GO Electronics
Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
New Blog
Blogs
Exams
Dark Mode
Recent activity
0
votes
0
answers
1
TIFR ECE 2023 | Question: 15
Let $\left\{x_{n}\right\}_{n \geq 0}$ be a sequence of real numbers which satisfy \[ x_{n+1}\left(1+x_{n+1}\right) \leq x_{n}\left(1+x_{n}\right), \quad n \geq 0 . \] Choose the correct option from the ... is always bounded but does not necessarily converge. The sequence always converges to a non-zero limit. The sequence always converges to zero. None of the above.
makhdoom ghaya
edited
in
Others
Mar 20
by
makhdoom ghaya
160
points
7
views
tifrece2023
0
votes
0
answers
2
TIFR ECE 2023 | Question: 14
Suppose that $Z \sim \mathcal{N}(0,1)$ is a Gaussian random variable with mean zero and variance $1$. Let $F(z) \equiv \mathbb{P}(Z \leq z)$ be the cumulative distribution function $\operatorname{(CDF)}$ of $Z$. Define a new random variable $Y$ as $Y=F(Z)$. This means that the ... of $\mathbb{E}[Y]$ is: $F(1)$ $1$ $\frac{1}{2}$ $\frac{1}{\sqrt{2 \pi}}$ $\frac{\pi}{4}$
makhdoom ghaya
edited
in
Others
Mar 20
by
makhdoom ghaya
160
points
6
views
tifrece2023
0
votes
0
answers
3
TIFR ECE 2023 | Question: 13
Let $X$ be a random variable which takes values $1$ and $-1$ with probability $1 / 2$ each. Suppose $Y=X+N$, where $N$ is a random variable independent of $X$ with the following probability density function (p.d.f.): \[ f_{N}(n)=\left\{\begin{array} ... $0$ $1 / 8$ $1 / 4$ $1 / 2$ None of the above
makhdoom ghaya
edited
in
Others
Mar 20
by
makhdoom ghaya
160
points
6
views
tifrece2023
0
votes
0
answers
4
TIFR ECE 2023 | Question: 12
Consider a disk $D$ of radius 1 centered at the origin. Let $X$ be a point uniformly distributed on $D$ and let the distance of $X$ from the origin be $R$. Let $A$ be the (random) area of the disk with radius $R$ centered at the origin. Then $\mathbb{E}[A]$ is $\frac{\pi}{3}$ $\frac{\pi}{6}$ $\frac{\pi}{4}$ $\frac{\pi}{2}$ None of the above
makhdoom ghaya
edited
in
Others
Mar 20
by
makhdoom ghaya
160
points
6
views
tifrece2023
0
votes
0
answers
5
TIFR ECE 2023 | Question: 11
Consider the function \[ f(x)=x e^{|x|}+4 x^{2} \] for values of $x$ which lie in the interval $[-1,1]$. In this domain, suppose the function attains the minimum value at $x^{*}$. Which of the following is true? $-1 \leq x^{*}<-0.5$ $-0.5 \leq x^{*}<0$ $x^{*}=0$ $0<x^* \leq 0.5$ $0.5<x^* \leq 1$
makhdoom ghaya
edited
in
Others
Mar 20
by
makhdoom ghaya
160
points
7
views
tifrece2023
0
votes
0
answers
6
TIFR ECE 2023 | Question: 10
Convolution between two functions $f(t)$ and $g(t)$ is defined as follows: \[ f(t) * g(t)=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau \] Let $u(t)$ be the unit-step function, i.e., $u(t)=1$ for $t \geq 0$ and $u(t)=0$ for $t<0$. What is $f(t) * g(t)$ ... $\frac{1}{2}(\exp (-t)+\sin (t)-2 \cos (t)) u(t)$ $\frac{1}{2}(\exp (-t)-\sin (t)+2 \cos (t)) u(t)$
makhdoom ghaya
edited
in
Others
Mar 20
by
makhdoom ghaya
160
points
4
views
tifrece2023
0
votes
0
answers
7
TIFR ECE 2023 | Question: 9
Consider an $n \times n$ matrix $A$ with the property that each element of $A$ is non-negative and the sum of elements of each row is $1$ . Consider the following statements. 1. $1$ is an eigenvalue of $A$ 2. The magnitude of any eigenvalue of $A$ ... statements $1$ and $3$ are correct Only statements $2$ and $3$ are correct All statements $1,2$ , and $3$ are correct
makhdoom ghaya
edited
in
Others
Mar 20
by
makhdoom ghaya
160
points
8
views
tifrece2023
0
votes
0
answers
8
TIFR ECE 2023 | Question: 8
Suppose a bag contains 5 red balls, 3 blue balls, and 2 black balls. Balls are drawn without replacement until the bag is empty. Let $X_{i}$ be a random variable which takes value 1 if the $i$-th ball drawn is red, value 2 if that ball is blue, and 3 if it is black. Let the ... Only (i) and (ii) Only (i) and (iii) All of (i), (ii), and (iii) None of (i), (ii), or (iii)
makhdoom ghaya
edited
in
Others
Mar 20
by
makhdoom ghaya
160
points
10
views
tifrece2023
0
votes
0
answers
9
TIFR ECE 2023 | Question: 7
Let $f(x)$ be a positive continuous function on the real line that is the density of a random variable $X$. The differential entropy of $X$ is defined to be $-\int_{-\infty}^{\infty} f(x) \ln f(x) d x$. In which case does $X$ have the least differential entropy? You may use these facts: The ... $f(x):=(1 / 4) e^{-|x| / 2}$. $f(x):=e^{-2|x|}$.
