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1
GATE20132
Consider a vector field $\vec{A}(\vec{r}).$ The closed loop line integral $\displaystyle {} \int \vec{A}\bullet\vec{dl}$ can be expressed as $\displaystyle {} \iint (\triangledown \times \vec{A}) \bullet\vec{ds}$ over the closed surface bounded by the ... bounded by the loop $\displaystyle {} \iiint (\triangledown \times \vec{A}) \bullet\vec{ds}$ over the open surface bounded by the loop
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
2
GATE20131
A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles an AND gate an OR gate an XOR gate a NAND gate
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
3
GATE20133
Two systems with impulse responses $h_{1}(t)$ and $h_{2}(t)$ are connected in cascade. Then the overall impulse response of the cascaded system is given by product of $h_{1}(t)$ and $h_{2}(t)$ sum of $h_{1}(t)$ and $h_{2}(t)$ convolution of $h_{1}(t)$ and $h_{2}(t)$ subtraction of $h_{2}(t)$ from $h_{1}(t)$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
4
GATE20134
In a forward biased $pn$ junction diode, the sequence of events that best describes the mechanism of current flow is injection, and subsequent diffusion and recombination of minority carriers injection, and subsequent drift and generation ... extraction, and subsequent diffusion and generation of minority carriers extraction, and subsequent drift and recombination of minority carriers
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
5
GATE20135
In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces superior quality oxide with a higher growth rate inferior quality oxide with a higher growth rate inferior quality oxide with a lower growth rate superior quality oxide with a lower growth rate
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
6
GATE20136
The maximum value of $\theta$ until which the approximation $\sin\theta \approx \theta $ holds to within $10\%$ error is $10^{\circ}$ $18^{\circ}$ $50^{\circ}$ $90^{\circ}$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
7
GATE20137
The divergence of the vector field $\vec{A} = x\hat{a}_{x} + y\hat{a}_{x} + z\hat{a}_{z}$ is $0$ $1/3$ $1$ $3$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
8
GATE20138
The impulse response of a system is $h(t) = tu(t).$ For an input $u(t − 1),$ the output is $\frac{t^{2}}{2}u(t)$ $\frac{t(t1)}{2}u(t1)$ $\frac{(t1)^{2}}{2}u(t1)$ $\frac{t^{2}1}{2}u(t1)$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
9
GATE20139
The Bode plot of a transfer function $G(s)$ is shown in the figure below. The gain $(20\log \mid G(s)\mid)$ is $32\:dB$ and $8\:dB$ at $1\:rad/s$ and $10\:rad/s$ respectively. The phase is negative for all $\omega.$ Then $G(s)$ is $\frac{39.8}{s}$ $\frac{39.8}{s^{2}}$ $\frac{32}{s}$ $\frac{32}{s^{2}}$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
10
GATE201310
In the circuit shown below what is the output voltage $(V_{out})$ if a silicon transistor $Q$ and an ideal opamp are used? $15\: V$ $0.7\: V$ $+0.7\: V$ $+15\: V$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
1
answer
11
GATE201236
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$
answered
Nov 26
in
Others
by
Naveen Kumar 3
(
150
points)
gate2012ec
0
votes
0
answers
12
GATE201311
Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor $k, k> 0,$ the elements of the corresponding star equivalent will be scaled by a factor of $k^{2}$ $k$ $1/k$ $\sqrt{k}$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
13
GATE201312
For $8085$ microprocessor, the following program is executed. $ MVI\: A, 05H;$ $ MVI\: B, 05H;$ $PTR:ADD \:B;$ $ DCR \:B;$ $JNZ\: PTR;$ $ADI\: 03H;$ $HLT;$ At the end of program, accumulator contains $17H$ $20H $ $23H$ $ 05H$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
14
GATE201313
The bit rate of a digital communication system is $R\: kbits/s.$ The modulation used is $32$QAM. The minimum bandwidth required for ISI free transmission is $R/10\: Hz$ $R/10\: kHz$ $R/5\: Hz$ $R/5\: kHz$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
15
GATE201314
