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
Filter
No answer
No selected answer
No upvoted answer
Previous GATE
Featured
Recent questions without a selected answer
1
vote
0
answers
81
TIFR ECE 2011 | Question: 6
Let $\mathrm{H}(\mathrm{z})$ be the $z$-transform of the transfer function corresponding to an input output relation $y(n)-\frac{1}{2} y(n-1)=x(n)+\frac{1}{3} x(n-1)$. Then which of the following is TRUE The $\operatorname{ROC}$ ... $|z|<\frac{1}{2}$. $\operatorname{Both}$ (a) and (b). System is necessarily causal. None of the above.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
7
views
tifr2011
1
vote
0
answers
82
TIFR ECE 2011 | Question: 7
Assume you are using a binary code error correcting code $C$. If the minimum Hamming distance between any two codewords of $C$ is $3$. Then We can correct and detect $2$ bit errors. We can correct $1$ bit errors and detect $2$ bit errors. We can correct $2$ bit errors and detect $1$ bit errors. We can correct $1$ bit errors and detect $1$ bit errors. None of the above.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
6
views
tifr2011
1
vote
0
answers
83
TIFR ECE 2011 | Question: 8
Let $f(x, y)$ be a function in two variables $x, y$. Then which of the following is true $\max _{x} \min _{y} f(x, y) \leq \min _{y} \max _{x} f(x, y)$. $\max _{x} \min _{y} f(x, y) \geq \min _{y} \max _{x} f(x, y)$ ... $\max _{x} \min _{y} f(x, y)=\min _{y} \max _{x} f(x, y)+\min _{y} \min _{x} f(x, y)$. None of the above.
admin
asked
in
Calculus
Dec 5, 2022
by
admin
41.3k
points
6
views
tifr2011
calculus
maxima-minima
1
vote
0
answers
84
TIFR ECE 2011 | Question: 9
Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1,1]$. The probability that $X^{2}+Y^{2}>1$ is $\pi / 4$ $1-\pi / 4$ $\pi / 2-1$ Probability that $X^{2}+Y^{2}<0.5$ None of the above
admin
asked
in
Probability and Statistics
Dec 5, 2022
by
admin
41.3k
points
7
views
tifr2011
probability-and-statistics
probability
probability-density-function
1
vote
0
answers
85
TIFR ECE 2011 | Question: 10
Let $f(x)=|x|$, for $x \in(-\infty, \infty)$. Then $f(x)$ is not continuous but differentiable. $f(x)$ is continuous and differentiable. $f(x)$ is continuous but not differentiable. $f(x)$ is neither continuous nor differentiable. None of the above.
admin
asked
in
Calculus
Dec 5, 2022
by
admin
41.3k
points
8
views
tifr2011
calculus
continuity-and-differentiability
1
vote
0
answers
86
TIFR ECE 2011 | Question: 11
What is the value of $\lambda$ such that $\operatorname{Prob}\{X>\operatorname{mean}\{X\}\}=1 / e$, where $\text{PDF}$ of $X$ is $p_{X}(x)=\lambda e^{-\lambda x}, x \geq 0, \lambda>0?$ $1$ $1 / e$ $1 / \sqrt{e}$ $1 / e^{2}$ All of the above
admin
asked
in
Probability and Statistics
Dec 5, 2022
by
admin
41.3k
points
6
views
tifr2011
probability-and-statistics
probability
poisson-distribution
1
vote
0
answers
87
TIFR ECE 2011 | Question: 12
Consider two communication systems $C_{1}$ and $C_{2}$ that use pulse amplitude modulation $\text{(PAM)}$, $P A M_{1}$ and $P A M_{2}$. Let the distance between any two points of $P A M_{1}$ be $d$, and $P A M_{2}$ be $2 d$, respectively. Assume that $C_{1}$ ... $P_{1}=P_{2}$. $P_{1} < P_{2}$ $P_{1}>P_{2}$. $P_{1}=P_{2}+\frac{1}{2}$ None of the above.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
11
views
tifr2011
1
vote
0
answers
88
TIFR ECE 2011 | Question: 13
If $a_k$ is an increasing function of $k$, i.e. $a_1<a_2<\ldots<a_k \ldots$. Then which of the following is $\text{TRUE.}$ $\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{1}{a_{k}}=\infty$ ... . Either $(a)$ or $(b)$. $\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{1}{a_{k}}=0$. None of the above.
