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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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TIFR ECE 2010 | Question: 6
If we convolve $\sin (t) / t$ with itself, then we get $C \sin (t) / t$ for some constant $C$ $C \cos (t) / t$ for some constant $C$ $C \cos (t) / t^{2}$ for some constant $C$ $C_{1} \sin (t) / t^{2}+C_{2} \cos (t) / t^{2}$ for some constants $C_{1}, C_{2}$ None of the above
If we convolve $\sin (t) / t$ with itself, then we get$C \sin (t) / t$ for some constant $C$$C \cos (t) / t$ for some constant $C$$C \cos (t) / t^{2}$ for some constant $...
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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...
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TIFR ECE 2017 | Question: 4
A Schmitt trigger circuit is a comparator circuit with a hysteresis. Consider the Schmitt trigger circuit in the figure implemented using an opamp. What are the trigger levels for this circuit? $\pm \frac{R_{1}}{R_{2}} V_{s}$ $\pm \frac{R_{2}}{R_{1}} V_{s}$ $\pm \frac{R_{1}}{R_{1}+R_{2}} V_{s}$ $\pm \frac{R_{2}}{R_{1}+R_{2}} V_{s}$ None of the above
A Schmitt trigger circuit is a comparator circuit with a hysteresis. Consider the Schmitt trigger circuit in the figure implemented using an opamp. What are the trigger l...
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TIFR ECE 2010 | Question: 9
The $z$-transform of a sequence $\left\{x_{n}\right\}_{n=-\infty}^{\infty}$ is defined to be $X(z)=\sum_{n=-\infty}^{\infty} x_{n} z^{-n}$. The $z$-transform of the sequence $y_{n}=x_{2 n+1}$ is $Y(z)=z(X(z)-X(-z)) / 2$ ... $Y(z)=z(X(\sqrt{z})-X(-\sqrt{z})) / 2$ $Y(z)=(X(\sqrt{z})-X(-\sqrt{z})) / 2$
The $z$-transform of a sequence $\left\{x_{n}\right\}_{n=-\infty}^{\infty}$ is defined to be $X(z)=\sum_{n=-\infty}^{\infty} x_{n} z^{-n}$. The $z$-transform of the seque...
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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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TIFR ECE 2018 | Question: 1
Consider a discrete-time system which in response to input sequence $x[n] \;( n$ integer) outputs the sequence $y[n]$ such that \[y[n]=\left\{\begin{array}{ll} 0, & n=-1,-2,-3, \ldots, \\ \frac{1}{2 ... describes the system? Linear, time-invariant Linear, time-variant Non-linear, time-invariant Non-linear, time-variant Cannot be determined from the information given
Consider a discrete-time system which in response to input sequence $x[n] \;( n$ integer) outputs the sequence $y[n]$ such that\[y[n]=\left\{\begin{array}{ll}0, & n=-1,-2...
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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) \\...
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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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TIFR ECE 2010 | Question: 12
Consider a system with input $x(t)$ and the output $y(t)$ is given by \[ y(t)=x(t)-\sin (t) x(t-1)-0.5 x(t+2)+1 . \] The system is Non-linear Non-causal Time varying All of the above None of the above
Consider a system with input $x(t)$ and the output $y(t)$ is given by\[y(t)=x(t)-\sin (t) x(t-1)-0.5 x(t+2)+1 .\]The system isNon-linearNon-causalTime varyingAll of the a...
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TIFR ECE 2018 | Question: 13
Consider five distinct binary vectors $X_{1}, \ldots, X_{5}$ each of length $10$. Let \[d_{i j}=\sum_{k=1}^{10}\left(X_{i k} \text { XOR } X_{j k}\right),\] (i.e., $d_{i j}$ is the number of coordinates where $X_{i}$ ... to $X_{5}$, and argue about the result noting that there are five binary vectors.] $d=10$ $d=9$ $d=8$ $d<8$ Information is not sufficient
Consider five distinct binary vectors $X_{1}, \ldots, X_{5}$ each of length $10$. Let\[d_{i j}=\sum_{k=1}^{10}\left(X_{i k} \text { XOR } X_{j k}\right),\](i.e., $d_{i j}...
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TIFR ECE 2017 | Question: 15
Suppose that $f(x)$ is a real valued continuous function such that $f(x) \rightarrow \infty$ as $x \rightarrow \infty$. Further, let \[a_{n}=\sum_{j=1}^{n} 1 / j\] and \[b_{n}=\sum_{j=1}^{n} 1 / j^{2} .\] Which of the following statements is true ... any number $M$ so that $f\left(b_{n}\right)$ and $f\left(a_{n}\right)$ are greater than $M$ for all $n$ None of the above
Suppose that $f(x)$ is a real valued continuous function such that $f(x) \rightarrow \infty$ as $x \rightarrow \infty$. Further, let\[a_{n}=\sum_{j=1}^{n} 1 / j\]and\[b_{...