For a periodic signal $v(t) = 30\sin100\:t + 10\cos300\:t + 6\sin(500\:t+\pi/4),$ the fundamental frequency in $rad/sec$ is $100$ $300$ $500$ $1500$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
16
GATE201315
In a voltagevoltage feedback as shown below, which one of the following statements is TRUE if the gain $k$ is increased? The input impedance increases and output impedance decreases The input impedance increases and output impedance also increases The input impedance decreases and output impedance also decreases The input impedance decreases and output impedance increases
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
17
GATE201316
A bandlimited signal with a maximum frequency of $5\: kHz$ is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is $5\: kHz $ $12\: kHz$ $15\: kHz$ $20\: kHz$
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
18
GATE201317
In a MOSFET operating in the saturation region, the channel length modulation effect causes an increase in the gatesource capacitance a decrease in the transconductance a decrease in the unitygain cutoff frequency a decrease in the output resistance
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
19
GATE201318
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system? All the poles of the system must lie on the left side of the $j\omega$ axis Zeros of the system can lie anywhere in the $s$plane All the poles must lie within $\mid s \mid =1$ All the roots of the characteristic equation must be located on the left side of the $j\omega$ axis
edited
Nov 26
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
1
answer
20
GATE201319
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
answered
Nov 26
in
Linear Algebra
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
linearalgebra
eigenvalues
0
votes
0
answers
21
GATE201320
A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x  a_{0}$ with all coefficients positive has no real roots no negative real root odd number of real roots at least one positive and one negative real root
edited
Nov 25
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
22
GATE201321
Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is $u(t)$ $tu(t)$ $\frac{t^{2}}{2}u(t)$ $e^{t}u(t)$
edited
Nov 25
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
23
GATE201322
The transfer function $\dfrac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is $\frac{0.5s+1}{s+1}$ $\frac{3s+6}{s+2}$ $\frac{s+2}{s+1}$ $\frac{s+1}{s+2}$
edited
Nov 25
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
24
GATE201323
A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\Omega$ should be $3$ $4$ $5$ $7$
edited
Nov 25
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
25
GATE201324
The return loss of a device is found to be $20\:dB.$ The voltage standing wave ratio $(VSWR)$ and magnitude of reflection coefficient are respectively $1.22$ and $0.1$ $0.81$ and $0.1$ $1.22$ and $0.1$ $2.44$ and $0.2$
edited
Nov 25
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
26
GATE201325
Let $g(t) = e^{\pi t^{2}},$ and $h(t)$ is a filter matched to $g(t).$ If $g(t)$ is applied as input to $h(t),$ then the Fourier transformation of the output is $ e^{\pi f^{2}}$ $ e^{\pi f^{2}/ 2}$ $ e^{\pi \mid f \mid }$ $ e^{2\pi f^{2}}$
edited
Nov 25
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
27
GATE2017 EC2: 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
edited
Nov 25
in
Digital Circuits
by
jothee
(
100
points)
gate2017ec2
logicgates
+1
vote
0
answers
28
GATE2017 EC1: 27
A three dimensional region R of finite volume is described by $x^2 + y^2 \leq z^3; \: \: 0 \leq z \leq 1,$ where $x,y,z$ are real. The volume of R (up to two decimal places) is _________
edited
Nov 25
in
Network Solution Methods
by
jothee
(
100
points)
gate2017ec1
0
votes
0
answers
29
GATE201326
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is $4/9$ $1/2$ $2/3$ $5/9$
recategorized
Nov 24
in
Probability and Statistics
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
probability
randomvariable
0
votes
0
answers
30
GATE201327
