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
0
votes
0
answers
81
GATE ECE 2023 | Question: 21
The signal-to-noise ratio $\mathrm{SNR}$ of an $\mathrm{ADC}$ with a full-scale sinusoidal input is given to be $61.96 \mathrm{~dB}$. The resolution of the $\mathrm{ADC}$ is_____________bits (rounded off to the nearest integer).
The signal-to-noise ratio $\mathrm{SNR}$ of an $\mathrm{ADC}$ with a full-scale sinusoidal input is given to be $61.96 \mathrm{~dB}$. The resolution of the $\mathrm{ADC}$...
admin
46.4k
points
352
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
82
GATE ECE 2023 | Question: 22
In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).
In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).
admin
46.4k
points
194
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
83
GATE ECE 2023 | Question: 23
For the two port network shown below, the $[\mathrm{Y}] – $parameters is given as $[Y]=\frac{1}{100}\left[\begin{array}{cc}2 & -1 \\ -1 & 4 / 3\end{array}\right] S$ The value of load impedance $\mathrm{Z}_{\mathrm{L},}$ in $\Omega$, for maximum power transfer will be ____________ (rounded off to the nearest integer).
For the two port network shown below, the $[\mathrm{Y}] – $parameters is given as$$[Y]=\frac{1}{100}\left[\begin{array}{cc}2 & -1 \\ -1 & 4 / 3\end{array}\right] S$$The...
admin
46.4k
points
528
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
2
votes
0
answers
84
GATE ECE 2023 | Question: 24
For the circuit shown below, the propagation delay of each $ \mathrm{NAND}$ gate is $1 \mathrm{~ns}$. The critical path delay, in $\text{ns,}$ is______________(rounded off to the nearest integer).
For the circuit shown below, the propagation delay of each $ \mathrm{NAND}$ gate is $1 \mathrm{~ns}$. The critical path delay, in $\text{ns,}$ is______________(rounded of...
admin
46.4k
points
427
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
85
GATE ECE 2023 | Question: 25
In the circuit shown below, switch $\mathrm{S}$ was closed for a long time. If the switch is opened at $t=0$, the maximum magnitude of the voltage $\mathrm{V}_{\mathrm{R}}, \text{in volts,}$ is_____________ (rounded off to the nearest integer).
In the circuit shown below, switch $\mathrm{S}$ was closed for a long time. If the switch isopened at $t=0$, the maximum magnitude of the voltage $\mathrm{V}_{\mathrm{R}}...
admin
46.4k
points
131
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
86
GATE ECE 2023 | Question: 26
A random variable $\mathrm{X}$, distributed normally as $\mathrm{N(0,1)}$ undergoes the transformation $\mathrm{Y}=\mathrm{h}(\mathrm{X})$, given in the figure. The form of the probability density function of $\mathrm{Y}$ is (In the options given below, $a, b, c$ are non-zero ... $a \delta(y+2)+b \delta(y)+c \delta(y-2)+g(y)$ $a \delta(y+2)+b \delta(y-2)+g(y)$
A random variable $\mathrm{X}$, distributed normally as $\mathrm{N(0,1)}$ undergoes the transformation$\mathrm{Y}=\mathrm{h}(\mathrm{X})$, given in the figure. The form o...
admin
46.4k
points
270
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
87
GATE ECE 2023 | Question: 27
The value of the line integral $\int_{P}^{Q}\left(z^{2} d x+3 y^{2} d y+2 x z \; d z\right)$ along the straight line joining the points $P(1,1,2)$ and $Q(2,3,1)$ is $20$ $24$ $29$ $-5$
The value of the line integral $\int_{P}^{Q}\left(z^{2} d x+3 y^{2} d y+2 x z \; d z\right)$ along the straight line joining the points $P(1,1,2)$ and $Q(2,3,1)$ is$20$$2...
admin
46.4k
points
239
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
88
GATE ECE 2023 | Question: 29
The $\frac{V_{\text {OUT }}}{V_{\text {IN }}}$ of the circuit shown below is $-\frac{\mathrm{R}_4}{\mathrm{R}_3}$ $\frac{\mathrm{R}_4}{\mathrm{R}_3}$ $1+\frac{\text{R}_4}{\text{R}_3}$ $1-\frac{\mathrm{R}_4}{\mathrm{R}_3}$
The $\frac{V_{\text {OUT }}}{V_{\text {IN }}}$ of the circuit shown below is$-\frac{\mathrm{R}_4}{\mathrm{R}_3}$$\frac{\mathrm{R}_4}{\mathrm{R}_3}$$1+\frac{\text{R}_4}{\t...
