GO Electronics
Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Hot questions
1
votes
0
answers
281
TIFR ECE 2010 | Question: 18
Under what conditions is the following inequality true for $a, b>0$ $ \log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda)) $ $\lambda=0.5$ $0<a / \lambda \leq 1, b /(1-\lambda)>0$ $a / \lambda>0,0<b /(1-\lambda) \leq 1$ All of the above None of the above
Under what conditions is the following inequality true for $a, b>0$$$\log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda))$$$\lambda=0.5$$0<a...
admin
46.4k
points
96
views
admin
asked
Nov 30, 2022
Quantitative Aptitude
tifr2010
quantitative-aptitude
inequality
+
–
1
votes
0
answers
282
TIFR ECE 2010 | Question: 3
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. When $\alpha \geq 1$, the probability that $\max (\text{X, Y})>\alpha \min (\text{X, Y})$ is $1 /(2 \alpha)$ $\exp (1-\alpha)$ $1 / \alpha$ $1 / \alpha^{2}$ $1 / \alpha^{3}$
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. When $\alpha \geq 1$, the probab...
admin
46.4k
points
92
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifr2010
probability-and-statistics
probability
probability-density-function
+
–
1
votes
0
answers
283
TIFR ECE 2010 | Question: 14
Define $\operatorname{sign}(x)=0$ for $x=0, \operatorname{sign}(x)=1$ for $x>0$ and $\operatorname{sign}(x)=-1$ for $x<0$. For $n \geq 0$ ... $-1,1,-1,1, \ldots$. $0,1,-1,1,-1, \ldots$ $0,1,1,1,-1,1,-1,1, \ldots$ None of the above
Define $\operatorname{sign}(x)=0$ for $x=0, \operatorname{sign}(x)=1$ for $x>0$ and $\operatorname{sign}(x)=-1$ for $x<0$. For $n \geq 0$, let\[Y_{n}=\operatorname{sign}\...
admin
46.4k
points
92
views
admin
asked
Nov 30, 2022
Others
tifr2010
+
–
1
votes
0
answers
284
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
105
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
maxima-minima
+
–
1
votes
0
answers
285
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
104
views
admin
asked
Nov 30, 2022
Quantitative Aptitude
tifrece2021
quantitative-aptitude
geometry
area
+
–
1
votes
0
answers
286
TIFR ECE 2010 | Question: 7
A voltage source with internal resistance $\text{R}$ is connected to an inductor $\text{L}$ and a capacitor $\text{C}$ connected in parallel. The output is the common voltage across the inductor and the capacitor. What is the nature of the transfer ... depending upon the values of $\text{L}$ and $\text{C}$. The circuit is not stable and no transfer function exists.
A voltage source with internal resistance $\text{R}$ is connected to an inductor $\text{L}$ and a capacitor $\text{C}$ connected in parallel. The output is the common vol...
admin
46.4k
points
90
views
admin
asked
Nov 30, 2022
Others
tifr2010
+
–
1
votes
0
answers
287
TIFR ECE 2010 | Question: 17
Let $a_{1} \geq a_{2} \geq \cdots \geq a_{k} \geq 0$. Then the limit \[ \lim _{n \rightarrow \infty}\left(\sum_{i=1}^{k} a_{i}^{n}\right)^{1 / n} \] is $0$ $\infty$ $a_{k}$ $a_{1}$ $\left(\sum_{i=1}^{k} a_{k}\right) / k$
Let $a_{1} \geq a_{2} \geq \cdots \geq a_{k} \geq 0$. Then the limit\[\lim _{n \rightarrow \infty}\left(\sum_{i=1}^{k} a_{i}^{n}\right)^{1 / n}\]is$0$$\infty$$a_{k}$$a_{1...
admin
46.4k
points
89
views
admin
asked
Nov 30, 2022
Calculus
tifr2010
calculus
limits
+
–
1
votes
0
answers
288
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
100
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
289
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
99
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
definite-integrals
+
–
1
votes
0
answers
290
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
98
views
admin
asked
Nov 30, 2022
Calculus
tifrece2021
calculus
limits
+
–
1
votes
0
answers
291
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
97
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
292
TIFR ECE 2010 | Question: 11
Consider \[ \text{F}=\frac{1}{2}\left[\begin{array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & -1 & 1 \\ 1 & -1 & 1 & -1 \end{array}\right], \quad x=\left[\begin{array}{l} 2.1 \\ 1.2 \\ ... 2 \\ -1 \end{array}\right] \] The inner product between $\text{F}x$ and $\text{F}y$ is $0$ $1$ $-1$ $-1.2$ None of the above
Consider\[\text{F}=\frac{1}{2}\left[\begin{array}{cccc}1 & 1 & 1 & 1 \\1 & 1 & -1 & -1 \\1 & -1 & -1 & 1 \\1 & -1 & 1 & -1\end{array}\right], \quad x=\left[\begin{array}{...
