GO Electronics
Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
No answer
No selected answer
No upvoted answer
Previous GATE
Featured
Recent questions without answers
1
votes
0
answers
241
TIFR ECE 2010 | Question: 19
Let us define an interval $A(n)$ as a function of $n$ as $A(n)=(-1 / n, 1 / n)$. Then the set of points that lie in the intersection of $A_{n}{ }^{\prime} s, n=1, \ldots, \infty$ is an interval is a single point is an empty set cannot be determined has two disjoint intervals
Let us define an interval $A(n)$ as a function of $n$ as $A(n)=(-1 / n, 1 / n)$. Then the set of points that lie in the intersection of $A_{n}{ }^{\prime} s, n=1, \ldots,...
admin
46.4k
points
85
views
admin
asked
Nov 30, 2022
Quantitative Aptitude
tifr2010
quantitative-aptitude
sets
+
–
1
votes
0
answers
242
TIFR ECE 2010 | Question: 20
The function $f(t)$ is a convolution of $t^{2}$ with $\exp \left(-t^{2} / 2\right) / \sqrt{2 \pi}$. Its derivative is $2 t$ $t^{2}$ $2 t+t e^{-t^{2} / 2}$ Does not have a simple closed form expression None of the above
The function $f(t)$ is a convolution of $t^{2}$ with $\exp \left(-t^{2} / 2\right) / \sqrt{2 \pi}$. Its derivative is$2 t$$t^{2}$$2 t+t e^{-t^{2} / 2}$Does not have a sim...
admin
46.4k
points
103
views
admin
asked
Nov 30, 2022
Calculus
tifr2010
calculus
derivatives
+
–
1
votes
0
answers
243
TIFR ECE 2022 | Question: 1
Suppose that a random variable $X$ can take $5$ values $\{1,2,3,4,5\}$ with probabilities that depend upon $n \geq 0$ and are given by \[P(X=k)=\frac{e^{k n}}{e^{n}+e^{2 n}+e^{3 n}+e^{4 n}+e^{5 n}}\] for $k=1,2,3,4,5$. ... $1$ as $n \rightarrow \infty$ It converges to $5$ as $n \rightarrow \infty$ It converges to $0$ as $n \rightarrow \infty$
Suppose that a random variable $X$ can take $5$ values $\{1,2,3,4,5\}$ with probabilities that depend upon $n \geq 0$ and are given by\[P(X=k)=\frac{e^{k n}}{e^{n}+e^{2 n...
admin
46.4k
points
81
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
random-variable
expectation
+
–
1
votes
0
answers
244
TIFR ECE 2022 | Question: 2
Consider a coin flip game between Amar, Akbar and Anthony. A fair coin (so that heads and tails each have probability $0.5)$ is independently flipped five times. Amar wins if at least three consecutive draws of heads are observed in the five coin tosses. Akbar wins if at least three ... What is the probability of Anthony winning? $9 / 16$ $1 / 3$ $1 / 2$ $5 / 8$ $7 / 12$
Consider a coin flip game between Amar, Akbar and Anthony. A fair coin (so that heads and tails each have probability $0.5)$ is independently flipped five times. Amar win...
admin
46.4k
points
77
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
245
TIFR ECE 2022 | Question: 3
Consider two linear time invariant $\text{(LTI)}$ systems $T_{1}$ and $T_{2}$ with impulse responses $h_{1}(n)$ and $h_{2}(n)$, respectively. Let there be two cascades $C_{1}$ and $C_{2}$, where in $C_{1}, T_{2}$ follows after ... statement $1$ is correct Only statement $3$ is correct Both statements $1, 2$ are correct Both statements $2, 3$ are correct None of the above
Consider two linear time invariant $\text{(LTI)}$ systems $T_{1}$ and $T_{2}$ with impulse responses $h_{1}(n)$ and $h_{2}(n)$, respectively. Let there be two cascades $C...
