The magnitude of the transmitted electric field component in $\left(\mathrm{V}/\mathrm{m}\right)$ after it has travelled a distance of 10 cm inside the dielectric region is______