admin
46.4k
points
83
views
admin
asked
Nov 30, 2022
Linear Algebra
tifr2010
linear-algebra
matrices
+
–
1
votes
0
answers
293
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
96
views
admin
asked
Nov 30, 2022
Calculus
tifrece2021
calculus
definite-integrals
+
–
1
votes
0
answers
294
TIFR ECE 2010 | Question: 15
Let $\imath=\sqrt{-1}$. Then $\imath^{\imath}$ could be $\exp (\pi / 2)$ $\exp (\pi / 4)$ Can't determine Takes infinite values Is a complex number
Let $\imath=\sqrt{-1}$. Then $\imath^{\imath}$ could be$\exp (\pi / 2)$$\exp (\pi / 4)$Can't determineTakes infinite valuesIs a complex number
admin
46.4k
points
80
views
admin
asked
Nov 30, 2022
Complex Analysis
tifr2010
complex-analysis
complex-number
+
–
1
votes
0
answers
295
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
92
views
admin
asked
Nov 30, 2022
Vector Analysis
tifrece2022
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
296
TIFR ECE 2010 | Question: 10
$\text{H}$ is a circulant matrix (row $n$ is obtained by circularly shifting row $1$ to the right by $n$ positions) and $\text{F}$ is the $\text{DFT}$ matrix. Which of the following is true? $F H F^{H}$ is circulant, where $F^{H}$ is the inverse $\text{DFT}$ matrix. $F H F^{H}$ is tridiagonal $F H F^{H}$ is diagonal $F H F^{H}$ has real entries None of the above
$\text{H}$ is a circulant matrix (row $n$ is obtained by circularly shifting row $1$ to the right by $n$ positions) and $\text{F}$ is the $\text{DFT}$ matrix. Which of th...
admin
46.4k
points
78
views
admin
asked
Nov 30, 2022
Linear Algebra
tifr2010
linear-algebra
matrices
+
–
1
votes
0
answers
297
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
91
views
admin
asked
Nov 30, 2022
Linear Algebra
tifrece2022
linear-algebra
matrices
+
–
1
votes
0
answers
298
TIFR ECE 2017 | Question: 6
Let $a, b \in\{0,1\}$. Consider the following statements where $*$ is the $\text{AND}$ operator, $\oplus$ is $\text{EXCLUSIVE-OR,}$ and ${ }^{c}$ denotes the complement function. $\max \left\{a * b, b \oplus a^{\mathrm{c}}\right\}=1$ ... $\text{(iii)}$ only $\text{(iii)}$ and $\text{(iv)}$ only $\text{(iv)}$ and $\text{(i)}$ only None of the above
Let $a, b \in\{0,1\}$. Consider the following statements where $*$ is the $\text{AND}$ operator, $\oplus$ is $\text{EXCLUSIVE-OR,}$ and ${ }^{c}$ denotes the complement f...
admin
46.4k
points
134
views
admin
asked
Nov 29, 2022
Calculus
tifrece2017
calculus
functions
+
–
1
votes
0
answers
299
TIFR ECE 2010 | Question: 4
Let $Y_{n}=s_{n}+W_{n}$ where $\left\{s_{n}\right\}$ is the desired signal bandlimited to $[-W, W]$ and $\left\{W_{n}\right\}$ is a noise component, which is sparse (that is, only few samples are non-zero), bursty (that is, runs of non-zero samples are ... of $\left\{Y_{n+k}\right\}_{k=-K}^{K}$ for suitably chosen $K$ Both $a)$ and $b)$ are better than the other options
Let $Y_{n}=s_{n}+W_{n}$ where $\left\{s_{n}\right\}$ is the desired signal bandlimited to $[-W, W]$ and $\left\{W_{n}\right\}$ is a noise component, which is sparse (that...
admin
46.4k
points
77
views
admin
asked
Nov 30, 2022
Others
tifr2010
+
–
1
votes
0
answers
300
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
90
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
301
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
90
views
admin
asked
Nov 30, 2022
Others
tifrece2021
+
–
1
votes
0
answers
302
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
89
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
303
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
88
views
admin
asked
Nov 30, 2022
Others
tifrece2020
+
–
1
votes
0
answers
304
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
87
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
random-variable
expectation
+
–
1
votes
0
answers
305
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
85
views
admin
asked
Nov 30, 2022
Others
tifrece2021
+
–
1
votes
0
answers
306
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
84
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
307
TIFR ECE 2020 | Question: 10
Consider two independent random variables $\left(U_{1}, U_{2}\right)$ both are uniformly distributed between $[0,1]$. The conditional expectation \[E\left[\left(U_{1}+U_{2}\right) \mid \max \left(U_{1}, U_{2}\right) \geq 0.5\right]\] equals $7 / 6$ $8 / 7$ $6 / 7$ $1.1$ None of the above
Consider two independent random variables $\left(U_{1}, U_{2}\right)$ both are uniformly distributed between $[0,1]$. The conditional expectation\[E\left[\left(U_{1}+U_{2...