admin
46.4k
points
108
views
admin
asked
Nov 30, 2022
Others
tifrece2022
+
–
1
votes
0
answers
246
TIFR ECE 2022 | Question: 4
Evaluate the value of \[\max \left(x^{2}+(1-y)^{2}\right),\] where the maximisation above is over $x$ and $y$ such that $0 \leq x \leq y \leq 1$. $0$ $2$ $1 / 2$ $1 / 4$ $1$
Evaluate the value of\[\max \left(x^{2}+(1-y)^{2}\right),\]where the maximisation above is over $x$ and $y$ such that $0 \leq x \leq y \leq 1$.$0$$2$$1 / 2$$1 / 4$$1$
admin
46.4k
points
81
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
maxima-minima
+
–
1
votes
0
answers
247
TIFR ECE 2022 | Question: 5
Let $Q$ be a unit square in the plane with corners at $(0,0),(0,1),(1,0)$ and $(1,1)$. Let $B$ be a ball of radius $1$ in the plane centered at the origin $(0,0)$. Let $Q+B$ denote the set of all vectors in the plane of the form $v+w,$ where $v \in Q$ and $w \in B$. The area of $Q+B$ is: $5+\pi$ $4+\pi$ $3+\pi$ $2+\pi$ $1+\pi$
Let $Q$ be a unit square in the plane with corners at $(0,0),(0,1),(1,0)$ and $(1,1)$. Let $B$ be a ball of radius $1$ in the plane centered at the origin $(0,0)$. Let $Q...
admin
46.4k
points
142
views
admin
asked
Nov 30, 2022
Vector Analysis
tifrece2022
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
248
TIFR ECE 2022 | Question: 6
Consider a degree-$5$ polynomial function $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$. If $f$ exhibits at least four local maxima, which of the following is necessarily true? (Note: A local maximum is a point where the function value is the maximum in a ... derivative of $f(x)$ is negative for some $x \in[0,100]$ $f$ has exactly $4$ local maxima None of the above
Consider a degree-$5$ polynomial function $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$. If $f$ exhibits at least four local maxima, which of the following is necess...
admin
46.4k
points
77
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
maxima-minima
+
–
1
votes
0
answers
249
TIFR ECE 2022 | Question: 7
Two players $\mathrm{A}$ and $\mathrm{B}$ of equal skill are playing a match. The first one to win $4$ rounds wins the match. Both players are equally likely to win each round independent of the outcomes of the other rounds. After $3$ rounds, $\mathrm{A}$ has won $2$ ... probability that $\mathrm{A}$ wins the match? $5 / 8$ $2 / 3$ $11 / 16$ $5 / 7$ None of the above
Two players $\mathrm{A}$ and $\mathrm{B}$ of equal skill are playing a match. The first one to win $4$ rounds wins the match. Both players are equally likely to win each ...
admin
46.4k
points
103
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
250
TIFR ECE 2022 | Question: 8
Let $a, b, c$ be real numbers such that the following system of equations has a solution \[\begin{aligned} x+2 y+3 z &=a & & (1)\\ 8 x+10 y+12 z &=b & & (2)\\ 7 x+8 y+9 z &=c-1 & & (3) \end{aligned}\] Let $A$ be a ... 1 & 0 \\ -1 & 0 & 1 \end{array}\right]\] What is the value of $\operatorname{det}(A)$? $1$ $2$ $3$ $4$ $5$
Let $a, b, c$ be real numbers such that the following system of equations has a solution\[\begin{aligned}x+2 y+3 z &=a & & (1)\\8 x+10 y+12 z &=b & & (2)\\7 x+8 y+9 z &=c...
admin
46.4k
points
119
views
admin
asked
Nov 30, 2022
Linear Algebra
tifrece2022
linear-algebra
system-of-equations
+
–
1
votes
0
answers
251
TIFR ECE 2022 | Question: 9
Suppose you throw a dart and it lands uniformly at random on a target which is a disk of unit radius. What is the probability density function $f(x)$ ... None of the above.
Suppose you throw a dart and it lands uniformly at random on a target which is a disk of unit radius. What is the probability density function $f(x)$ of the distance of t...
admin
46.4k
points
124
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
probability-density-function
+
–
1
votes
0
answers
252
TIFR ECE 2022 | Question: 10
Find the vector which is closest (in Euclidean distance) to $\left(\begin{array}{lll}-1 & 1 & 1\end{array}\right)$ which can be written in the form \[a\left(\begin{array}{lll} 1 & 1 & 1 \end{array}\right)+b\left(\begin{array}{lll} 0 ... None of the above
Find the vector which is closest (in Euclidean distance) to $\left(\begin{array}{lll}-1 & 1 & 1\end{array}\right)$ which can be written in the form\[a\left(\begin{array}{...
