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GATE ECE 2017 Set 2 | Question: 54
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 $25 \%$ ... $6.55 \: GHz \leq f \leq 13.1 \: GHz$ $1.64 \: GHz \leq f \leq 10.24 \: GHz$

admin asked in Electromagnetics Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 53
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 ____________$\times 10^{-8}$ ... $e=-1.6\times 10^{-19}$ C, and permittivity $\varepsilon _0=(1/36\pi)\times 10^{-9}$ F/m]

admin asked in Electronic Devices Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 55
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 _______________

admin asked in Electromagnetics Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 52
Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure. The channel is lossless noiseless useless deterministic

admin asked in Communications Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 51
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 ____________

admin asked in Communications Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 44
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 ... $Y_3Y_2Y_1Y_0=0100$ and $Z_0=1$. The output of the ripple carry adder will be stable at $t$ (in ns) = ___________

admin asked in Number Representations Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 43
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 ____________

admin asked in Number Representations Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 45
A programmable logic array (PLA) is shown in the figure. The Boolean function $F$ implemented is $\overline{P} \: \overline{Q}R+ \overline{P}QR+P \overline{Q} \: \overline{R}$ $(\overline{P}+\overline{Q}+R)(\overline{P}+Q+R)(P+\overline{Q}+\overline{R})$ ... $(\overline{P}+\overline{Q}+R)(\overline{P}+Q+R)(P+\overline{Q}+R)$

admin asked in Digital Circuits Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 50
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 _________

admin asked in Communications Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 47
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 undamped (oscillatory) underdamped critically damped overdamped

admin asked in Control Systems Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 48
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 $0$ $1$ $2$ $3$

admin asked in Control Systems Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 46
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 $k$ for which the system oscillates at $2$ rad/s is ___________

admin asked in Control Systems Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 49
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 $H(f)$ ... $= 3$, frequencies $= 2,7,11$ Number $= 2$, frequencies $= 2,7$ Number $= 2$, frequencies $= 7,11$

admin asked in Continuous-time Signals Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 42
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 $(Ic)$ ... is $0.7$ V and the thermal voltage $V_T = 26$ mV. The output voltage $V_{out}$ (in volts) is ______________

admin asked in Analog Circuits Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 41
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 place).

admin asked in Analog Circuits Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 40
Assuming that transistors $M_1$ and $M_2$ are identical and have a threshold voltage of $1$ V, the state of transistors $M_1$ and $M_2$ are respectively Saturation, Saturation Linear, Linear Linear, Saturation Saturation, Linear

admin asked in Analog Circuits Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 37
For a particular intensity of incident light on a silicon $pn$ junction solar cell, the photocurrent density $(J_L)$ is $2.5 mA/cm^2$ and the open-circuit voltage ($V_{oc}$) is $0.451$ V. Consider thermal voltage ($V_T$) to ... the incident light is increased by $20$ times, assuming that the temperature remains unchanged, $V_{oc}$ (in volts) will be ____________

admin asked in Analog Circuits Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 32
Consider the circuit shown in the figure. The Thevenin equivalent resistance (in Ω) across P-Q is _____________

admin asked in Network Solution Methods Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 31
The switch in the circuit, shown in the figure, was open for a long time and is closed at $t=0$. The current $i(t)$ (in ampere) at $t=0.5$ seconds is ____________

admin asked in Electronic Devices Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 39
An abrupt $pn$ junction (located at $x=0$) is uniformly doped on both $p$ and $n$ sides. The width of the depletion region is $W$ and the electric field variation in the $x$-direction is $E(x)$. Which of the following figures represents the electric field profile near the $pn$ junction?

admin asked in Electronic Devices Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 34
The transfer function of a causal LTI system is $H(s)=1/s$. If the input to the system is $x(t)=[\sin(t)/\pi t] u(t)$, where $u(t)$ is a unit step function, the system output $y(t)$ as $t\to \infty$ is ____________

admin asked in Control Systems Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 33
Consider an LTI system with magnitude response $\mid H(f) \mid=\begin{cases} 1-\frac{\mid f \mid}{20}, & \mid f \mid \leq 20 \\ 0,& \mid f \mid > 20 \end{cases}$ and phase response $\arg \{ H(f) \}= - 2f.$ If the input to the ... $y(t)$ is ____________

admin asked in Control Systems Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 35
Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are $ \begin{array} {} h_1(t)=2\delta (t+2)-3\delta (t+1) \\ h_2(t)=\delta (t-2). \end{array}$ If the input $x(t)$ is a unit step signal, then the energy of $y(t)$ is ____________

admin asked in Continuous-time Signals Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 36
A MOS capacitor is fabricated on $p$-type Si (Silicon) where the metal work function is $4.1$ eV and electron affinity of Si is $4.0$ eV. $E_C-E_F=0.9$ eV, where $E_C$ and $E_F$ are the conduction band minimum and the Fermi energy ... capacitor is $-1$ V, then the magnitude of the fixed charge at the oxide-semiconductor interface, in $nC/cm^2$, is ___________.