makhdoom ghaya
edited
in
Others
Mar 19
by
makhdoom ghaya
160
points
6
views
tifrece2023
0
votes
0
answers
10
TIFR ECE 2023 | Question: 2
$\begin{array}{rlr}a^*=\max _{x, y} & x^2+y^2-8 x+7 \\ \text { s.t. } & x^2+y^2 \leq 1 \\ & y \geq 0\end{array}$ Then $a^{\star}$ is $16$ $14$ $12$ $10$ None of the above
makhdoom ghaya
edited
in
Others
Mar 19
by
makhdoom ghaya
160
points
8
views
tifrece2023
0
votes
0
answers
11
TIFR ECE 2023 | Question: 6
An ant in the plane travels in a spiral such that its position $(x(t), y(t))$ at time $t \geq 0$ is $\left(e^{t} \cos t, e^{t} \sin t\right)$. At time $t=1$, find the real part of $\ln (x(t)+i y(t))$. $-2$ $1$ $0$ $-1$ $2$
makhdoom ghaya
edited
in
Others
Mar 18
by
makhdoom ghaya
160
points
9
views
tifrece2023
0
votes
0
answers
12
TIFR ECE 2023 | Question: 5
Let $\mathrm{B}$ denote the unit ball in $\mathbb{R}^{2}$, and $\mathrm{Q}$ a square of side length $2$. Let $\mathrm{K}$ be the set of all vectors $z$ such that for some $x \in \mathrm{B}$ and some $y \in \mathrm{Q}, z=x+y$. The area of $\mathrm{K}$ is $4+\pi$ $6+\pi$ $8+\pi$ $10+\pi$ $12+\pi$
makhdoom ghaya
edited
in
Others
Mar 18
by
makhdoom ghaya
160
points
10
views
tifrece2023
0
votes
0
answers
13
TIFR ECE 2023 | Question: 4
Recall that the entropy (in bits) of a random variable $\mathrm{X}$ which takes values in $\mathbb{N}$ ... random variable which denotes the number of tosses made. What is the entropy of $\mathrm{X}$ in bits? $1$ $2$ $4$ Infinity None of the above
makhdoom ghaya
edited
in
Others
Mar 18
by
makhdoom ghaya
160
points
7
views
tifrece2023
0
votes
0
answers
14
TIFR ECE 2023 | Question: 3
Let \[ \mathcal{P}=\left\{(x, y): x+y \geq 1,2 x+y \geq 2, x+2 y \geq 2,(x-1)^{2}+(y-1)^{2} \leq 1\right\} . \] Compute \[ \min _{(x, y) \in \mathcal{P}} 2 x+3 y \] $2$ $3$ $4$ $6$ None of the above
makhdoom ghaya
edited
in
Others
Mar 18
by
makhdoom ghaya
160
points
11
views
tifrece2023
0
votes
0
answers
15
TIFR ECE 2023 | Question: 1
Consider a fair coin with probability of heads and tails equal to $1 / 2$. Moreover consider two dice, first $\mathrm{D}_{1}$ that has three faces numbered $1,3,5$ and second $\mathrm{D}_{2}$ that has three faces numbered $2,4,6$ ... rolled dice in the experiment. What is $\mathbb{E}[X]$ ? $\frac{7}{2}$ 4 3 $\frac{9}{2}$ None of the above
makhdoom ghaya
edited
in
Others
Mar 18
by
makhdoom ghaya
160
points
13
views
tifrece2023
1
vote
1
answer
16
GATE ECE 2020 | Question: 18
In the circuit shown below, all the components are ideal. If $V_{i}$ is $+2\:V$, the current $I_{o}$ sourced by the op-amp is __________ $\text{mA}$.
