GATE EC 2016 Question Paper (31-Jan-2016) (Shift 2)

Consider the signal $x(t)=\cos (6\pi t)+\sin (8\pi t)$, where $t$ is in seconds. The Nyquist sampling rate (in samples/second) for the signal $y(t)=x(2t+5)$ is

If the signal $x(t)=\frac{\sin (t)}{\pi t}\ast \frac{\sin (t)}{\pi t}$ with $\ast$ denoting the convolution operation, then $x(t)$ is equal to

A discrete-time signal $x[n]=\delta [n-3]+2\delta [n\text{–}5]$ has z-transform $X(z)$. If $Y(z)=X(-z)$ is the z-transform of another signal $y[n]$, then

In the RLC circuit shown in the figure, the input voltage is given by

$v_i(t)=2\cos (200t)+4\sin (500t)$.

The output voltage $v_o(t)$ is

The I-V characteristics of three types of diodes at the room temperature, made of semiconductors X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in all respects except their materials. If $E_{gX}$, $E_{gY}$ and $E_{gZ}$ are the band gaps of X, Y and Z, respectively, then