GATE EC question library

In the circuit shown, transistors $Q_1$ and $Q_2$ are biased at a collector current of $2.6$ mA. Assuming that transistor current gains are sufficiently large to assume collector current equal to emitter current and thermal voltage of $26$ mV, the magnitude of voltage gain $V_0/V_s$ in the mid-band frequency range is __________(up to second decimal …

In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors $Q_1, Q_2, \dots ,Q_{32}$ are identical in all respects and have infinitely large values of common-emitter current gain $(\beta)$. The collector current $(Ic)$ of the transistors is related to their base-emitter voltage ($V_{BE}$) by the relation …

The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input 'In' and an output 'Out'. The initial state of the FSM is $S_0$. If the input sequence is $10101101001101$, starting with the left-most bit, then the number of times 'Out' will be $1$ is ____________

Figure Ⅰ shows a $4$-bit ripple carry adder realized using full adders and Figure Ⅱ shows the circuit of a full-adder (FA). The propagation delay of the XOR, AND and OR gates in Figure Ⅱ are $20$ ns, $15$ ns and $10$ ns, respectively. Assume all the inputs to the $4$-bit adder are initially reset to $0$. Figure I Figure II At $t = 0$, the …

A programmable logic array (PLA) is shown in the figure. The Boolean function $F$ implemented is

A unity feedback control system is characterized by the open-loop transfer function $$G(s)=\frac{2(s+1)}{s^3+ks^2+2s+1}$$ The value of $</em>k$ for which the system oscillates at $2$ rad/s is ___________

A second-order LTI system is described by the following state equations, $$\begin{array}{ll} \frac{d}{dt}x_1(t)-x_2(t)=0 \\ \frac{d}{dt}x_2(t)+2x_1(t)+3x_2(t)=r(t) \end{array}$$ where $x_1(t)$ and $x_2(t)$ are the two state variables and $r(t)$ denotes the input. The output $c(t)=x_1(t)$. The system is

A unity feedback control system is characterized by the open-loop transfer function $$G(s)=\frac{10K(s+2)}{s^3+3s^2+10}$$ The Nyquist path and the corresponding Nyquist plot of $G(s)$ are shown in the figures below. If $0 < K < 1$, then the number of poles of the closed-loop transfer function that lie in the right-half of the $s$-plane is

The signal $x(t)=\sin (14000\pi t)$, where $t$ is in seconds, is sampled at a rate of $9000$ samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response $H(f)$ as follows: $$H(f)=\begin{cases} 1, & \mid f \mid \leq 12 kHz .\\ 0,& \mid f \mid> 12 kHz. \end{cases}$$ What is the number of sinusoids …

The unmodulated carrier power in an AM transmitter is $5$ kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is $50 \%$. If it is reduced to $40 \%$, then the maximum unmodulated carrier power (in kW) that can be used without overloading the transmitter is _________

A modulating signal given by $x(t)=5\sin (4\pi 10^3t -10\pi \cos 2\pi 10^3t)V$ is fed to a phase modulator with phase deviation constant $k_p=5$ rad/V. If the carrier frequency is $20$ kHz, the instantaneous frequency(in kHz) at $t=0.5$ ms is ____________

Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure. The channel is

An electron $(q_1)$ is moving in free space with velocity $10^5$ m/s towards a stationary electron $(q_2)$ far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is ____________$\times 10^{-8}$ m. [Given, mass of electron $m=9.11\times 10^{-31}$ kg, charge of electron …

Standard air-filled rectangular waveguides of dimensions $a=2.29$ cm and $b=1.02$ cm are designed for radar applications. It is desired that these waveguides operate only in the dominant $TE_{10}$ mode with the operating frequency at least $25 \%$ above the cutoff frequency of the $TE_{10}$ mode but not higher than $95 \%$ of the next higher …

The permittivity of water at optical frequencies is $1.75 \varepsilon _0$. It is found that an isotropic light source at a distance $d$ under water forms an illuminated circular area of radius $5$ m, as shown in the figure. The critical angle is $\theta _c$. The value of $d$ (in meter) is _______________

Which of the following is CORRECT with respect to grammar and usage? Mount Everest is ____________

The policeman asked the victim of a theft, “What did you______?”

Despite the new medicine’s_____________ in treating diabetes, it is not _____________ widely.

In a huge pile of apples and oranges, both ripe and unripe mixed together,$15\%$ are unripe fruits. Of the unripe fruits, $45 \%$ are apples. Of the ripe ones, $66 \%$ are oranges. If the pile contains a total of $5692000$ fruits, how many of them are apples?

Michael lives $10$ km away from where I live. Ahmed lives $5$ km away and Susan lives $7$ km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?