GATE EC question library

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

A discrete-time signal $x[n] = \delta[n – 3] + 2 \delta[n – 5]$ 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

The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in

The figure shows the $I-V$ characteristics of a solar cell illuminated uniformly with solar light of power $100\ mW/cm^2$. The solar cell has an area of $3\ cm^2$ and a fill factor of $0.7$. The maximum efficiency (in $\%$) of the device is _______

The diodes $D1$ and $D2$ in the figure are ideal and the capacitors are identical. The product $RC$ is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage $V_o$(in volt) at the steady state is _______

Consider the circuit shown in the figure. Assuming $V_{EE1} = V_{EE2} = 0.7$ volt, the value of the dc voltage $V_{C2}$(in volt) is _______

In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the output pin $3$ is _______

In an $8085$ microprocessor, the contents of the accumulator and the carry flag are $A7$ (in hex) and $0$, respectively. If the instruction $RLC$ is executed, then the contents of the accumulator (in hex) and the carry flag, respectively, will be

The logic functionality realized by the circuit shown below is

The minimum number of $2$-input $NAND$ gates required to implement a $2$-input $XOR$ gate is

The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain of $G$ of the system is

For the unity feedback control system shown in the figure, the open-loop transfer function $G(s)$ is given as $$G(s) = \frac{2}{s(s+1)}$$ The steady state error $e_{ss}$ due to a unit step input is

For a superheterodyne receiver, the intermediate frequency is $15\ MHz$ and the local oscillator frequency is $3.5\ GHz$. If the frequency of the received signal is greater than the local oscillator frequency, then the image frequency (in $MHz$) is _______

An analog baseband signal, bandlimited to $100\ Hz$, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $p_1 = p_4 = 0.125$ and $p_2 = p_3$. The information rate (bits/sec) of the message source is _______

A binary baseband digital communication system employs the signal $$p(t) = \begin{cases}\large\frac{1}{\sqrt T_s},&0\leq t\leq T_s \\ \: 0, & \text{otherwise} \end{cases}$$ for transmission of bits. The graphical representation of the matched filter output $y(t)$ for this signal will be

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

Faraday’s law of electromagnetic induction is mathematically described by which one of the following equations?