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161
TIFR ECE 2021 | Question: 6
Consider a fair coin (i.e., both heads and tails have equal probability of appearing). Suppose we toss the coin repeatedly until both sides have been seen. What is the expected number of times we would have seen heads? $1$ $5 / 4$ $3 / 2$ $2$ None of the above
Consider a fair coin (i.e., both heads and tails have equal probability of appearing). Suppose we toss the coin repeatedly until both sides have been seen. What is the ex...
1 votes
0 answers
162
TIFR ECE 2021 | Question: 13
Consider a unit Euclidean ball in $4$ dimensions, and let $V_{n}$ be its volume and $S_{n}$ its surface area. Then $S_{n} / V_{n}$ is equal to: $1$ $4$ $5$ $2$ $3$
Consider a unit Euclidean ball in $4$ dimensions, and let $V_{n}$ be its volume and $S_{n}$ its surface area. Then $S_{n} / V_{n}$ is equal to:$1$$4$$5$$2$$3$
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164
TIFR ECE 2020 | Question: 2
Convolution between two functions $f(t)$ and $g(t)$ is defined as follows: $f(t) * g(t)=$ $\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$. If $f(t) * g(t)=h(t)$, what is $f(t-1) * g(t+1)?$ $h(2 t)$ $h(t)$ $h(t-1)$ $h(t+1)$ None of the above
Convolution between two functions $f(t)$ and $g(t)$ is defined as follows: $f(t) * g(t)=$ $\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$. If $f(t) * g(t)=h(t)$, what ...
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166
TIFR ECE 2020 | Question: 6
For all values of $r>0$, the area of the set of all points outside the unit square whose Euclidean distance to the unit square is less than $r$ is: $=\pi r^{2}+4 r$ $<4 \pi r^{2}$ $>4 \pi r^{3}+4 r$ $=\frac{4 \pi r^{3}}{3}+6 r+2 \pi r^{2}$ None of the above
For all values of $r>0$, the area of the set of all points outside the unit square whose Euclidean distance to the unit square is less than $r$ is:$=\pi r^{2}+4 r$$<4 \pi...
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171
TIFR ECE 2018 | Question: 6
Consider the system shown below. If $K>0$, which of the following describes the system? Stable, causal Stable, non-causal Unstable, non-causal Unstable, causal Cannot be determined from the information given
Consider the system shown below.If $K>0$, which of the following describes the system?Stable, causalStable, non-causalUnstable, non-causalUnstable, causalCannot be determ...
1 votes
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174
TIFR ECE 2017 | Question: 1
Consider a system which in response to input $x(t)$ outputs \[ y(t)=2 x(t-2)+x(2 t-1)+1 . \] Which of the following describes the system? linear, time-invariant, causal linear, time-invariant, non-causal non-linear, time-invariant, causal non-linear, time-invariant, non-causal non-linear, time-variant
Consider a system which in response to input $x(t)$ outputs\[y(t)=2 x(t-2)+x(2 t-1)+1 .\]Which of the following describes the system?linear, time-invariant, causallinear,...
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176
TIFR ECE 2017 | Question: 3
What is the maximum average power that can be dissipated by a load connected to the output terminals of the following circuit with an alternating current source? $23 \mathrm{~W}$ $11.5 \mathrm{~W}$ $8.1317 \mathrm{~W}$ $2.875 \mathrm{~W}$ None of the above
What is the maximum average power that can be dissipated by a load connected to the output terminals of the following circuit with an alternating current source?$23 \math...
1 votes
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180
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,...
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181
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
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182
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
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183
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
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187
GATE ECE 2005 | Question: 84b
Statement of Linked Answer Questions $84a$ and $84b$ Voltage standing wave pattern in a lossless transmission line with characteristic impedance $50 \mathrm{W}$ and a resistive load is shown in the figure. The reflection coefficient is given by $-0.6$ $-1$ $0.6$ $0$
Statement of Linked Answer Questions $84a$ and $84b$Voltage standing wave pattern in a lossless transmission line with characteristic impedance $50 \mathrm{W}$ and a resi...
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188
GATE ECE 2005 | Question: 85b
Statement of Linked Answer Questions $85 a$ and $85b$ A sequence $x(n)$ has non-zero values as shown in the figure The Fourier transform of $y(2 n)$ will be $e^{-j2w} [\cos 4 w+2 \cos 2 w+2]$ $[\cos 2 w+2 \cos w+2]$ $e^{-jw} [\cos 2 w+2 \cos w+2]$ $e^{-j2w} [\cos 2 w+2 \cos w+2]$
Statement of Linked Answer Questions $85 a$ and $85b$A sequence $x(n)$ has non-zero values as shown in the figureThe Fourier transform of $y(2 n)$ will be$e^{-j2w} [\cos ...