admin
asked
in
Calculus
Dec 5, 2022
by
admin
41.3k
points
8
views
tifr2011
calculus
limits
1
vote
0
answers
89
TIFR ECE 2011 | Question: 14
In household electrical wiring which configuration is used to connect different electrical equipments. Series. Parallel Combination of series and parallel. Any of the above. None of the above.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
11
views
tifr2011
1
vote
0
answers
90
TIFR ECE 2011 | Question: 15
Consider a channel where $x_{n} \in\{0,1\}$ is the input and $y_{n}=x_{n} * z_{n}$ is the output, where $*$ is $\text{EX-OR}$ operation, and $P\left(z_{n}=x_{n-1}\right)=P\left(z_{n}=y_{n-1}\right)=\frac{1}{2}$ ... $\frac{1}{2}.$ $1$. $<1.$ $\geq 0.$ Both $(c)$ and $(d)$.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
10
views
tifr2011
1
vote
0
answers
91
TIFR ECE 2011 | Question: 16
Consider a triangular shaped pulse $x$ of base $2 T$ and unit height centered at $0$ , i.e. $x(t)=0$ for $|t|>T, x(t)=1-|t|$ for $t \in[-T, T]$. Then if $x$ is convolved with itself, the output is Square shape. Triangular shape. Bell shape. Inverted $\text{U}$ shape. None of the above.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
10
views
tifr2011
1
vote
0
answers
92
TIFR ECE 2011 | Question: 17
Let $x[n]$ and $y[n]$ be the input and output of a linear time invariant $\text{(LTI)}$ system. Then which of following system is $\text{LTI}$. $z[n]=y[n]+c$ for a constant $c$. $z[n]=x[n] y[n]$. $z[n]=y[n]+x[n]+c$ for a constant $c$. $z[n]=y[n]+x[n]$. None of the above.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
12
views
tifr2011
1
vote
0
answers
93
TIFR ECE 2011 | Question: 18
Which of the following statements is TRUE. The cascade of a non-causal linear time invariant $\text{(LTI)}$ system with a causal $\text{LTI}$ system can be causal. If $h[n] \leq 2$ for all $n$, then the $\text{LTI}$ system with $h[n]$ as its impulse response is stable and ... $u[n]=1, n \geq 0, u[n]=0, n<0$, the $\text{LTI}$ system is stable. Both $(c)$ and $(d)$.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
7
views
tifr2011
1
vote
0
answers
94
TIFR ECE 2011 | Question: 19
Let $R_{X}(\tau)$ be the autocorrelation function of a zero mean stationary random process $X(t)$. Which of following statements is FALSE. If $R_{X}(\tau)=0, \forall \tau, X(n)$ and $X(m), n \neq m$ are independent. $R_{X}(\tau)=R_{X}(-\tau)$. $R_{X}(0)=E\left[X^{2}\right]$, where $E$ denotes the expectation. $R_{X}(0) \geq R_{X}(\tau), \forall \tau.$ None of the above.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
9
views
tifr2011
1
vote
0
answers
95
TIFR ECE 2011 | Question: 20
Let $x(t)$ be a signal whose Fourier transform $X(f)$ is zero for $|f|>W$. Using a sampler with sampling frequency $4 W$, which of the following filters can be used to exactly reconstruct $x(t)$ ... $\text{[-3W} \;5 \mathrm{W}]$. All the above. None of the above.
admin
asked
in
Others
Dec 5, 2022
by
admin
41.3k
points
8
views
tifr2011
1
vote
0
answers
96
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
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
16
views
tifr2010
1
vote
0
answers
97
TIFR ECE 2010 | Question: 2
For $x \in[0, \pi / 2], \alpha$ for which $\sin (x) \geq x-\alpha x^{3}$ is $\alpha>1 /(2 \pi)$ $\alpha \geq 1 / 6$ $\alpha \leq 1 /(2 \pi)$ $\alpha=1 / 4$ None of the above
admin
asked
in
Calculus
Dec 1, 2022
by
admin
41.3k
points
10
views
tifr2010
calculus
maxima-minima
1
vote
0
answers
98
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 $1 /(2 \alpha)$ $\exp (1-\alpha)$ $1 / \alpha$ $1 / \alpha^{2}$ $1 / \alpha^{3}$
admin
asked
in
Probability and Statistics
Dec 1, 2022
by
admin
41.3k
points
9
views
tifr2010
probability-and-statistics
probability
probability-density-function
1
vote
0
answers
99
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
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
9
views
tifr2010
1
vote
0
answers
100
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
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
11
views
tifr2010
1
vote
0
answers
101
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
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
8
views
tifr2010
1
vote
0
answers
102
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.