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TIFR ECE 2017 | Question: 2
Suppose a $1 \mu \mathrm{H}$ inductor and a $1 \Omega$ resistor are connected in series to a $1 \mathrm{ V}$ battery. What happens to the current in the circuit? The current starts at $0 \mathrm{ A}$, and gradually rises to $1 \mathrm{ A}$ The current ... $1 \mathrm{ A}$ The current oscillates over time between $1 \mathrm{ A}$ and $-1 \mathrm{ A}$
Suppose a $1 \mu \mathrm{H}$ inductor and a $1 \Omega$ resistor are connected in series to a $1 \mathrm{ V}$ battery. What happens to the current in the circuit?The curre...
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TIFR ECE 2019 | Question: 1
Consider a discrete-time system which in response to input sequence $x[n]$ ( $n$ integer) outputs the sequence $y[n]$ such that \[y[n]=\left\{\begin{array}{ll} 0, & n=-1,-2,-3, \ldots, \\ \alpha y[2 n-1]+\beta ... -linear, but time-invariant only if $\alpha=0$ (parameters $\beta$ and $\gamma$ can take arbitrary values) Cannot be determined from the information given
Consider a discrete-time system which in response to input sequence $x[n]$ ( $n$ integer) outputs the sequence $y[n]$ such that\[y[n]=\left\{\begin{array}{ll}0, & n=-1,-2...
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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}+...
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TIFR ECE 2018 | Question: 14
Define the $\ell_{p}$ ball in two dimensions as the set of points $(x, y)$ such that $|x|^{p}+|y|^{p} \leq 1$. Which of the following is $\text{FALSE:}$ The $\ell_{2}$ ball is contained in the $\ell_{3}$ ball The $\ell_{2}$ ball is contained in ... $\ell_{2}$ ball is contained in the $\ell_{5}$ ball The $\ell_{1}$ ball is contained in the $\ell_{3}$ ball
Define the $\ell_{p}$ ball in two dimensions as the set of points $(x, y)$ such that $|x|^{p}+|y|^{p} \leq 1$. Which of the following is $\text{FALSE:}$The $\ell_{2}$ bal...
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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...
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TIFR ECE 2020 | Question: 5
Let $f(t)$ be a periodic signal of period $1$, i.e. $f(t+1)=f(t) \forall t$. Define the averaging operator depending on a fixed parameter $h>0$ as below: \[g(x)=\frac{1}{2 h} \int_{x-h}^{x+h} f(t) d t .\] Which of the following is ... $\frac{1}{2}$ $g(x)$ is periodic with period $1$ The value of $h$ determines whether or not $g(x)$ is periodic None of the above
Let $f(t)$ be a periodic signal of period $1$, i.e. $f(t+1)=f(t) \forall t$. Define the averaging operator depending on a fixed parameter $h>0$ as below:\[g(x)=\frac{1}{2...
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TIFR ECE 2019 | Question: 8
Let $K$ be a cube of side $1$ in $\mathbb{R}^{3}$, with its centre at the origin, and its sides parallel to the co-ordinate axes. For $t \geq 0$, let $K_{t}$ be the set of all points in $\mathbb{R}^{3}$ whose Euclidean distance to $K$ is less than or equal to $t$ ... $V \leq \frac{4}{3} \pi\left(\frac{\sqrt{3}}{2}+t\right)^{3}$ $V \geq(1+2 t)^{3}$
Let $K$ be a cube of side $1$ in $\mathbb{R}^{3}$, with its centre at the origin, and its sides parallel to the co-ordinate axes. For $t \geq 0$, let $K_{t}$ be the set o...
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TIFR ECE 2017 | Question: 8
Consider the two positive integer sequences, defined for a fixed positive integer $c \geq 2$ \[f(n)=\frac{1}{n}\left\lfloor\frac{n}{c}\right\rfloor, \quad g(n)=n\left\lfloor\frac{c}{n}\right\rfloor\] where $\lfloor t\rfloor$ denotes the ... $0$ The first sequence converges to $1 / c$, while the second sequence converges to $c$
Consider the two positive integer sequences, defined for a fixed positive integer $c \geq 2$\[f(n)=\frac{1}{n}\left\lfloor\frac{n}{c}\right\rfloor, \quad g(n)=n\left\lflo...