admin asked in Electronic Devices Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 38
Two n-channel MOSFETs, T1 and T2, are identical in all respects except that the width of T2 is double that of T1. Both the transistors are biased in the saturation region of operation, but the gate overdrive voltage ($V_{GS}-V_{TH}$ ... $2g_{m1}$ $8I_{D1}$ and $4g_{m1}$ $4I_{D1}$ and $4g_{m1}$ $4I_{D1}$ and $2g_{m1}$

admin asked in Analog Circuits Nov 25, 2017

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GATE ECE 2017 Set 2 | Question: 29
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is __________

admin asked in Probability and Statistics Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 30
The minimum value of the function $f(x)=\frac{1}{3} x(x^2-3)$ in the interval $-100≤x≤100$ occurs at $x =$ ________.

admin asked in Calculus Nov 23, 2017

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28

GATE ECE 2017 Set 2 | Question: 28
If the vector function $\overrightarrow{F}=\widehat{a_x}(3y-k_1z)+\widehat{a_y}(k_2x-2z)-\widehat{a_z}(k_3y+z)$ is irrotational, then the values of the constants $k_1$,$k_2$ and $k_3$, respectively, are $0.3, -2.5, 0.5$ $0.0, 3.0, 2.0$ $0.3, 0.33, 0.5$ $4.0, 3.0, 2.0$

admin asked in Vector Analysis Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 26
The values of the integrals $\int_{0}^{1}\left ( \int_{0}^{1}\frac{x-y}{(x+y)^3}dy \right )dx$ and $\int_{0}^{1}\left ( \int_{0}^{1}\frac{x-y}{(x+y)^3}dx \right )dy$ are same and equal to $0.5$ same and equal to $-0.5$ $0.5$ and $-0.5$, respectively $-0.5$ and $0.5$, respectively

admin asked in Calculus Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 23
A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is $40$ dB. The minimum number of bits per sample needed to achieve the desired SQNR is __________

admin asked in Communications Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 24
Two conducting spheres $S1$ and $S2$ of radii $a$ and $b$ ($b>a$) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure. For some charge placed on this structure, the potential and surface electric ... $E_a<E_b$ $V_a>V_b$ and $E_a>E_b$ $V_a=V_b$ and $E_a>E_b$ $V_a>V_b$ and $E_a=E_b$

admin asked in Electromagnetics Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 25
A two-wire transmission line terminates in a television set. The VSWR measured on the line is $5.8$. The percentage of power that is reflected from the television set is _________

admin asked in Electromagnetics Nov 23, 2017

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33

GATE ECE 2017 Set 2 | Question: 27
An integral $I$ over a counterclockwise circle $\textbf{C}$ is given by $I=\oint _c \frac{z^2-1}{z^2+1} e^z dz.$ If $\textbf{C}$ is defined as$\mid z \mid=3$ , then the value of $I$ is $-\pi i \sin(1)$ $- 2\pi i \sin(1)$ $-3\pi i \sin(1)$ $-4\pi i \sin(1)$

admin asked in Electromagnetics Nov 23, 2017

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34

GATE ECE 2017 Set 2 | Question: 16
Consider the circuit shown in the figure. The Boolean expression $F$ implemented by the circuit is $\overline{X} \overline{Y} \overline{Z} + X Y +\overline{Y} Z $ $\overline{X} Y \overline{Z} + X Z + \overline{Y} Z $ $\overline{X} Y \overline{Z} +XY + \overline{Y} Z $ $\overline{X} \overline{Y} \overline{Z} + XZ+ \overline{Y}Z $

admin asked in Number Representations Nov 23, 2017

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35

GATE ECE 2017 Set 2 | Question: 15
For the circuit shown in the figure, P and Q are the inputs and Y is the output. The logic implemented by the circuit is XNOR XOR NOR OR

admin asked in Number Representations Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 22
Consider the random process $X(t)=U+Vt,$ Where $U$ is a zero-mean Gaussian random variable and V is a random variable uniformly distributed between $0$ and $2$. Assume that $U$ and $V$ are statistically independent. The mean value of the random process at $t = 2$ is ________

admin asked in Probability and Statistics Nov 23, 2017

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37

GATE ECE 2017 Set 2 | Question: 17
In a DRAM, periodic refreshing is not required information is stored in a capacitor information is stored in a latch both read and write operations can be performed simultaneously

admin asked in Digital Circuits Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 21
Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memoryless binary symmetric channel with crossover probability $p$ ?

admin asked in Communications Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 14
Consider the circuit shown in the figure. Assume base-to-emitter voltage $V_{BE}=0.8 V$ and common-base current gain ($\alpha$) of the transistor is unity. The value of the collector-to-emitter voltage $V_{CE}$ (in volt) is ____________

admin asked in Analog Circuits Nov 23, 2017

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GATE ECE 2017 Set 2 | Question: 13
In the figure, $D1$ is a real silicon $pn$ junction diode with a drop of $0.7V$ under forward bias condition and $D2$ is a Zener diode breakdown voltage of $-6.8V$. The input $V_{in}(t)$ is a periodic square wave of period $T$ ... $-20.5 V$ $6.1 V$ and $-21.9 V$ $7.5 V$ and $-21.2 V$ $6.1 V$ and $-22.6 V$

admin asked in Electronic Devices Nov 23, 2017

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