admin
46.4k
points
84
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
308
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
83
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
maxima-minima
+
–
1
votes
0
answers
309
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
83
views
admin
asked
Nov 30, 2022
Calculus
tifrece2021
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
310
TIFR ECE 2010 | Question: 5
Let $Y(t)=\sum_{n=-\infty}^{\infty} x_{n} h(t-n T)$. We sample $Y(t)$ at time instants $n T / 2$ and let $Y_{n}=Y(n T / 2)$. Which of the following is true? $\left\{Y_{n}\right\}$ can be interpreted as the output of a discrete time, ... of a discrete time, linear, time-invariant system with input $\left\{X_{n}\right\}$. Both $a)$ and $b)$ above Both $b)$ and $c)$ above
Let $Y(t)=\sum_{n=-\infty}^{\infty} x_{n} h(t-n T)$. We sample $Y(t)$ at time instants $n T / 2$ and let $Y_{n}=Y(n T / 2)$. Which of the following is true?$\left\{Y_{n}\...
admin
46.4k
points
69
views
admin
asked
Nov 30, 2022
Others
tifr2010
+
–
1
votes
0
answers
311
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
82
views
admin
asked
Nov 30, 2022
Quantitative Aptitude
tifrece2021
quantitative-aptitude
geometry
area
+
–
1
votes
0
answers
312
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
82
views
admin
asked
Nov 30, 2022
Others
tifrece2020
+
–
1
votes
0
answers
313
TIFR ECE 2018 | Question: 3
Let $\lim _{n \rightarrow \infty} f(n)=\infty$ and $\lim _{n \rightarrow \infty} g(n)=\infty$. Then which of the following is necessarily $\text{TRUE.}$ $\lim _{n \rightarrow \infty}|f(n)-g(n)|=\infty$ $\lim _{n \rightarrow \infty}|f(n)-g(n)|=0$ $\lim _{n \rightarrow \infty}|f(n) / g(n)|=\infty$ $\lim _{n \rightarrow \infty}|f(n) / g(n)|=1$ None of the above
Let $\lim _{n \rightarrow \infty} f(n)=\infty$ and $\lim _{n \rightarrow \infty} g(n)=\infty$. Then which of the following is necessarily $\text{TRUE.}$$\lim _{n \rightar...
admin
46.4k
points
124
views
admin
asked
Nov 29, 2022
Calculus
tifrece2018
calculus
limits
+
–
1
votes
0
answers
314
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
81
views
admin
asked
Nov 30, 2022
Others
tifrece2021
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
315
TIFR ECE 2020 | Question: 9
Let $A$ be an $n \times n$ matrix with the the property that $A^{m}=0$ for some $m \in \mathbb{N}$. Consider the following statements: At least one entry of $A$ is zero All eigenvalues of $A$ are zero All diagonal entries of $A$ are zero ... $2$ alone is correct Only statement $3$ is correct Only statements $1$ and $2$ are correct Only statements $2$ and $3$ are correct
Let $A$ be an $n \times n$ matrix with the the property that $A^{m}=0$ for some $m \in \mathbb{N}$. Consider the following statements:At least one entry of $A$ is zeroAll...
admin
46.4k
points
81
views
admin
asked
Nov 30, 2022
Linear Algebra
tifrece2020
linear-algebra
matrices
+
–
1
votes
0
answers
316
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
81
views
admin
asked
Nov 30, 2022
Others
tifrece2020
+
–
1
votes
0
answers
317
TIFR ECE 2010 | Question: 1
A linear system could be a composition of Two non-linear systems a non-causal non-linear system and a linear system a time varying non-linear system and a time varying linear system All of the above None of the above
A linear system could be a composition ofTwo non-linear systemsa non-causal non-linear system and a linear systema time varying non-linear system and a time varying linea...
admin
46.4k
points
67
views
admin
asked
Nov 30, 2022
Others
tifr2010
+
–
1
votes
0
answers
318
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
80
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
maxima-minima
+
–
1
votes
0
answers
319
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
77
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
320
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
76
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
random-variable
+
–
Page:
« prev
1
...
5
6
7
8
9
10
11
...
79
next »
GO Electronics
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register