admin
46.4k
points
85
views
admin
asked
Nov 30, 2022
Vector Analysis
tifrece2022
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
253
TIFR ECE 2022 | Question: 11
A drunken man walks on a straight lane. At every integer time (in seconds) he moves a distance of $1$ unit randomly, either forwards or backwards. What is the expectation of the square of the distance after $100$ seconds from the initial position? Hint: ... sum of independent and identically distributed random variables. $100$ $\frac{\sqrt{300}}{4}$ $40$ $200$ $20 \pi$
A drunken man walks on a straight lane. At every integer time (in seconds) he moves a distance of $1$ unit randomly, either forwards or backwards. What is the expectation...
admin
46.4k
points
138
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
random-variable
expectation
+
–
1
votes
0
answers
254
TIFR ECE 2022 | Question: 12
An $n \times n$ matrix $\mathbf{P}$ is called a Permutation Matrix if each of its $n$ columns and $n$ rows contain exactly one $1$ and $n-1 \; 0$ 's. Consider the following statements: $\operatorname{det}(\mathbf{P})$ is either $+1$ or ... $1,3$ are correct Only statements $2, 3$ are correct All statements $1, 2,$ and $3$ are correct
An $n \times n$ matrix $\mathbf{P}$ is called a Permutation Matrix if each of its $n$ columns and $n$ rows contain exactly one $1$ and $n-1 \; 0$ 's. Consider the followi...
admin
46.4k
points
86
views
admin
asked
Nov 30, 2022
Linear Algebra
tifrece2022
linear-algebra
matrices
+
–
1
votes
0
answers
255
TIFR ECE 2022 | Question: 13
Calculate the minimum value attained by the function \[\sin (\pi x)-\sqrt{2} \pi x^{2}\] for values of $x$ which lie in the interval $[0,1]$. $\frac{1}{\sqrt{2}}\left(1-\frac{\pi}{8}\right)$ $0$ $1-\frac{\pi}{2 \sqrt{2}}$ $-\frac{1}{\sqrt{2}}\left(1+\frac{9 \pi}{2}\right)$ $-\sqrt{2} \pi$
Calculate the minimum value attained by the function\[\sin (\pi x)-\sqrt{2} \pi x^{2}\]for values of $x$ which lie in the interval $[0,1]$.$\frac{1}{\sqrt{2}}\left(1-\fra...
admin
46.4k
points
98
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
maxima-minima
+
–
1
votes
0
answers
256
TIFR ECE 2022 | Question: 14
Let a bag contain ten balls numbered $1,2, \ldots, 10$. Let three balls be drawn at random in sequence without replacement, and the number on the ball drawn on the $i^{\text {th }}$ choice be $n_{i} \in\{1,2, \ldots, 10\}.$ What is the probability that $n_{1} < n_{2} < n_{3} ?$ $\frac{1}{3}$ $\frac{1}{12}$ $\frac{1}{4}$ $\frac{1}{6}$ None of the above
Let a bag contain ten balls numbered $1,2, \ldots, 10$. Let three balls be drawn at random in sequence without replacement, and the number on the ball drawn on the $i^{\t...
admin
46.4k
points
110
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
257
TIFR ECE 2022 | Question: 15
Consider the difference below for $m \geq 5$: \[\sum_{n=1}^{m-1} \frac{1}{(1+n)^{2}}-\int_{x=1}^{m} \frac{1}{(1+x)^{2}} d x .\] Which statement about the difference is $\text{TRUE}?$ It is positive for infinitely many $m \geq 5$ ... is positive for infinitely many $m$ It is positive for all $m \geq 5,$ and is decreasing as $m$ increases It is negative for all $m \geq 5$
Consider the difference below for $m \geq 5$:\[\sum_{n=1}^{m-1} \frac{1}{(1+n)^{2}}-\int_{x=1}^{m} \frac{1}{(1+x)^{2}} d x .\]Which statement about the difference is $\te...
admin
46.4k
points
96
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
definite-integrals
+
–
1
votes
0
answers
258
TIFR ECE 2021 | Question: 1
Consider a system with input $x(t)$ and output $y(t)$ such that \[y(t)=t \;x(t) .\] Consider the following statements: The system is linear. The system is time-invariant. The system is causal. Then which of the following is $\text{TRUE?}$ Only ... Only statement $3$ is correct. Only statements $1$ and $3$ are correct. All three statements $1, 2,$ and $3$ are correct.