Let $A$ be an $m \times n$ matrix and $B$ an $n \times m$ matrix. It is given that determinant $(I_{m} + AB)$ determinant $(I_{n} + BA),$ where $I_{k}$ is the $k \times k$ ... $2$ $5$ $8$ $16$
recategorized
Nov 24
in
Linear Algebra
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
linearalgebra
matrix
determinant
0
votes
0
answers
31
GATE201328
In the circuit shown below, if the source voltage $VS = 100\angle 53.13^{\circ}\: V$ then the Thevenin’s equivalent voltage in Volts as seen by the load resistance $R_{L}$ is $100\angle 90^{\circ}$ $800\angle 0^{\circ}$ $800\angle 90^{\circ}$ $100\angle 60^{\circ}$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
32
GATE201329
The openloop transfer function of a dc motor is given as $\dfrac{\omega(s)}{V_{a}(s)} = \dfrac{10}{1+10s}.$ When connected in feedback as shown below, the approximate value of $K_{a}$ that will reduce the time constant of the closed loop system by one hundred times as compared to that of the openloop system is $1$ $5$ $10$ $100$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
33
GATE201330
In the circuit shown below, the knee current of the ideal Zener diode is $10\: mA.$ To maintain $5\: V$ across $R_{L},$ the minimum value of $R_{L}$ in $\Omega$ and the minimum power rating of the Zener diode in $mW,$ respectively, are $125$ and $125$ $125$ and $250$ $250$ and $125$ $250$ and $250$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
34
GATE201331
The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of $0.8.$ An ac voltage $V_{WX1} = 100V$ is applied across $WX$ to get an open circuit voltage $V_{YZ1}$ across $YZ.$ Next, an ac voltage $V_{YZ2}= 100V$ is applied across ... respectively, $125/100$ and $80/100$ $100/100$ and $80/100$ $100/100$ and $100/100$ $80/100$ and $80/100$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
35
GATE201332
Two magnetically uncoupled inductive coils have $Q$ factors $q_{1}$ and $q_{2}$ at the chosen operating frequency. Their respective resistances are $R_{1}$ and $R_{2}.$ When connected in series, their effective $Q$ factor at the same operating frequency is $q_{1} + q_{2}$ $(1/q_{1}) + (1/q_{2})$ $(q_{1}R_{1} + q_{2}R_{2})/(R_{1} + R_{2})$ $(q_{1}R_{2} + q_{2}R_{1})/(R_{1} + R_{2})$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
36
GATE201333
The impulse response of a continuous time system is given by $h(t) = \delta(t1) + \delta(t3).$ The value of the step response at $t = 2$ is $0$ $1$ $2$ $3$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
37
GATE201334
The smallsignal resistance $(i.e., dV_{B}/dI_{D})$ in $k\Omega$ offered by the $n$channel $MOSFET\: M$ shown in the figure below, at a bias point of $V_{B} = 2\: V$ is (device data for $M:$ ... $V_{TN} = 1\: V,$ and neglect body effect and channel length modulation effects) $12.5$ $25$ $50$ $100$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
38
GATE201335
The ac schematic of an $NMOS$ commonsource stage is shown in the figure below, where part of the biasing circuits has been omitted for simplicity. For the $n$channel $MOSFET\: M,$ the transconductance $g_{m} = 1\; mA/V,$ and body effect and channel length modulation effect are to be neglected. The lower cutoff frequency in $Hz$ of the circuit is approximately at $8$ $32$ $50$ $200$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
39
GATE201336
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$ Let $x(t)$ be a rectangular pulse given by $x(t) = \left\{\begin{matrix} 1&0<t<2 \\ 0&\text{otherwise} \end{matrix}\right.$ Assuming that ... $\frac{e^{2x}}{(s+2)(s+3)}$ $\frac{1e^{2x}}{s(s+2)(s+3)}$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
0
votes
0
answers
40
GATE201337
A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0,$ when the forcing function is $x(t)$ and the initial condition is $y(0).$ If one wishes to modify the system so that ... the forcing function to $j\sqrt{2}x(t)$ change the initial condition to $−2y(0)$ and the forcing function to $−2x(t)$
edited
Nov 24
in
Others
by
Lakshman Patel RJIT
(
190
points)
gate2013ec
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