0 votes
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189
GATE ECE 1997 | Question 1.1
The current $i_4$ in the circuit of the figure is equal to $12 \mathrm{~A}$ $-12 \mathrm{~A}$ $4 \mathrm{~A}$ None of these
The current $i_4$ in the circuit of the figure is equal to$12 \mathrm{~A}$$-12 \mathrm{~A}$$4 \mathrm{~A}$None of these
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190
GATE ECE 1997 | Question: 1.2
The voltage $\mathrm{V}$ in the figure is equal to $3 \mathrm{~V}$ $-3 \mathrm{~V}$ $5 \mathrm{~V}$ None of these
The voltage $\mathrm{V}$ in the figure is equal to$3 \mathrm{~V}$$-3 \mathrm{~V}$$5 \mathrm{~V}$None of these
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191
GATE ECE 1997 | Question 1.3
The voltage $\mathrm{V}$ in the figure is always equal to $9 \mathrm{~V}$ $5 \mathrm{~V}$ $1 \mathrm{~V}$ None of the above
The voltage $\mathrm{V}$ in the figure is always equal to$9 \mathrm{~V}$$5 \mathrm{~V}$$1 \mathrm{~V}$None of the above
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192
GATE ECE 1997 | Question 1.4
The function $f(t)$ has the Fourier Transform $g(\omega)$. The Fourier Transform $f f(t) g(t)\left(=\int_{-\infty}^{\infty} g(t) e^{-j \omega t} d t\right)$ is $\frac{1}{2 \pi} f(\omega)$ $\frac{1}{2 \pi} f(-\omega)$ $2 \pi f(-\omega)$ None of the above
The function $f(t)$ has the Fourier Transform $g(\omega)$. The Fourier Transform$f f(t) g(t)\left(=\int_{-\infty}^{\infty} g(t) e^{-j \omega t} d t\right)$ is$\frac{1}{2 ...
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193
GATE ECE 1997 | Question 1.5
The Laplace Transform of $e \alpha t \cos (\alpha \; t)$ is equal to $\frac{(s-\alpha)}{(s-\alpha)^2+\alpha^2}$ $\frac{(s+\alpha)}{(s-\alpha)^2+\alpha^2}$ $\frac{1}{(s-\alpha)^2}$ None of the above
The Laplace Transform of $e \alpha t \cos (\alpha \; t)$ is equal to$\frac{(s-\alpha)}{(s-\alpha)^2+\alpha^2}$$\frac{(s+\alpha)}{(s-\alpha)^2+\alpha^2}$$\frac{1}{(s-\alph...
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194
GATE ECE 1997 | Question 1.6
A transmission line of $50 \; \Omega$ characteristic impedance is terminated with a $100 \; \Omega$ resistance. The minimum impedance measured on the line is equal to $0 \; \Omega$ $25 \; \Omega$ $50 \; \Omega$ $100 \; \Omega$
A transmission line of $50 \; \Omega$ characteristic impedance is terminated with a $100 \; \Omega$ resistance. The minimum impedance measured on the line is equal to$0 ...
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195
GATE ECE 1997 | Question 1.7
A rectangular air-filled waveguide has cross section of $4 \mathrm{~cm} \times 10 \mathrm{~cm}$. The minimum frequency which can propagate in the waveguide is $1.5\; \mathrm{GHz}$ $2.0\; \mathrm{GHz}$ $2.5\; \mathrm{GHz}$ $3.0\; \mathrm{GHz}$
A rectangular air-filled waveguide has cross section of $4 \mathrm{~cm} \times 10 \mathrm{~cm}$. The minimum frequency which can propagate in the waveguide is$1.5\; \math...
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196
GATE ECE 1997 | Question 1.8
The line code that has zero $\text{dc}$ component for pulse transmission of random binary data is Non-return to zero $\text{(NRZ)}$ Retrun to zero $\text{(RZ)}$ Alternate Mark Inversion $\text{(AM)}$ None of the above
The line code that has zero $\text{dc}$ component for pulse transmission of random binary data isNon-return to zero $\text{(NRZ)}$Retrun to zero $\text{(RZ)}$Alternate Ma...
0 votes
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197
GATE ECE 1997 | Question 1.9
A probability density fucntion is given by $p(x)=\mathrm{K} e^{-x^2 / 2}-\infty<x<\infty$. The value of $K$ should be $\frac{1}{\sqrt{2 \pi}}$ $\sqrt{\frac{2}{\pi}}$ $\frac{1}{2 \sqrt{\pi}}$ $\frac{1}{\pi \sqrt{2}}$
A probability density fucntion is given by $p(x)=\mathrm{K} e^{-x^2 / 2}-\infty<x<\infty$. The value of $K$ should be$\frac{1}{\sqrt{2 \pi}}$$\sqrt{\frac{2}{\pi}}$$\frac{...
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198
GATE ECE 1997 | Question 1.10
A deterministic signal has the power spectrum given in the figure is, The minimum sampling rate needed to completely represent this signal is $1 \; \mathrm{kHz}$ $2 \; \mathrm{kHz}$ $3 \; \mathrm{kHz}$ None of the above
A deterministic signal has the power spectrum given in the figure is, The minimum sampling rate needed to completely represent this signal is$1 \; \mathrm{kHz}$$2 \; \mat...
0 votes
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199
GATE ECE 1997 | Question 1.11
The voltage $V$ in the figure is $10 \mathrm{~V}$ $15 \mathrm{~V}$ $5 \mathrm{~V}$ None of the above
The voltage $V$ in the figure is$10 \mathrm{~V}$$15 \mathrm{~V}$$5 \mathrm{~V}$None of the above
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