shanmukh2099
answered
in
Analog Circuits
Mar 9
by
shanmukh2099
140
points
118
views
gate2020-ec
numerical-answers
op-amps
analog-circuits
1
vote
0
answers
17
GATE ECE 2006 | Question: 35
Consider two transfer functions $ \mathrm{G}_1(s)=\frac{1}{s^2+a s+b} \text { and } \mathrm{G}_2(s)=\frac{s}{s^2+a s+b} $ The $3\text{-dB}$ bandwidths of their frequency responses are, respectively $\sqrt{a^2-4 b}, \sqrt{a^2+4 b}$ $\sqrt{a^2+4 b}, \sqrt{a^2-4 b}$ $\sqrt{a^2-4 b}, \sqrt{a^2-4 b}$ $\sqrt{a^2+4 b}, \sqrt{a^2+4 b}$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
22
views
gate2006-ec
1
vote
0
answers
18
GATE ECE 2006 | Question: 34
In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by $8 e^{-0.004 t}$ Volts $8\left(1-e^{-0.004 t}\right)$ Volts $8 u(t)$ Volts $8$ Volts
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
20
views
gate2006-ec
1
vote
0
answers
19
GATE ECE 2006 | Question: 33
A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is $0.5 \mathrm{~A}$ $2.0 \mathrm{~A}$ $1.0 \mathrm{~A}$ $0.0 \mathrm{~A}$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
26
views
gate2006-ec
1
vote
0
answers
20
GATE ECE 2006 | Question: 32
The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by $\text{RL}$ network only $\text{RC}$ network only $\text{LC}$ network only $\mathrm{RC}$ as well as $\mathrm{RL}$ networks
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
21
views
gate2006-ec
1
vote
0
answers
21
GATE ECE 2006 | Question: 31
In the two port network shown in the figure below, $z_{12}$ and $z_{21}$ are, respectively $r_e$ and $\beta r_o$ $0$ and $-\beta r_o$ $0,$ and $\beta r_o$ $r_e$ and $-\beta r_o$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
23
views
gate2006-ec
1
vote
0
answers
22
GATE ECE 2006 | Question: 30
A two-port network is represented by $\text{ABCD}$ ... $\frac{\mathrm{B}+\mathrm{AR}_{\mathrm{L}}}{\mathrm{D}+\mathrm{CR}_{\mathrm{L}}}$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
22
views
gate2006-ec
1
vote
0
answers
23
GATE ECE 2006 | Question: 29
As $x$ is increased from $-\infty$ to $\infty$, the function $ f(x)=\frac{e^x}{1+e^x} $ monotonically increases monotonically decreases increases to a maximum value and then decreases decreases to a minimum value and then increases
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
22
views
gate2006-ec
1
vote
0
answers
24
GATE ECE 2006 | Question: 28
Consider the function $f(t)$ having Laplace transform $ \text{F}(s)=\frac{\omega_0}{s^2+\omega_0^2} \operatorname{Re}[s]>0 $ The final value of $f(t)$ would be $0$ $1$ $-1 \leq f(\infty) \leq 1$ $\infty$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
22
views
gate2006-ec
1
vote
0
answers
25
GATE ECE 2006 | Question: 27
For the differential equation $\dfrac{d^2 y}{d x^2}+k^2 y=0$, the boundary conditions are $y=0$ for $x=0$, and $y=0$ for $x=a$ The form of non-zero solutions of $y$ (where $m$ ... $y=\displaystyle{}\sum_m\;\mathrm{~A}_{m} \;e^{-\frac{m \pi x}{a}}$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
23
views
gate2006-ec
1
vote
0
answers
26
GATE ECE 2006 | Question: 26
For the matrix $\left[\begin{array}{ll}4 & 2 \\ 2 & 4\end{array}\right]$, the eigen value corresponding to the eigenvector $\left[\begin{array}{l}101 \\ 101\end{array}\right]$ is $2$ $4$ $6$ $8$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
24
views
gate2006-ec
1
vote
0
answers
27
GATE ECE 2006 | Question: 25
Three companies $\text{X, Y}$ and $\text{Z}$ ... computer is defective, the probability that it was supplied by $\text{Y}$ is $0.1$ $0.2$ $0.3$ $0.4$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
24
views
gate2006-ec
1
vote
0
answers
28
GATE ECE 2006 | Question: 24
The integral $\displaystyle{}\int_0^\pi \sin ^3 \theta\; d \theta$ is given by $\frac{1}{2}$ $\frac{2}{3}$ $\frac{4}{3}$ $\frac{8}{3}$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
24
views
gate2006-ec
1
vote
0
answers
29
GATE ECE 2006 | Question: 23