admin
46.4k
points
161
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
1
votes
0
answers
89
GATE ECE 2023 | Question: 30
In the circuit shown below, $D_1$ and $D_2$ are silicon diodes with cut-in voltage of $0.7 \mathrm{~V}$. $\mathrm{V}_{\mathrm{IN}}$ and $\mathrm{V}_{\mathrm{OUT}}$ are input and output voltages in volts. The transfer characteristic is
In the circuit shown below, $D_1$ and $D_2$ are silicon diodes with cut-in voltage of $0.7 \mathrm{~V}$. $\mathrm{V}_{\mathrm{IN}}$ and $\mathrm{V}_{\mathrm{OUT}}$ are in...
admin
46.4k
points
246
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
90
GATE ECE 2023 | Question: 31
A closed loop system is shown in the figure where $\mathrm{k}>0$ and $\alpha>0$. The steady state error due to a ramp input $\left(\mathrm{R}(\mathrm{s})=\alpha / \mathrm{s}^2\right)$ is given by $\frac{2 \alpha}{\mathrm{k}}$ $\frac{\alpha}{\mathrm{k}}$ $\frac{\alpha}{2 \mathrm{k}}$ $\frac{\alpha}{4 \mathrm{k}}$
A closed loop system is shown in the figure where $\mathrm{k}>0$ and $\alpha>0$. The steady state error due to a ramp input $\left(\mathrm{R}(\mathrm{s})=\alpha / \mathrm...
admin
46.4k
points
132
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
91
GATE ECE 2023 | Question: 32
In the following block diagram, $\mathrm{R}(\mathrm{s})$ and $\mathrm{D}(\mathrm{s})$ are two inputs. The output $\mathrm{Y}(\mathrm{s})$ is expressed as $Y(s)=G_1(s) R(s)+G_2(s) D(s)$. $\mathrm{G}_1(\mathrm{~s})$ and $\mathrm{G}_2(\mathrm{~s})$ ...
In the following block diagram, $\mathrm{R}(\mathrm{s})$ and $\mathrm{D}(\mathrm{s})$ are two inputs. The output $\mathrm{Y}(\mathrm{s})$ is expressed as $Y(s)=G_1(s) R(s...
admin
46.4k
points
97
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
92
GATE ECE 2023 | Question: 33
The state equation of a second order system is $\dot{\boldsymbol{x}}(t)=\mathrm{A} \boldsymbol{x}(t), \; \boldsymbol{x}(0)$ is the initial condition. Suppose $\lambda_1$ and $\lambda_2$ are two distinct eigenvalues of $\mathrm{A}$ and $v_1$ and $v_2$ are ... $\sum_{i=1}^2 \alpha_i e^{4 \lambda_i \mathrm{t}} \boldsymbol{v}_i$
The state equation of a second order system is$\dot{\boldsymbol{x}}(t)=\mathrm{A} \boldsymbol{x}(t), \; \boldsymbol{x}(0)$ is the initial condition.Suppose $\lambda_1$ an...
admin
46.4k
points
91
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
93
GATE ECE 2023 | Question: 34
The switch $\mathrm{S}_{1}$ was closed and $\mathrm{S}_{2}$ was open for a long time. At $t=0$, switch $\mathrm{S}_{1}$ is opened and $\mathrm{S}_{2}$ is closed, simultaneously. The value of $\mathrm{i}_{\mathrm{c}}\left(0^{+}\right)$, in amperes, is $1$ $-1$ $0.2$ $0.8$
The switch $\mathrm{S}_{1}$ was closed and $\mathrm{S}_{2}$ was open for a long time. At $t=0$, switch $\mathrm{S}_{1}$ is opened and $\mathrm{S}_{2}$ is closed, simultan...
admin
46.4k
points
93
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
94
GATE ECE 2023 | Question: 35
Let a frequency modulated $\text{(FM)}$ signal $x(t)=A \cos \left(\omega_{c} t+k_{f} \int_{-\infty}^{t} m(\lambda) d \lambda\right)$, where $m(t)$ is a message signal of bandwidth $\text{W.}$ ... to recover $x(t)$ from $y(t)$ is $B_{T}+W$ $\frac{3}{2} B_{T}$ $2 B_{T}+W$ $\frac{5}{2} B_{T}$
Let a frequency modulated $\text{(FM)}$ signal$x(t)=A \cos \left(\omega_{c} t+k_{f} \int_{-\infty}^{t} m(\lambda) d \lambda\right)$, where $m(t)$ is a message signal of b...
