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246
TIFR ECE 2016 | Question: 1
Suppose $f(x)=c x^{-\alpha}$ for some $c>0$ and $\alpha>0$ such that $\int_{1}^{\infty} f(x) \mathrm{d} x=1$. Then, which of the following is possible? $\int_{1}^{\infty} x f(x) \mathrm{d} x=\infty$ ... $\int_{1}^{\infty} \frac{f(x)}{1+\ln x} \mathrm{~d} x=\infty$ None of the above
Suppose $f(x)=c x^{-\alpha}$ for some $c>0$ and $\alpha>0$ such that $\int_{1}^{\infty} f(x) \mathrm{d} x=1$. Then, which of the following is possible?$\int_{1}^{\infty} ...
1 votes
0 answers
249
TIFR ECE 2016 | Question: 4
Consider a system which in response to input $x(t)$ outputs \[y(t)=x\left(t^{2}\right) .\] Which of the following describes the system? linear, time-invariant, causal linear, time-invariant, non-causal linear, time-variant non-linear, time-invariant non-linear, time-variant
Consider a system which in response to input $x(t)$ outputs\[y(t)=x\left(t^{2}\right) .\]Which of the following describes the system?linear, time-invariant, causallinear,...
1 votes
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250
TIFR ECE 2016 | Question: 5
Consider the opamp circuit in the figure. Approximately what is $V_{0}$? $-\left(\frac{V_{1}}{2}+V_{2}\right)$ $-\left(\frac{V_{1}}{4}+\frac{V_{2}}{2}\right)$ $-\left(V_{1}+2 V_{2}\right)$ $-\left(4 V_{1}+2 V_{2}\right)$ None of the above
Consider the opamp circuit in the figure. Approximately what is $V_{0}$?$-\left(\frac{V_{1}}{2}+V_{2}\right)$$-\left(\frac{V_{1}}{4}+\frac{V_{2}}{2}\right)$$-\left(V_{1}+...
1 votes
0 answers
251
TIFR ECE 2016 | Question: 6
What is the Laplace transform $F(s)$ of the signal $f(t), t \geq 0$ defined below? In $t \in[0,1),$ ... $\frac{1}{s\left(1-e^{-s / 2}\right)}$ $\frac{1}{s\left(1+e^{-s / 2}\right)}$
What is the Laplace transform $F(s)$ of the signal $f(t), t \geq 0$ defined below? In $t \in[0,1),$\[f(t)=\left\{\begin{array}{ll}1, & t \in\left[0, \frac{1}{2}\right) \\...
1 votes
0 answers
252
TIFR ECE 2016 | Question: 7
Suppose $X$ and $Y$ are independent Gaussian random variables, whose pdfs are represented below. Which of the following describes the pdf of the $X+Y?$
Suppose $X$ and $Y$ are independent Gaussian random variables, whose pdfs are represented below. Which of the following describes the pdf of the $X+Y?$
1 votes
0 answers
253
TIFR ECE 2016 | Question: 8
In terms of their frequency responses, which of the following is the odd one out? All four circuits are equivalent
In terms of their frequency responses, which of the following is the odd one out? All four circuits are equivalent
1 votes
0 answers
260
TIFR ECE 2016 | Question: 15
What is \[ \max _{x, y}\left[\begin{array}{ll} x & y \end{array}\right]\left[\begin{array}{cc} 3 & \sqrt{2} \\ \sqrt{2} & 2 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right] \] subject to \[ x^{2}+y^{2}=1 ? \] $1$ $\sqrt{2}$ $2$ $3$ $4$
What is\[\max _{x, y}\left[\begin{array}{ll}x & y\end{array}\right]\left[\begin{array}{cc}3 & \sqrt{2} \\\sqrt{2} & 2\end{array}\right]\left[\begin{array}{l}x \\y\end{arr...