Consider a system with input $x(t)$ and output $y(t)$ such that\[y(t)=t \;x(t) .\]Consider the following statements:The system is linear.The system is time-invariant.The ...
admin
46.4k
points
79
views
admin
asked
Nov 30, 2022
Others
tifrece2021
+
–
1
votes
0
answers
259
TIFR ECE 2021 | Question: 2
Given a fixed perimeter of $1,$ among the following shapes, which one has the largest area? Square A regular pentagon A regular hexagon A regular septagon A regular octagon
Given a fixed perimeter of $1,$ among the following shapes, which one has the largest area?SquareA regular pentagonA regular hexagonA regular septagonA regular octagon
admin
46.4k
points
75
views
admin
asked
Nov 30, 2022
Quantitative Aptitude
tifrece2021
quantitative-aptitude
geometry
area
+
–
1
votes
0
answers
260
TIFR ECE 2021 | Question: 3
Consider the following statements: $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$. $\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}}=1$. $\lim _{x \rightarrow 0} \frac{1-\cos x}{x}=1$. Which of the following is $\text{TRUE?}$ Only Statement $1$ ... $1$ and $3$ are correct. All of Statements $1, 2,$ and $3$ are correct. None of the three Statements $1,2,$ and $3$ are correct.
Consider the following statements:$\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$.$\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}}=1$.$\lim _{x \rightarrow 0} \frac{1-\cos x}...
admin
46.4k
points
94
views
admin
asked
Nov 30, 2022
Calculus
tifrece2021
calculus
limits
+
–
1
votes
0
answers
261
TIFR ECE 2021 | Question: 4
The first-order differential equation $\frac{d y(t)}{d t}+2 y(t)=x(t)$ describes a particular continuous-time system initially at rest at origin i.e., $x(0)=0$. Consider the following statements? System is memoryless. System is causal. System is stable. Which of the ... correct. All $(1), (2)$ and $(3)$ are correct. Only $(2)$ and $(3)$ are correct. None of the above
The first-order differential equation $\frac{d y(t)}{d t}+2 y(t)=x(t)$ describes a particular continuous-time system initially at rest at origin i.e., $x(0)=0$. Consider ...
admin
46.4k
points
108
views
admin
asked
Nov 30, 2022
Differential Equations
tifrece2021
differential-equations
first-order-differential-equation
+
–
1
votes
0
answers
262
TIFR ECE 2021 | Question: 5
Recall that \[\operatorname{sinc}(t)=\frac{\sin (\pi t)}{\pi t}\] and convolution of functions $x(t)$ and $y(t)$ is defined as \[x(t) \star y(t)=\int_{-\infty}^{\infty} x(t-\tau) y(\tau) d \tau .\] What is the necessary and sufficient condition on positive real ... \quad \text { for all real } t \text {. }\] $f<a$ $f>a$ $f<a^{-1}$ $f>a^{-1}$ None of the above
Recall that\[\operatorname{sinc}(t)=\frac{\sin (\pi t)}{\pi t}\]and convolution of functions $x(t)$ and $y(t)$ is defined as\[x(t) \star y(t)=\int_{-\infty}^{\infty} x(t-...
admin
46.4k
points
84
views
admin
asked
Nov 30, 2022
Others
tifrece2021
+
–
1
votes
0
answers
263
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...
admin
46.4k
points
70
views
admin
asked
Nov 30, 2022
Others
tifrece2021
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
264
TIFR ECE 2021 | Question: 7
Consider the function \[f(y)=\int_{1}^{y} \frac{1}{1+x^{2}} d x-\log _{e}(1+y)\] where $\log _{e}(x)$ denotes the natural logarithm of $x$. Which of the following is true: The function $f(y)$ ... $y \geq 1$. The derivative of function $f(y)$ does not exist at $y=1$.
