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TIFR ECE 2012 | Question: 18
Under a certain coordinate transformation from $(x, y)$ to $(u, v)$ the circle $x^{2}+y^{2}=1$ shown below on the left side was transformed into the ellipse shown on the right side. If the transformation is of the form \[ \left[\begin{array}{l} u \\ v \end{array}\right]=\mathbf{A}\ ... \] $A_{1}$ only $A_{2}$ only $A_{1}$ or $A_{2}$ $A_{1}$ or $A_{3}$ $A_{2}$ or $A_{3}$
Under a certain coordinate transformation from $(x, y)$ to $(u, v)$ the circle $x^{2}+y^{2}=1$ shown below on the left side was transformed into the ellipse shown on the ...
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46.4k
points
80
views
admin
asked
Dec 8, 2022
Linear Algebra
tifr2012
linear-algebra
matrices
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242
TIFR ECE 2012 | Question: 7
A linear time-invariant system has a transfer function $H(s)=1 /(1+s)$. If the input to the system is $\cos (t)$, the output is $\left(e^{j t}+e^{-j t}\right) / 2$ where $j=\sqrt{-1}$ $\cos (t) / 2$ $(\cos (t)+\sin (t)) / 2 \sqrt{ }$ $\sin (t) / 2$. The system is unstable and the output is not well-defined.
A linear time-invariant system has a transfer function $H(s)=1 /(1+s)$. If the input to the system is $\cos (t)$, the output is$\left(e^{j t}+e^{-j t}\right) / 2$ where $...
admin
46.4k
points
78
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admin
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Dec 8, 2022
Others
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243
TIFR ECE 2012 | Question: 11
A Poisson random variable $X$ is given by $\operatorname{Pr}\{X=k\}=\mathrm{e}^{-\lambda} \lambda^{k} / k !, k=0,1,2, \ldots$ for $\lambda>0$. The variance of $X$ scales as $\lambda$ $\lambda^{2}$ $\lambda^{3}$ $\sqrt{\lambda}$ None of the above
A Poisson random variable $X$ is given by $\operatorname{Pr}\{X=k\}=\mathrm{e}^{-\lambda} \lambda^{k} / k !, k=0,1,2, \ldots$ for $\lambda>0$. The variance of $X$ scales ...
admin
46.4k
points
75
views
admin
asked
Dec 8, 2022
Probability and Statistics
tifr2012
probability-and-statistics
probability
poisson-distribution
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244
TIFR ECE 2012 | Question: 4
The signal $x_{n}=0$ for $n<0$ and $x_{n}=a^{n} / n$ ! for $n \geq 0$. Its $z$-transform $X(z)=\sum_{n=-\infty}^{\infty} x_{n} z^{-n}$ is $1 /\left(z^{-1}-a\right)$, region of convergence $\text{(ROC)}$: $|z| \leq 1 / a$ ... $|z|>a$ Item $(a)$ if $a>1$, Item $(b)$ if $a<1$ $\exp \left(a z^{-1}\right)$, $\text{ROC}$: entire complex plane.
The signal $x_{n}=0$ for $n<0$ and $x_{n}=a^{n} / n$ ! for $n \geq 0$. Its $z$-transform $X(z)=\sum_{n=-\infty}^{\infty} x_{n} z^{-n}$ is$1 /\left(z^{-1}-a\right)$, regio...
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72
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Dec 8, 2022
Others
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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 $(d)$.
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)=...
admin
46.4k
points
169
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admin
asked
Dec 5, 2022
Others
tifr2011
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246
TIFR ECE 2011 | Question: 2
The minimum number of unit delay elements required for realizing an infinite impulse response $\text{(IIR)}$ filter is/are $0$ $1$ $\infty$. $>1$. None of the above.
The minimum number of unit delay elements required for realizing an infinite impulse response $\text{(IIR)}$ filter is/are$0$$1$$\infty$.$>1$.None of the above.
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Others
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247
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.
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} \fr...
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46.4k
points
107
views
admin
asked
Dec 5, 2022
Calculus
tifr2011
calculus
limits
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248
TIFR ECE 2011 | Question: 3
The Fourier transform of \[x(t)=\frac{t^{n-1}}{(n-1) !} \mathrm{e}^{-a t} u(t), \quad a>0\] $(\jmath=\sqrt{-1}, u(t)=1$ for $t \geq 0, u(t)=0, t<0)$ is $(a+\jmath \omega)^{n}$ $\sum_{k=1}^{n} \frac{(a+\jmath \omega)^{k}}{k !}$ $na\jmath \omega$ $\frac{1}{(a+\jmath \omega)^{n}}$ None of the above.
The Fourier transform of\[x(t)=\frac{t^{n-1}}{(n-1) !} \mathrm{e}^{-a t} u(t), \quad a>0\]$(\jmath=\sqrt{-1}, u(t)=1$ for $t \geq 0, u(t)=0, t<0)$ is$(a+\jmath \omega)^{n...
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46.4k
points
102
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admin
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Dec 5, 2022
Others
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249
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.
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 differe...
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46.4k
points
101
views
admin
asked
Dec 5, 2022
Calculus
tifr2011
calculus
continuity-and-differentiability
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1
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250
TIFR ECE 2011 | Question: 1
Output of a linear system with input $x(t)$ is given by \[y(t)=\int_{-\infty}^{\infty} h(t, \tau) x(\tau)+1.\] The system is linear if $h(t, \tau)=h(t-\tau)$ $h(t, \tau)=h(\tau)$ $h(t, \tau)=h(t)$ $h(t, \tau)=$ constant None of the above.