1 votes
0 answers
261
GATE ECE 1999 | Question 2.12
The ripple counter shown in the given figure is works as a $\bmod -3$ up counter $\bmod -5$ up counter $\bmod - 3$ down counter $\bmod - 5$ down counter
The ripple counter shown in the given figure is works as a$\bmod -3$ up counter$\bmod -5$ up counter$\bmod - 3$ down counter$\bmod - 5$ down counter
1 votes
0 answers
262
GATE ECE 2005 | Question: 3
A fair dice is rolled twice. The probability that an odd number will follow an even number is $\frac{1}{2}$ $\frac{1}{6}$ $\frac{1}{3}$ $\frac{1}{4}$
A fair dice is rolled twice. The probability that an odd number will follow an even number is$\frac{1}{2}$$\frac{1}{6}$$\frac{1}{3}$$\frac{1}{4}$
1 votes
0 answers
263
GATE ECE 1995 | Question 1.31
When a $\text{CPU}$ is interrupted, it stops execution of instructions acknowledges interrupt and branches of subroutine acknowledges interrupt and continues acknowledges interrupt and waits for the next instruction from the interrupting device
When a $\text{CPU}$ is interrupted, itstops execution of instructionsacknowledges interrupt and branches of subroutineacknowledges interrupt and continuesacknowledges int...
1 votes
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264
GATE ECE 2006 | Question: 1
The rank of the matrix $\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{array}\right]$ is $0$ $1$ $2$ $3$
The rank of the matrix $\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{array}\right]$ is$0$$1$$2$$3$
1 votes
0 answers
265
GATE ECE 2006 | Question: 2
$\nabla \times \nabla \times \mathrm{P},$ where $\mathrm{P}$ is a vector, is equal to $\mathrm{P} \times \nabla \times \mathrm{P}-\nabla^{2} \mathrm{P}$ $\nabla^{2} \text{P} +\nabla(\nabla \bullet \text{P})$ $\nabla^{2} \mathrm{P}+\nabla \times \mathrm{P}$ $\nabla(\nabla \bullet \mathrm{P})-\nabla^{2} \mathrm{P}$
$\nabla \times \nabla \times \mathrm{P},$ where $\mathrm{P}$ is a vector, is equal to$\mathrm{P} \times \nabla \times \mathrm{P}-\nabla^{2} \mathrm{P}$$\nabla^{2} \text{P...
1 votes
0 answers
267
GATE ECE 2006 | Question: 4
A probability density function is of the form $\qquad p(x)=\mathrm{Ke}^{-\alpha|x|}, x \in(-\infty, \infty)$ The value of $\text{K}$ is $0.5$ $1$ $0.5 \alpha$ $\alpha$
A probability density function is of the form$\qquad p(x)=\mathrm{Ke}^{-\alpha|x|}, x \in(-\infty, \infty)$The value of $\text{K}$ is$0.5$$1$$0.5 \alpha$$\alpha$
1 votes
0 answers
268
GATE ECE 2006 | Question: 5
A solution for the differential equation $ \qquad \dot{x}(t)+2 x(t)=\delta(t)$ with initial condition $x(0-)=0$ is $e^{-2 t} \; u(t)$ $e^{2 t} \; u(t)$ $e^{-t} \; u(t)$ $e^{t} \; u(t)$
A solution for the differential equation$ \qquad \dot{x}(t)+2 x(t)=\delta(t)$with initial condition $x(0-)=0$ is$e^{-2 t} \; u(t)$$e^{2 t} \; u(t)$$e^{-t} \; u(t)$$e^{t} ...
1 votes
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269
GATE ECE 2006 | Question: 6
A low-pass filter having a frequency response $\mathrm{H}(\mathrm{j} \omega)=\mathrm{A}(\omega) \;e^{j{\phi(\omega)}}$ does not produce any phase distortion, if $\mathrm{A}(\omega)=\mathrm{C}\omega^{2}, \phi(\omega)=k \omega^{3}$ ... $\mathrm{A}(\omega)=\mathrm{C}, \phi(\omega)=k \omega^{-1}$
A low-pass filter having a frequency response $\mathrm{H}(\mathrm{j} \omega)=\mathrm{A}(\omega) \;e^{j{\phi(\omega)}}$ does not produce any phase distortion, if$\mathrm{A...
1 votes
0 answers
270
GATE ECE 2006 | Question: 7
The values of voltage $\left(\mathrm{V}_{\mathrm{D}}\right)$ across a tunnel-diode corresponding to peak and valley currents are $\text{V}_{\text{P}}$ and $\text{V}_{\text{V}}$ respectively. The range of tunnel-diode voltage $\text{V}_{\text{D}}$ for which the ... $\mathrm{V}_{\mathrm{D}} \geq \mathrm{V}_{\mathrm{V}}$
The values of voltage $\left(\mathrm{V}_{\mathrm{D}}\right)$ across a tunnel-diode corresponding to peak and valley currents are $\text{V}_{\text{P}}$ and $\text{V}_{\tex...