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TIFR ECE 2019 | Question: 13
For $t>0$, let $S_{t}$ denote the ball of radius $t$ centered at the origin in $\mathbb{R}^{n}$. That is, \[S_{t}=\left\{\mathbf{x} \in \mathbb{R}^{n} \mid \sum_{i=1}^{n} x_{i}^{2} \leq t^{2}\right\} .\] Let $N_{t}$ be the number of ... $\lim _{t \rightarrow \infty} \frac{N_{t}}{V_{t}}=1$ $N_{t}$ is a monotonically decreasing function of $t$
For $t>0$, let $S_{t}$ denote the ball of radius $t$ centered at the origin in $\mathbb{R}^{n}$. That is,\[S_{t}=\left\{\mathbf{x} \in \mathbb{R}^{n} \mid \sum_{i=1}^{n} ...
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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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GATE ECE 2005 | Question: 83b
Statement for Linked Answer Questions 83a and 83b Asymmetric three-level midtread quantizer is to be designed assuming equiprobable occurence of all quantization levels. The quantization noise power for the quantization region between $-a$ and $+a$ in the figure is $\frac{4}{81}$ $\frac{1}{9}$ $\frac{5}{81}$ $\frac{2}{81}$
Statement for Linked Answer Questions 83a and 83bAsymmetric three-level midtread quantizer is to be designed assuming equiprobable occurence of all quantization levels.Th...
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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 ...
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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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GATE ECE 2005 | Question: 81b
Statement for Linked Answer Questions $81 a$ and $81 b$: Consider an $8085$ microprocessor system If in addition following code exists from $019 \mathrm{H}$ onwards, $\text{ORI 40 H}$ $\text{ADD M}$ What will be the result in the accumulator after the last instruction is executed? $40 \; \mathrm{H}$ $20 \; \mathrm{H}$ $60 \; \mathrm{H}$ $42 \; \mathrm{H}$
Statement for Linked Answer Questions $81 a$ and $81 b$:Consider an $8085$ microprocessor systemIf in addition following code exists from $019 \mathrm{H}$ onwards,$\text{...
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GATE ECE 2005 | Question: 82b
Statement for Linked Answer Questions $82a$ and $82b:$ The dopen loop transfer function of a unity feedback system is given by \[\mathrm{G}(s)=\frac{3 e^{-2}}{s(s+2)}\] Based on the above results, the gain and phase margins of the system will be $-7.09$ ... $87.5^{\circ}$ $7.09 \mathrm{~dB}$ and $-87.5^{\circ}$ $-7.09 \mathrm{~dB}$ and $-87.5^{\circ}$
Statement for Linked Answer Questions $82a$ and $82b:$The dopen loop transfer function of a unity feedback system is given by\[\mathrm{G}(s)=\frac{3 e^{-2}}{s(s+2)}\]Base...
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GATE ECE 1997 | Question 4.2
The decoding circuit shown in the figure is has been used to generate the active low chip select signal for a microprocessor peripheral. (The address lines are designated as $\mathrm{AO}$ to $\mathrm{A} 7$ for $\mathrm{l} / \mathrm{O}$ ... $30 \; \mathrm{H}$ to $33 \; \mathrm{H}$ $70 \; \mathrm{H}$ to $73 \; \mathrm{H}$
The decoding circuit shown in the figure is has been used to generate the active low chip select signal for a microprocessor peripheral. (The address lines are designated...
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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}$$2 \; \mat...
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GATE ECE 2000 | Question 2.12
One period $(0, T)$ each of two periodic waveforms $W_{1}$ and $W_{2}$ are shown in figure. The magnitudes of the $n$th Fourier series coefficients of $W_{1}$ and $W_{2}$. for $n \geq 1, n$ odd, are respectively proportional to $n^{-3} \mid$ and $n^{-2} \mid$ $n^{-2} \mid$ and $n^{-3} \mid$ $n^{-1}$ and $n^{-2} \mid$ $n^{-4} \mid$ and $n^{-2} \mid$
One period $(0, T)$ each of two periodic waveforms $W_{1}$ and $W_{2}$ are shown in figure. The magnitudes of the $n$th Fourier series coefficients of $W_{1}$ and $W_{2}$...
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GATE ECE 1997 | Question 3.11
The skin depth at $10\; \mathrm{MHz}$ for a conductor is $1 \; \mathrm{cm}$. The phase velocity of an electromagnetic wave in the conductor at $1,000 \; \mathrm{MHz}$ is about $6 \times 10^{6} \mathrm{~m} / \mathrm{sec}$ $6 \times 10^{7} \mathrm{~m} / \mathrm{sec}$ $3 \times 10^{8} \mathrm{~m} / \mathrm{sec}$ $6 \times 10^{8} \mathrm{~m} / \mathrm{sec}$
The skin depth at $10\; \mathrm{MHz}$ for a conductor is $1 \; \mathrm{cm}$. The phase velocity of an electromagnetic wave in the conductor at $1,000 \; \mathrm{MHz}$ is ...
