GATE EC question library

In the given figure, $A_{1}, A_{2}$ and $A_{3}$ are ideal ammeters. If $\mathrm{A}_{2}$ and $\mathrm{A}_{3}$ read $3 \mathrm{~A}$ and $4 \mathrm{~A}$ respectvely, then $A_{1}$ should read

Some unknown material has a conductivity of $10^{6} \; \mathrm{mho} / \mathrm{m}$ and a permeability of $4 \pi \times 10^{-7} \; \mathrm{H} / \mathrm{m}$. The skin depth for the material at $1 \; \mathrm{GHz}$ is

A $1 \mathrm{~km}$ long microwave link uses two antennas each having $30 \mathrm{~dB}$ gain. If the power transmitted by one antenna is $1 \mathrm{~W}$ at $3 \; \mathrm{GHz}$, the power received by the other antenna is approximately

The critical frequency of an ionospheric layer is $10 \; \mathrm{MHz}$. What is the maximum launching angle from the horizon for which $20 \; \mathrm{MHz}$ wave will be reflected by the layer?

An $\text{FM}$ signal with a modulation index $9$ is applied to a frequency tripler. The modulation index in the output signal will be

The autocorrelation function of an energy signal has

The number of bits in a binary $\mathrm{PCM}$ system is increased from $n$ to $n+1$. As a result, the signal to quantization noise ratio will improve by a factor

The following sequence of instructions are executed by an $8085$ microprocessor: $\begin{matrix} 1000 &LXI & SP &27 \; FF \\ 1000 &CALL & & 1006\\ 1006 &POP \; H & & \end{matrix}$ The contents of the stack pointer $\text{(SP)}$ and the $\text{HL,}$ register pair on completion of execution of these instructions are

A memory system of size $26 \mathrm{~K}$ bytes is required to be designed using memory chips which have $12$ address lines and $4$ data lines each. The number of such chips required to design the memory system is

A $10$ - bit $\text{ADC}$ with a full scale output voltage of $10.24 \mathrm{~V}$ is designed to have $\mathrm{a} \pm \mathrm{LSB} / 2$ accuracy. If the $\mathrm{ADC}$ is calibrated at $25^{\circ} \mathrm{C}$ and the operating temperature ranges from $0^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$, then the maximum net temperature …

A dynamic $\text{RAM}$ cell which hold $5 \mathrm{~V}$ has to be refreshed every $20 \mathrm{~m}$ secs, so that the stored voltage does not fall by more than $0.5 \mathrm{~V}$. If the cell has a constant discharge current of $0.1 \; \mathrm{pA}$, the storage capacitance of the cell is

A Zener diode in the circuit shown in the figure is has a knee current of $5 \mathrm{~mA}$, and a maximum allowed power dissipation of $300 \mathrm{~mW}$. What are the minimum and maximum load currents that can be drawn safely from the circuit, keeping the output voltage $\mathrm{V}_{\mathrm{o}}$ constant at $6 \mathrm{~V}$?

Value of $R$ in the oscillator circuit shown in the given figure, so chosen that it just oscillates at an angular frequency of $\omega$. The value of $\omega$ and the required value of $R$ will respectively be

A Darlington stage is shown in the figure is. If the transconductance of $Q_{1}$ is $g_{m 1}$ and $Q_{2}$ is $g_{m 2}$, then the overall transconductance $g_{m c}\left[\triangleq \frac{i_{c}^{c}}{v_{b c}^{c}}\right]$ is given by

A silicon $n$ $\text{MOSFET}$ has a threshold voltage of $1$ $\mathrm{V}$ and oxide thickness of $\mathrm{AO}$. $\left[\varepsilon_{r}\left(\mathrm{siO}_{2}\right)=3.9, \varepsilon_{\mathrm{o}}=8.854 \times 10^{-14} \mathrm{~F} / \mathrm{cm}\right.$, $\left.q=1.6 \times 10^{-19} \mathrm{C}\right]$ The region under the gate is ion-implanted for …

An $\text{npn}$ transistor has a beta cut-off frequency $f \beta$ of $1 \; \mathrm{MHz}$, and common emitter short circuit low frequency current gain $\beta \mathrm{O}$ of $200$. It unity gain frequency $f \mathrm{T}$ and the alpha cut-off frequency $f \alpha$ respectively are

In a bipolar transistor at room temperature, if the emitter current is doubled the voltage across its base-emitter junction

A uniform plane wave in air is normally incident on infinitely thick slab. If the refractive index of the glass slab is $1.5$, then the percentage of incident power that is reflected from the air-glass interface is

The voltages $\mathrm{V}_{\mathrm{C} 1}, \mathrm{~V}_{\mathrm{C} 2}$, and $\mathrm{V}_{\mathrm{C} 3}$ across the capacitors in the circuit in the given figure, under steady state, are respectively.

The inverse Laplace transform of the function $\frac{s+5}{(s+1)(s+3)}$ is