Consider the function\[f(y)=\int_{1}^{y} \frac{1}{1+x^{2}} d x-\log _{e}(1+y)\]where $\log _{e}(x)$ denotes the natural logarithm of $x$.Which of the following is true:Th...
admin
46.4k
points
93
views
admin
asked
Nov 30, 2022
Calculus
tifrece2021
calculus
definite-integrals
+
–
1
votes
0
answers
265
TIFR ECE 2021 | Question: 8
The maximum area of a parallelogram inscribed in the ellipse (i.e. all the vertices of the parallelogram are on the ellipse) $x^{2}+4 y^{2}=1$ is: $2$ $4$ $1$ $5$ $3$
The maximum area of a parallelogram inscribed in the ellipse (i.e. all the vertices of the parallelogram are on the ellipse) $x^{2}+4 y^{2}=1$ is:$2$$4$$1$$5$$3$
admin
46.4k
points
98
views
admin
asked
Nov 30, 2022
Quantitative Aptitude
tifrece2021
quantitative-aptitude
geometry
area
+
–
1
votes
0
answers
266
TIFR ECE 2021 | Question: 9
A stick of length $1$ is broken at a point chosen uniformly at random. Which of the following is false? Twice the length of the smaller piece is greater than the length of the larger piece with positive probability. One half of the length of the ... . The product of the length of the smaller piece and the larger piece is greater than $1 / 4$ with positive probability.
A stick of length $1$ is broken at a point chosen uniformly at random. Which of the following is false?Twice the length of the smaller piece is greater than the length of...
admin
46.4k
points
41
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
267
TIFR ECE 2021 | Question: 10
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$. Let the real number $a_{1}^{*}$ be such that it solves the following optimization problem \[d_{1}=\min _{a_{1} \in \mathbb{R}}\left\|\vec{u}-a_{1} \vec{v}_{1}\right\|,\] where we denote the length ... $\left\|\vec{u}-\left(\vec{p}_{2}-\vec{p}_{1}\right)\right\|$ $0$
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$. Let the real number $a_{1}^{*}$ be such that it solves the following optimization problem\[d_{1}=\min _{a_...
admin
46.4k
points
79
views
admin
asked
Nov 30, 2022
Calculus
tifrece2021
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
268
TIFR ECE 2021 | Question: 11
Suppose that $X_{1}$ and $X_{2}$ denote the output of rolls of two independent dices that can each take integer values $\{1,2,3,4,5,6\}$ with probability $1 / 6$ for each outcome. Further, $U$ denotes a continuous random variable that is independent of $X_{1}$ and $X_{2}$ ... on this sum what is the probability that $X_{1}$ equals $2?$ $2.21$ $3$ $1 / 6$ $1 / 5$ $1 / 3$
Suppose that $X_{1}$ and $X_{2}$ denote the output of rolls of two independent dices that can each take integer values $\{1,2,3,4,5,6\}$ with probability $1 / 6$ for each...
admin
46.4k
points
87
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
269
TIFR ECE 2021 | Question: 12
An ant does a random walk in a two dimensional plane starting at the origin at time $0.$ At every integer time greater than $0,$ it moves one centimeter away from its earlier position in a random direction independent of its past. After $4$ steps, what is the expected square of the distance (measured in centimeters) from its starting point? $4$ $1$ $2$ $\pi$ $0$
An ant does a random walk in a two dimensional plane starting at the origin at time $0.$ At every integer time greater than $0,$ it moves one centimeter away from its ear...
admin
46.4k
points
105
views
admin
asked
Nov 30, 2022
Quantitative Aptitude
tifrece2021
quantitative-aptitude
geometry
+
–
1
votes
0
answers
270
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$
admin
46.4k
points
116
views
admin
asked
Nov 30, 2022
Others
tifrece2021
+
–
1
votes
0
answers
271
TIFR ECE 2021 | Question: 14
A tourist starts by taking one of the $n$ available paths, denoted by $1,2, \cdots, n$. An hour into the journey, the path $i$ subdivides into further $1+i$ subpaths, only one of which leads to the destination. The tourist has no map and makes random choices of the path and the ... $\frac{10}{36}$ $\frac{11}{36}$ $\frac{12}{36}$ $\frac{13}{36}$ $\frac{14}{36}$
A tourist starts by taking one of the $n$ available paths, denoted by $1,2, \cdots, n$. An hour into the journey, the path $i$ subdivides into further $1+i$ subpaths, onl...