The value of the contour integral $\displaystyle{}\oint_{\mid z-j \mid =2} \;\frac{1}{z^2+4} d z$ in positive sense is $\frac{j \pi}{2}$ $-\frac{\pi}{2}$ $-\frac{j \pi}{2}$ $\frac{\pi}{2}$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
24
views
gate2006-ec
1
vote
0
answers
30
GATE ECE 2006 | Question: 22
For the function of a complex variable $\text{W}=\ln \text{Z}\; ($where, $\mathrm{W}=u+j \mathrm{v}$ and $\mathrm{Z}=x+j y),$ the $u=$ constant lines get mapped in $\text{Z}$-plane as set of radial straight lines set of concentric circles set of confocal hyperbolas set of confocal ellipses
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
27
views
gate2006-ec
1
vote
0
answers
31
GATE ECE 2006 | Question: 21
The eigenvalues and the corresponding eigen vectors of a $2 \times 2$ ... $\left[\begin{array}{ll}4 & 8 \\ 8 & 4\end{array}\right]$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
22
views
gate2006-ec
1
vote
0
answers
32
GATE ECE 2006 | Question: 20
A transmission line is feeding $1 \mathrm{Watt}$ of power to a horn antenna having a gain of $10 \mathrm{~dB}$. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is $10$ Watts $1$ Watt $0.1$ Watt $0.01$ Watt
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
25
views
gate2006-ec
1
vote
0
answers
33
GATE ECE 2006 | Question: 19
The electric field of an electomagnetic wave propagating in the positive $z$-direction is given by $ \left.\text{E}=\hat{a_x} \sin (\omega t-\beta z\right)+\hat{a_y} \sin \left(\omega t-\beta z+\frac{\pi}{2}\right) $ The wave is linearly polarized in the $z$-direction elliptically polarized left-hand circularly polarized right-hand circularly polarized
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
29
views
gate2006-ec
1
vote
0
answers
34
GATE ECE 2006 | Question: 18
In the system shown below, $x(t)=(\sin t) u(t)$. In steady-steady-state, the response $y(t)$ will be $\frac{1}{\sqrt{2}} \sin \left(t-\frac{\pi}{4}\right)$ $\frac{1}{\sqrt{2}} \sin \left(t+\frac{\pi}{4}\right)$ $\frac{1}{\sqrt{2}} e^{-t} \sin t$ $\sin t-\cos t$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
23
views
gate2006-ec
1
vote
0
answers
35
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 $
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
26
views
gate2006-ec
1
vote
0
answers
36
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 $\frac{1}{3}<|z|<3$ $\frac{2}{3}<|z|<3$ $\frac{2}{3}<|z|<3$ $\frac{1}{3}<|z|<\frac{2}{3}$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
25
views
gate2006-ec
1
vote
0
answers
37
GATE ECE 2006 | Question: 15
The Dirac delta function $\delta(t)$ is defined as $\delta(t)= \begin{cases}1, & t=0 \\ 0, & \text { otherwise }\end{cases}$ $\delta(t)= \begin{cases}\infty, & t=0 \\ 0, & \text { otherwise }\end{cases}$ ... $\displaystyle{}\int_{-\infty}^\infty \delta(t) d t=1$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
31
views
gate2006-ec
1
vote
0
answers
38
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 $\frac{1}{5} e^ - \frac{j 3\omega }{5} \times\left(\frac{j \omega}{5}\right)$ ... $\frac{1}{5} e^{j 3 \omega} \times\left(\frac{j \omega}{5}\right)$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
29
views
gate2006-ec
1
vote
0
answers
39
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, " $d$ ... $2$ $3$ $4$ $5$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
24
views
gate2006-ec
1
vote
0
answers
40
GATE ECE 2006 | Question: 12
An $n$-channel depletion MOSFET has following two points on its $\mathrm{I}_\text{D}-\mathrm{V}_{\text {GS}}$ curve $\text{V}_{\text{Gs}}=0$ at $\text{I}_\text{D}=12 \mathrm{~mA}$ and $\mathrm{V}_{\mathrm{GS}}=-6$ Volts at $\mathrm{I}_{\mathrm{D}}=0$ Which ... $\text{V}_{\text {Gs }}=0 \; \text{Volts}$ $\mathrm{V}_{\mathrm{Gs}}=3 \; \text{Volts}$
Lakshman Patel RJIT
edited
in
Others
Feb 25
by
Lakshman Patel RJIT
11.2k
points
24
views
gate2006-ec
To see more, click for the
full list of questions
or
popular tags
.
Top Users
Mar 2023
Welcome to GO Electronics, where you can ask questions and receive answers from other members of the community.
Recent activity