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
12
views
tifr2010
1
vote
0
answers
103
TIFR ECE 2010 | Question: 8
Consider a discrete time channel with binary inputs and binary outputs. Let $x_{n}$ denote the input bit at time $n$ and $y_{k}$ denote the output bit at time $\text{k}$. The channel operation is such that to produce the output $y_{n}$ it drops one ... we do not make any error If $R<1 / 2$, then there exists a scheme with zero error All of the above None of the above
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
17
views
tifr2010
1
vote
0
answers
104
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 $Y(z)=z(X(z)-X(-z)) / 2$ ... $Y(z)=z(X(\sqrt{z})-X(-\sqrt{z})) / 2$ $Y(z)=(X(\sqrt{z})-X(-\sqrt{z})) / 2$
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
8
views
tifr2010
1
vote
0
answers
105
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
admin
asked
in
Linear Algebra
Dec 1, 2022
by
admin
41.3k
points
9
views
tifr2010
linear-algebra
matrices
1
vote
0
answers
106
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
admin
asked
in
Linear Algebra
Dec 1, 2022
by
admin
41.3k
points
9
views
tifr2010
linear-algebra
matrices
1
vote
0
answers
107
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
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
10
views
tifr2010
1
vote
0
answers
108
TIFR ECE 2010 | Question: 13
Output of a linear system with input $x(t)$ is given by \[ y(t)=\int_{-\infty}^{\infty} h(t, \tau) x(\tau) . \] The system is time invariant if $h(t, \tau)=h(t-\tau)$ $h(t, \tau)=h(\tau)$ $h(t, \tau)=h(t)$ $h(t, \tau)=$ constant $h(t, \tau)$ is a continuous function of $t$
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
12
views
tifr2010
1
vote
0
answers
109
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 $n \geq 0$, let \[ Y_{n}=\operatorname{sign}\left(X(n)-Z_{n}\right), \] where $Z_{n}=\sum_{k \leq n} Y_{k}, Z_{0}=0, X(t)=t$ ... $1$'s, followed by $-1,1,-1,1, \ldots$. $0,1,-1,1,-1, \ldots$ $0,1,1,1,-1,1,-1,1, \ldots$ None of the above
admin
asked
in
Others
Dec 1, 2022
by
admin
41.3k
points
8
views
tifr2010
1
vote
0
answers
110
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
admin
asked
in
Complex Analysis
Dec 1, 2022
by
admin
41.3k
points
8
views
tifr2010
complex-analysis
complex-number
1
vote
0
answers
111
TIFR ECE 2010 | Question: 16
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. The probability that $\text{X + Y}>1.5$ is $1 / 4$ $1 / 8$ $1 / 3$ $\operatorname{Pr}\{\text{X + Y} <0.25\}$ None of the above
admin
asked
in
Probability and Statistics
Dec 1, 2022
by
admin
41.3k
points
11
views
tifr2010
probability-and-statistics
probability
probability-density-function
1
vote
0
answers
112
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 $0$ $\infty$ $a_{k}$ $a_{1}$ $\left(\sum_{i=1}^{k} a_{k}\right) / k$
admin
asked
in
Calculus
Dec 1, 2022
by
admin
41.3k
points
13
views
tifr2010
calculus
limits
1
vote
0
answers
113
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
admin
asked
in
Quantitative Aptitude
Dec 1, 2022
by
admin
41.3k
points
12
views
tifr2010
quantitative-aptitude
inequality
1
vote
0
answers
114
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
admin
asked
in
Quantitative Aptitude
Dec 1, 2022
by
admin
41.3k
points
11
views
tifr2010
quantitative-aptitude
sets
1
vote
0
answers
115
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
admin
asked
in
Calculus
Dec 1, 2022
by
admin
41.3k
points
13
views
tifr2010
calculus
derivatives
1
vote
0
answers
116
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 $n \rightarrow \infty$
admin
asked
in
Probability and Statistics
Nov 30, 2022
by
admin
41.3k
points
12
views
tifrece2022
probability-and-statistics
probability
random-variable
expectation
1
vote
0
answers
117
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? $9 / 16$ $1 / 3$ $1 / 2$ $5 / 8$ $7 / 12$
admin
asked
in
Probability and Statistics
Nov 30, 2022
by
admin
41.3k
points
10
views
tifrece2022
probability-and-statistics
probability
independent-events
1
vote
0
answers
118
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
admin
asked
in
Others
Nov 30, 2022
by
admin
41.3k
points
9
views
tifrece2022
1
vote
0
answers
119
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 $0 \leq x \leq y \leq 1$. $0$ $2$ $1 / 2$ $1 / 4$ $1$
admin
asked
in
Calculus
Nov 30, 2022
by
admin
41.3k
points
11
views
tifrece2022
calculus
maxima-minima
1
vote
0
answers
120
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: $5+\pi$ $4+\pi$ $3+\pi$ $2+\pi$ $1+\pi$
admin
asked
in
Vector Analysis
Nov 30, 2022
by
admin
41.3k
points
11
views
tifrece2022
vector-analysis
vector-in-planes
Page:
« prev
1
2
3
4
5
6
...
74
next »
Welcome to GO Electronics, where you can ask questions and receive answers from other members of the community.