Output of a linear system with input $x(t)$ is given by\[y(t)=\int_{-\infty}^{\infty} h(t, \tau) x(\tau)+1.\]The system is linear if$h(t, \tau)=h(t-\tau)$$h(t, \tau)=h(\t...
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46.4k
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100
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Others
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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.
In household electrical wiring which configuration is used to connect different electrical equipments.Series.ParallelCombination of series and parallel.Any of the above.N...
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46.4k
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93
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Others
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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
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 /...
admin
46.4k
points
93
views
admin
asked
Dec 5, 2022
Probability and Statistics
tifr2011
probability-and-statistics
probability
probability-density-function
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253
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.
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...
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46.4k
points
92
views
admin
asked
Dec 5, 2022
Calculus
tifr2011
calculus
maxima-minima
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254
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.
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 ...
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46.4k
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91
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Dec 5, 2022
Others
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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
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 ...
admin
46.4k
points
90
views
admin
asked
Dec 5, 2022
Probability and Statistics
tifr2011
probability-and-statistics
probability
poisson-distribution
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256
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.
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 constan...
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46.4k
points
86
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Dec 5, 2022
Others
tifr2011
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257
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.
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 p...
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46.4k
points
86
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Dec 5, 2022
Others
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258
TIFR ECE 2011 | Question: 5
Consider a system with input $x(t)$ and the output $y(t)$ is given by \[y(t)=x(t)-0.5 x(t-1)-0.5 x(t-2)+1 .\] The system is 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\[y(t)=x(t)-0.5 x(t-1)-0.5 x(t-2)+1 .\]The system isLinearNon-causalTime varyingAll of the aboveNone ...
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46.4k
points
85
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Dec 5, 2022
Others
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259
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.
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 ex...
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46.4k
points
81
views
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Dec 5, 2022
Others
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260
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.
Assume you are using a binary code error correcting code $C$. If the minimum Hamming distance between any two codewords of $C$ is $3$. ThenWe can correct and detect $2$ b...
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46.4k
points
80
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Others
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261
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.
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,...
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46.4k
points
76
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Others
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262
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.
Let $\mathrm{H}(\mathrm{z})$ be the $z$-transform of the transfer function corresponding to an input output relation $y(n)-\frac{1}{2} y(n-1)=x(n)+\frac{1}{3} x(n-1)$. Th...
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46.4k
points
75
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Dec 5, 2022
Others
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263
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 $(d)$.
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]...
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46.4k
points
73
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Others
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264
TIFR ECE 2011 | Question: 4
Let $\lim _{n \rightarrow \infty} x_{n}=x$. Then which of the following is $\text{TRUE.}$ There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right|=0$. There exists an $n_{0}$ ... $n>n_{0},\left|\frac{x_{n}}{x}\right| \leq \epsilon$ for any $\epsilon>0$. None of the above.
Let $\lim _{n \rightarrow \infty} x_{n}=x$. Then which of the following is $\text{TRUE.}$There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right|=0$.There...
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46.4k
points
72
views
admin
asked
Dec 5, 2022
Calculus
tifr2011
calculus
limits
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265
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 $t$
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, \ta...
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46.4k
points
164
views
admin
asked
Nov 30, 2022
Others
tifr2010
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266
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...
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46.4k
points
147
views
admin
asked
Nov 30, 2022
Vector Analysis
tifrece2022
vector-analysis
vector-in-planes
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267
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...
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46.4k
points
141
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
random-variable
expectation
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0
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268
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...
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46.4k
points
129
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
probability-density-function
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269
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
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 + ...
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46.4k
points
112
views
admin
asked
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Probability and Statistics
tifr2010
probability-and-statistics
probability
probability-density-function
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270
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
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 $\text{k}$....
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46.4k
points
111
views
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Others
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271
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...
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46.4k
points
124
views
admin
asked
Nov 30, 2022
Linear Algebra
tifrece2022
linear-algebra
system-of-equations
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272
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...
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46.4k
points
108
views
admin
asked
Nov 30, 2022
Calculus
tifr2010
calculus
derivatives
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1
votes
0
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273
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$
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Others
tifrece2021
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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...
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Probability and Statistics
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probability-and-statistics
probability
conditional-probability
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1
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0
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275
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 ...
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Differential Equations
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differential-equations
first-order-differential-equation
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1
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0
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276
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,...
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Quantitative Aptitude
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quantitative-aptitude
sets
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1
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0
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277
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...
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Quantitative Aptitude
tifrece2021
quantitative-aptitude
geometry
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1
votes
0
answers
278
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...
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Others
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0
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279
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
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)$$\alpha=1 / 4$None of the above
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Calculus
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calculus
maxima-minima
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1
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0
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280
TIFR ECE 2010 | Question: 18
Under what conditions is the following inequality true for $a, b>0$ $ \log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda)) $ $\lambda=0.5$ $0<a / \lambda \leq 1, b /(1-\lambda)>0$ $a / \lambda>0,0<b /(1-\lambda) \leq 1$ All of the above None of the above
Under what conditions is the following inequality true for $a, b>0$$$\log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda))$$$\lambda=0.5$$0<a...
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Quantitative Aptitude
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quantitative-aptitude
inequality
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