admin
46.4k
points
86
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
95
GATE ECE 2023 | Question: 36
The $\text{h}$-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain $\frac{\mathrm{V}_{\text {out }}}{\mathrm{V}_{\mathrm{s}}}$ is $\mathrm{h}_{11}=0, \mathrm{~h}_{12}=0, \mathrm{~h}_{21}=$ ... $\mathrm{h}_{11}=0, \mathrm{~h}_{12}=0, \mathrm{~h}_{21}=$ very high and $\mathrm{h}_{22}=$ very high
The $\text{h}$-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain $\frac{\mathrm{V}_{\text {out }}}{\mathrm{V}_{\ma...
admin
46.4k
points
93
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
96
GATE ECE 2023 | Question: 37
Consider a discrete-time periodic signal with period $N=5$. Let the discrete-time Fourier series $\text{(DTFS}$) representation be $x[n]=\sum_{k=0}^4 a_k e^{\frac{j k 2 \pi n}{5}}$, where $a_0=1, a_1=$ $3 j, a_2=2 j, a_3=-2 j$ and $a_4=-3 j$. The value of the sum $\sum_{n=0}^4 x[n] \sin \frac{4 \pi n}{5}$ is $-10$ $10$ $-2$ $2$
Consider a discrete-time periodic signal with period $N=5$. Let the discrete-time Fourier series $\text{(DTFS}$) representation be $x[n]=\sum_{k=0}^4 a_k e^{\frac{j k 2 \...
admin
46.4k
points
100
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
97
GATE ECE 2023 | Question: 38
Let an input $x[n]$ having discrete-time Fourier transform $X\left(e^{j \Omega}\right)=1-e^{-j \Omega}+2 e^{-3 j \Omega}$ be passed through an LTI system. The frequency response of the LTI system is $H\left(e^{j \Omega}\right)=1-\frac{1}{2} e^{-j 2 \Omega}$. The ... $\delta[n]+\delta[n-1]+\frac{1}{2} \delta[n-2]+\frac{5}{2} \delta[n-3]+\delta[n-5]$
Let an input $x[n]$ having discrete-time Fourier transform$X\left(e^{j \Omega}\right)=1-e^{-j \Omega}+2 e^{-3 j \Omega}$ be passed through an LTI system. The frequency re...
admin
46.4k
points
102
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
98
GATE ECE 2023 | Question: 39
Let $x(t)=10 \cos (10.5 W t)$ be passed through an LTI system having impulse response $h(t)=\pi\left(\frac{\sin W t}{\pi t}\right)^{2} \cos 10 Wt$. The output of the system is $\left(\frac{15 W}{4}\right) \cos (10.5 W t)$ $\left(\frac{15 W}{2}\right) \cos (10.5 W t)$ $\left(\frac{15 W}{8}\right) \cos (10.5 W t)$ $(15 W) \cos (10.5 W t)$
Let $x(t)=10 \cos (10.5 W t)$ be passed through an LTI system having impulse response $h(t)=\pi\left(\frac{\sin W t}{\pi t}\right)^{2} \cos 10 Wt$. The output of the sys...
admin
46.4k
points
98
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
99
GATE ECE 2023 | Question: 40
Let $\mathrm{x}_1(\mathrm{t})$ and $\mathrm{x}_2(\mathrm{t})$ be two band-limited signals having bandwidth $B=4 \pi \times 10^3 \; \mathrm{rad} / \mathrm{s}$ each. In the figure below, the Nyquist sampling frequency, in $\mathrm{rad} / \mathrm{s}$, required to sample $y(\mathrm{t})$, is $20 \pi \times 10^3$ $40 \pi \times 10^3$ $8 \pi \times 10^3$ $32 \pi \times 10^3$
Let $\mathrm{x}_1(\mathrm{t})$ and $\mathrm{x}_2(\mathrm{t})$ be two band-limited signals having bandwidth $B=4 \pi \times 10^3 \; \mathrm{rad} / \mathrm{s}$ each. In the...
admin
46.4k
points
99
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
100
GATE ECE 2023 | Question: 41
The $S$-parameters of a two-port network is given as $ [S]=\left[\begin{array}{ll} S_{11} & S_{12} \\ S_{21} & S_{22} \end{array}\right] $ with reference to $Z_0$. Two lossless transmission line sections of electrical lengths $\theta_1=\beta l_1$ ...