admin
46.4k
points
70
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
272
TIFR ECE 2021 | Question: 15
We have the sequence, $a_{n}=\frac{1}{n \log ^{2} n}, n \geq 2$, where log is the logarithm to the base $2$ and let $A=\sum_{n=2}^{\infty} a_{n}$ ... $H(X)?$ $H(X) \leq 3$ $H(X) \in(3,5]$ $H(X) \in(5,10]$ $H(X)>10$ but finite $H(X)$ is unbounded
We have the sequence, $a_{n}=\frac{1}{n \log ^{2} n}, n \geq 2$, where log is the logarithm to the base $2$ and let $A=\sum_{n=2}^{\infty} a_{n}$ be the sum of the sequen...
admin
46.4k
points
73
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
273
TIFR ECE 2020 | 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[n-1] ... Non-linear, time-invariant, BIBO stable Linear, time-variant, BIBO unstable Non-linear, time-variant, BIBO stable 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...
admin
46.4k
points
75
views
admin
asked
Nov 30, 2022
Others
tifrece2020
+
–
1
votes
0
answers
274
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 ...
admin
46.4k
points
77
views
admin
asked
Nov 30, 2022
Others
tifrece2020
+
–
1
votes
0
answers
275
TIFR ECE 2020 | Question: 3
Balls are drawn one after the other uniformly at random without replacement from a set of eight balls numbered $1,2, \ldots, 8$ until all balls drawn. What is the expected number of balls whose value match their ordinality (i.e., their position in the order in which ... ? Now can you use linearity of expectation to solve the problem? $1$ $1.5$ $2$ $2.5$ None of the above
Balls are drawn one after the other uniformly at random without replacement from a set of eight balls numbered $1,2, \ldots, 8$ until all balls drawn. What is the expecte...
admin
46.4k
points
74
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
276
TIFR ECE 2020 | Question: 4
Let $f, g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions that are continuous and differentiable. Consider the following statements: $\min \{f, g\}$ is continuous $\max \{f, g\}$ is continuous $\max \{f, g\}$ is differentiable Which ... is correct Only statement $2$ is correct Only statement $3$ is correct Only statements $1$ and $2$ are correct None of the above
Let $f, g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions that are continuous and differentiable. Consider the following statements:$\min \{f, g\}$ is continuous$\ma...
admin
46.4k
points
36
views
admin
asked
Nov 30, 2022
Calculus
tifrece2020
calculus
continuity-and-differentiability
+
–
1
votes
0
answers
277
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...
admin
46.4k
points
33
views
admin
asked
Nov 30, 2022
Others
tifrece2020
+
–
1
votes
0
answers
278
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...
admin
46.4k
points
83
views
admin
asked
Nov 30, 2022
Others
tifrece2020
+
–
1
votes
0
answers
279
TIFR ECE 2020 | Question: 7
Given $n$ independent Bernoulli random variables, taking value $1$ with probability $p$ and $0$ with probability $1-p$. Then, which of the following is the value of $E\left[\left(z_{1}+\right.\right.$ $\left.\left.\ldots z_{n}\right)^{2}\right] ?$ $0$ $n p+n(n-1) p^{2}$ $n^{3} p^{2}$ $n^{2} p^{2}+n p$ None of the above
Given $n$ independent Bernoulli random variables, taking value $1$ with probability $p$ and $0$ with probability $1-p$. Then, which of the following is the value of $E\le...
admin
46.4k
points
96
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
280
TIFR ECE 2020 | Question: 8
Suppose that Dice $1$ has five faces numbered $1$ to $5,$ each of which is equally likely to occur once the dice is rolled. Dice $2$ similarly has eight equally likely faces numbered $1$ to $8.$ Suppose that the two dice are rolled, and the sum is equal to $8.$ Conditioned on this, ... $2?$ $1 / 4$ $1 / 3$ $1 / 2$ $2 / 7$ $2 / 5$
Suppose that Dice $1$ has five faces numbered $1$ to $5,$ each of which is equally likely to occur once the dice is rolled. Dice $2$ similarly has eight equally likely fa...
admin
46.4k
points
82
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
conditional-probability
+
–
Page:
« prev
1
...
4
5
6
7
8
9
10
...
75
next »
GO Electronics
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register