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GATE ECE 1997 | Question 1.1
The current $i_4$ in the circuit of the figure is equal to $12 \mathrm{~A}$ $-12 \mathrm{~A}$ $4 \mathrm{~A}$ None of these
The current $i_4$ in the circuit of the figure is equal to$12 \mathrm{~A}$$-12 \mathrm{~A}$$4 \mathrm{~A}$None of these
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GATE ECE 1997 | Question 3.1
In the circuit of the figure is the energy absorbed by the $4 \; \Omega$ resistor in the time interval $(0, \infty)$ is $36$ Joules $16$ Joules $256$ Joules None of the above
In the circuit of the figure is the energy absorbed by the $4 \; \Omega$ resistor in the time interval $(0, \infty)$ is$36$ Joules$16$ Joules$256$ JoulesNone of the above...
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GATE ECE 1997 | Question 3.6
A communication channel has first-order low pass transfer function. The channel is used to transmit pulses at a symbol rate greater than the half-power frequency of the low pass function. Which of the network shown in the figure is can be used to equalise the received pulses?
A communication channel has first-order low pass transfer function. The channel is used to transmit pulses at a symbol rate greater than the half-power frequency of the l...
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GATE ECE 1997 | Question 2.4
In a common emitter $\text{BJT}$ amplifier, the maximum usable supply voltage is limited by Avalanche breakdown of Base-Emitter junction Collector-Base breakdown voltage with emitter open $\left(\mathrm{BV}_{\mathrm{CBO}}\right)$ Collector-Emitter breakdown ... with base open $\left(\mathrm{BV}_{\mathrm{CBO}}\right)$ Zener breakdown voltage of the Emitter-Base junction
In a common emitter $\text{BJT}$ amplifier, the maximum usable supply voltage is limited byAvalanche breakdown of Base-Emitter junctionCollector-Base breakdown voltage wi...
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GATE ECE 1997 | Question 1.11
The voltage $V$ in the figure is $10 \mathrm{~V}$ $15 \mathrm{~V}$ $5 \mathrm{~V}$ None of the above
The voltage $V$ in the figure is$10 \mathrm{~V}$$15 \mathrm{~V}$$5 \mathrm{~V}$None of the above
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GATE ECE 2000 | Question 2.14
In given figure, the steady state output voltage corresponding to the input voltage $3+4 \sin 100 t \mathrm{~V}$ is $3+\frac{4}{\sqrt{2}} \sin \left(100 t-\frac{\pi}{4}\right) \mathrm{V}$ $3+4 \sqrt{2} \sin \left(100 t-\frac{\pi}{4}\right) \mathrm{V}$ ... $3+4 \sin \left(100 t \div \frac{\pi}{4}\right) \mathrm{V}$
In given figure, the steady state output voltage corresponding to the input voltage $3+4 \sin 100 t \mathrm{~V}$ is$3+\frac{4}{\sqrt{2}} \sin \left(100 t-\frac{\pi}{4}\ri...
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198
GATE ECE 1997 | Question 4.4
A signed integer has been stored in a byte using the $2$'s complement format. We wish to store the same integer in a $16$ bit word. We should copy the original byte to the less significant byte of the word and fill the more ... significant bit of the original byte copy the original byte to the less significant byte as well as the more significant byte of the word
A signed integer has been stored in a byte using the $2$'s complement format. We wish to store the same integer in a $16$ bit word. We shouldcopy the original byte to the...
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199
GATE ECE 1997 | Question 2.1
In the $\text{BJT}$ amplifier shown in the figure is the transistor is based in the forward active region. Putting a capacitor across $R_E$ will decrease the voltage gain and decrease the input impedance increase the voltage gain ... the input impedance decrease the voltage gain and increase the input impedance increase the voltage gain and increase the input impedance
In the $\text{BJT}$ amplifier shown in the figure is the transistor is based in the forward active region. Putting a capacitor across $R_E$ will decrease the voltage gain...
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200
GATE ECE 1997 | Question 3.7
The power spectral density of a deterministic signal is given by $\left[\sin (f) / f^{2}\right]$ where $f$ is frequency. The autocorrelation function of this signal in the time domain is a rectangular pulse a delta function a sine pulse a triangular pulse
The power spectral density of a deterministic signal is given by $\left[\sin (f) / f^{2}\right]$ where $f$ is frequency. The autocorrelation function of this signal in th...
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