The $S$-parameters of a two-port network is given as$$[S]=\left[\begin{array}{ll}S_{11} & S_{12} \\S_{21} & S_{22}\end{array}\right]$$with reference to $Z_0$. Two lossles...
admin
46.4k
points
100
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
101
GATE ECE 2023 | Question: 42
The standing wave ratio on a $50 \; \Omega$ lossless transmission line terminated in an unknown load impedance is found to be $2.0$. The distance between successive voltage minima is $30 \mathrm{~cm}$ and the first minimum is located at $10 \mathrm{~cm}$ ... $R_m=100 \; \Omega, l_m=5 \mathrm{~cm}$ $R_m=25 \; \Omega, l_m=5 \mathrm{~cm}$
The standing wave ratio on a $50 \; \Omega$ lossless transmission line terminated in an unknown load impedance is found to be $2.0$. The distance between successive volta...
admin
46.4k
points
97
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
102
GATE ECE 2023 | Question: 43
The electric field of a plane electromagnetic wave is $\boldsymbol{E}=\boldsymbol{a}_{x} C_{1 x} \cos (\omega t-\beta z)+\boldsymbol{a}_{y} C_{1 y} \cos (\omega t-\beta z+\theta) \quad \mathrm{V} / \mathrm{m}$. Which of the following combination(s) will give rise to a left handed ... $C_{1 x}=1, C_{1 y}=2, \theta=3 \pi / 2$ $C_{1 x}=2, C_{1 y}=1, \theta=3 \pi / 4$
The electric field of a plane electromagnetic wave is$\boldsymbol{E}=\boldsymbol{a}_{x} C_{1 x} \cos (\omega t-\beta z)+\boldsymbol{a}_{y} C_{1 y} \cos (\omega t-\beta z+...
admin
46.4k
points
107
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
103
GATE ECE 2023 | Question: 44
The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are
The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are
admin
46.4k
points
78
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
104
GATE ECE 2023 | Question: 46
In an extrinsic semiconductor, the hole concentration is given to be $1.5 n_{i}$ where $n_{i}$ is the intrinsic carrier concentration of $1 \times 10^{10} \mathrm{~cm}^{-3}$. The ratio of electron to hole mobility for equal hole and electron drift current is given as ________ (rounded off to two decimal places).
In an extrinsic semiconductor, the hole concentration is given to be $1.5 n_{i}$ where $n_{i}$ is the intrinsic carrier concentration of $1 \times 10^{10} \mathrm{~cm}^{-...
admin
46.4k
points
127
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
105
GATE ECE 2023 | Question: 47
The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $(s)=\frac{k(s+z)^{a}}{s^{b}(s+p)^{c}}$, where $k, z, p, a, b$ and $c$ are positive constants. The value of $(a+b+c)$ is ____________ (rounded off to the nearest integer).
The asymptotic magnitude Bode plot of a minimum phase system is shown in thefigure. The transfer function of the system is $(s)=\frac{k(s+z)^{a}}{s^{b}(s+p)^{c}}$, where ...
admin
46.4k
points
84
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
106
GATE ECE 2023 | Question: 48
Let $\mathrm{x}_1(\mathrm{t})=\mathrm{u}(\mathrm{t}+1.5)-\mathrm{u}(\mathrm{t}-1.5)$ and $\mathrm{x}_2(\mathrm{t})$ is shown in the figure below. For $\mathrm{y}(\mathrm{t})=\mathrm{x}_1(\mathrm{t}) * \mathrm{x}_2(\mathrm{t})$, the $\int_{-\infty}^{\infty} \mathrm{y}(\mathrm{t}) \mathrm{dt}$ is ______________ (rounded off to the nearest integer).
Let $\mathrm{x}_1(\mathrm{t})=\mathrm{u}(\mathrm{t}+1.5)-\mathrm{u}(\mathrm{t}-1.5)$ and $\mathrm{x}_2(\mathrm{t})$ is shown in the figure below. For $\mathrm{y}(\mathrm{...
admin
46.4k
points
77
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
107
GATE ECE 2023 | Question: 49
Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2} \mathrm{~W} / \mathrm{Hz}$. If $X(t)$ is input to an LTI system with impulse response $e^{-t} u(t)$. The average power of the system output is _____________ $\mathrm{W}$ (rounded off to two decimal places).
Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2} \mathrm{~W} / \mathrm{Hz}$. If $X(t)$ is input to an LTI system with impulse response $e^{-t...
admin
46.4k
points
91
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
108
GATE ECE 2023 | Question: 50
A transparent dielectric coating is applied to glass $\left(\varepsilon_r=4, \mu_r=1\right)$ to eliminate the reflection of red light $\left(\lambda_0=0.75 \; \mu \mathrm{m}\right)$. The minimum thickness of the dielectric coating, in $\mu \mathrm{m}$, that can be used is_____________(rounded off to two decimal places).
A transparent dielectric coating is applied to glass $\left(\varepsilon_r=4, \mu_r=1\right)$ to eliminate the reflection of red light $\left(\lambda_0=0.75 \; \mu \mathrm...
admin
46.4k
points
296
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
109
GATE ECE 2023 | Question: 51
In a semiconductor device, the Fermi-energy level is $0.35 \; \mathrm{eV}$ above the valence band energy. The effective density of states in the valence band at $T=300 \mathrm{~K}$ is $1 \times 10^{19} \mathrm{~cm}^{-3}$. The thermal equilibrium hole ... $\mathrm{kT}$ at $300 \mathrm{~K}$ is $0.026 \; \mathrm{eV}$.
In a semiconductor device, the Fermi-energy level is $0.35 \; \mathrm{eV}$ above the valence band energy. The effective density of states in the valence band at $T=300 \m...
admin
46.4k
points
102
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
110
GATE ECE 2023 | Question: 52
A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of $1 \; \mu \mathrm{s}$. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of $1 \mathrm{~V}$ with $12$-bit accuracy is ___________ $\mu \mathrm{s}$ (rounded off to two decimal places).
A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of $1 \; \mu \mathrm{s}$. The time for the sampling switch to stay ...
admin
46.4k
points
83
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
111
GATE ECE 2023 | Question: 54
In the circuit below, the voltage $V_L$ is _________ $\mathrm{V}$ (rounded off to two decimal places).
In the circuit below, the voltage $V_L$ is _________ $\mathrm{V}$ (rounded off to two decimal places).
admin
46.4k
points
135
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
112
GATE ECE 2023 | Question: 55
The frequency of occurrence of $8$ symbols $(a-h)$ is shown in the table below. A symbol is chosen and it is determined by asking a series of $\text{"yes/no"}$ questions which are assumed to be truthfully answered. The average number of questions when asked in the most ... $\frac{1}{16}$ $\frac{1}{32}$ $\frac{1}{64}$ $\frac{1}{128}$ $\frac{1}{128}$
The frequency of occurrence of $8$ symbols $(a-h)$ is shown in the table below. A symbol is chosen and it is determined by asking a series of $\text{"yes/no"}$ questions ...
admin
46.4k
points
114
views
admin
asked
May 20, 2023
Others
gateece-2023
+
–
0
votes
0
answers
113
TIFR ECE 2023 | Question: 1
Consider a fair coin with probability of heads and tails equal to $1 / 2$. Moreover consider two dice, first $\mathrm{D}_{1}$ that has three faces numbered $1,3,5$ and second $\mathrm{D}_{2}$ that has three faces numbered $2,4,6$ ... dice in the experiment. What is $\mathbb{E}[X]$ ? $\frac{7}{2}$ $4$ $3$ $\frac{9}{2}$ None of the above
Consider a fair coin with probability of heads and tails equal to $1 / 2$. Moreover consider two dice, first $\mathrm{D}_{1}$ that has three faces numbered $1,3,5$ and se...
admin
46.4k
points
306
views
admin
asked
Mar 14, 2023
Probability and Statistics
tifrece2023
probability
+
–
0
votes
0
answers
114
TIFR ECE 2023 | Question: 2
$\begin{array}{rlr}a^*=\max_{x, y} & x^2+y^2-8 x+7 \\ \text { s.t. } & \qquad x^2+y^2 \leq 1 \\ & \qquad \qquad y \geq 0\end{array}$ Then $a^{\star}$ is $16$ $14$ $12$ $10$ None of the above
$\begin{array}{rlr}a^*=\max_{x, y} & x^2+y^2-8 x+7 \\ \text { s.t. } & \qquad x^2+y^2 \leq 1 \\ & \qquad \qquad y \geq 0\end{array}$Then $a^{\star}$ is$16$$14$$12$$10$Non...