1 votes
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271
GATE ECE 2006 | Question: 8
The concentration of minority carriers in an extrinsic semiconductor under equilibrium is directly proportional to the doping concentration inversely proportional to the doping concentration directly proportional to the intrinsic concentration inversely proportional to the intrinsic concentration
The concentration of minority carriers in an extrinsic semiconductor under equilibrium isdirectly proportional to the doping concentrationinversely proportional to the do...
1 votes
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272
GATE ECE 2006 | Question: 9
Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the diffusion current drift current recombination current induced current
Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially thediffusion currentdrift currentrecombination c...
1 votes
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274
GATE ECE 2006 | Question: 11
The input impedance $\left(\text{Z}_i\right)$ and the output impedance $\left(\text{Z}_o\right)$ of an ideal transconductance (voltage controlled current source) amplifier are $\text{Z}_i=0, \text{Z}_o=0$ $\text{Z}_i=0, \text{Z}_o=\infty$ $\text{Z}_i=\infty, \text{Z}_o=0$ $\text{Z}_i=\infty, \text{Z}_o=\infty$
The input impedance $\left(\text{Z}_i\right)$ and the output impedance $\left(\text{Z}_o\right)$ of an ideal transconductance (voltage controlled current source) amplifie...
1 votes
0 answers
276
GATE ECE 2006 | Question: 13
The number of product terms in the minimized sum-of-product expression obtained through the following $\text{K}$-map is (where, " $d$ ... $2$ $3$ $4$ $5$
The number of product terms in the minimized sum-of-product expression obtained through the following $\text{K}$-map is (where, " $d$ " denotes don't care states)$$\begin...
1 votes
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277
GATE ECE 2006 | Question: 14
Let $x(t) \longleftrightarrow \mathrm{X}(j \omega)$ be Fourier Transform pair. The Fourier Transform of the signal $x(5 t-3)$ in terms of $X(j \omega)$ is given as $\frac{1}{5} e^ - \frac{j 3\omega }{5} \times\left(\frac{j \omega}{5}\right)$ ... $\frac{1}{5} e^{j 3 \omega} \times\left(\frac{j \omega}{5}\right)$
Let $x(t) \longleftrightarrow \mathrm{X}(j \omega)$ be Fourier Transform pair. The Fourier Transform of the signal $x(5 t-3)$ in terms of $X(j \omega)$ is given as$\frac{...
1 votes
0 answers
278
GATE ECE 2006 | Question: 15
The Dirac delta function $\delta(t)$ is defined as $\delta(t)= \begin{cases}1, & t=0 \\ 0, & \text { otherwise }\end{cases}$ $\delta(t)= \begin{cases}\infty, & t=0 \\ 0, & \text { otherwise }\end{cases}$ ... $\displaystyle{}\int_{-\infty}^\infty \delta(t) d t=1$
The Dirac delta function $\delta(t)$ is defined as$\delta(t)= \begin{cases}1, & t=0 \\ 0, & \text { otherwise }\end{cases}$$\delta(t)= \begin{cases}\infty, & t=0 \\ 0, & ...
1 votes
0 answers
279
GATE ECE 2006 | Question: 16
If the region of convergence of $x_1[n]+x_2[n]$ is $\frac{1}{3}<|z|<\frac{2}{3}$, then the region of convergence of $x_1[n]-x_2[n]$ includes $\frac{1}{3}<|z|<3$ $\frac{2}{3}<|z|<3$ $\frac{2}{3}<|z|<3$ $\frac{1}{3}<|z|<\frac{2}{3}$
If the region of convergence of $x_1[n]+x_2[n]$ is $\frac{1}{3}<|z|<\frac{2}{3}$, then the region of convergence of $x_1[n]-x_2[n]$ includes $\frac{1}{3}<|z|<3$$\frac{2}{...
1 votes
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280
GATE ECE 2006 | Question: 17
The open-loop transfer function of a unity-gain feedback control system is given by $ \text{G}(s)=\frac{\text{K}}{(s+1)(s+2)} $ The gain margin of the system in $\text{dB}$ is given by $0$ $1$ $20$ $\infty $
The open-loop transfer function of a unity-gain feedback control system is given by $$ \text{G}(s)=\frac{\text{K}}{(s+1)(s+2)} $$ The gain margin of the system in $\text{...
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