admin
46.4k
points
141
views
admin
asked
Mar 14, 2023
Linear Algebra
tifrece2023
engineering-mathematics
linear-algebra
+
–
0
votes
0
answers
115
TIFR ECE 2023 | Question: 3
Let \[ \mathcal{P}=\left\{(x, y): x+y \geq 1,2 x+y \geq 2, x+2 y \geq 2,(x-1)^{2}+(y-1)^{2} \leq 1\right\} . \] Compute \[ \min _{(x, y) \in \mathcal{P}} 2 x+3 y \] $2$ $3$ $4$ $6$ None of the above
Let\[\mathcal{P}=\left\{(x, y): x+y \geq 1,2 x+y \geq 2, x+2 y \geq 2,(x-1)^{2}+(y-1)^{2} \leq 1\right\} .\]Compute\[\min _{(x, y) \in \mathcal{P}} 2 x+3 y\]$2$$3$$4$$6$N...
admin
46.4k
points
275
views
admin
asked
Mar 14, 2023
Others
tifrece2023
+
–
0
votes
0
answers
116
TIFR ECE 2023 | Question: 4
Recall that the entropy (in bits) of a random variable $\mathrm{X}$ which takes values in $\mathbb{N}$, the set of natural numbers, is defined as $H(X)=\sum_{n=1}^{\infty} p_{n} \log _{2} \frac{1}{p_{n}},$ ... variable which denotes the number of tosses made. What is the entropy of $\mathrm{X}$ in bits? $1$ $2$ $4$ Infinity None of the above
Recall that the entropy (in bits) of a random variable $\mathrm{X}$ which takes values in $\mathbb{N}$, the set of natural numbers, is defined as$$H(X)=\sum_{n=1}^{\infty...
admin
46.4k
points
143
views
admin
asked
Mar 14, 2023
Others
tifrece2023
+
–
0
votes
0
answers
117
TIFR ECE 2023 | Question: 5
Let $\mathrm{B}$ denote the unit ball in $\mathbb{R}^{2}$, and $\mathrm{Q}$ a square of side length $2$. Let $\mathrm{K}$ be the set of all vectors $z$ such that for some $x \in \mathrm{B}$ and some $y \in \mathrm{Q}, z=x+y$. The area of $\mathrm{K}$ is $4+\pi$ $6+\pi$ $8+\pi$ $10+\pi$ $12+\pi$
Let $\mathrm{B}$ denote the unit ball in $\mathbb{R}^{2}$, and $\mathrm{Q}$ a square of side length $2$. Let $\mathrm{K}$ be the set of all vectors $z$ such that for some...
admin
46.4k
points
119
views
admin
asked
Mar 14, 2023
Others
tifrece2023
+
–
0
votes
0
answers
118
TIFR ECE 2023 | Question: 6
An ant in the plane travels in a spiral such that its position $(x(t), y(t))$ at time $t \geq 0$ is $\left(e^{t} \cos t, e^{t} \sin t\right)$. At time $t=1$, find the real part of $\ln (x(t)+i y(t))$. $-2$ $1$ $0$ $-1$ $2$
An ant in the plane travels in a spiral such that its position $(x(t), y(t))$ at time $t \geq 0$ is $\left(e^{t} \cos t, e^{t} \sin t\right)$. At time $t=1$, find the rea...
admin
46.4k
points
121
views
admin
asked
Mar 14, 2023
Others
tifrece2023
+
–
0
votes
0
answers
119
TIFR ECE 2023 | Question: 7
Let $f(x)$ be a positive continuous function on the real line that is the density of a random variable $X$. The differential entropy of $X$ is defined to be $-\int_{-\infty}^{\infty} f(x) \ln f(x) d x$. In which case does $X$ have the least differential entropy? You may use these facts: The ... $f(x):=(1 / 4) e^{-|x| / 2}$. $f(x):=e^{-2|x|}$.
Let $f(x)$ be a positive continuous function on the real line that is the density of a random variable $X$. The differential entropy of $X$ is defined to be $-\int_{-\inf...
admin
46.4k
points
120
views
admin
asked
Mar 14, 2023
Probability and Statistics
tifrece2023
engineering-mathematics
probability-and-statistics
+
–
0
votes
0
answers
120
TIFR ECE 2023 | Question: 8
Suppose a bag contains $5$ red balls, $3$ blue balls, and $2$ black balls. Balls are drawn without replacement until the bag is empty. Let $X_{i}$ be a random variable which takes value $1$ if the $i$-th ball drawn is red, value $2$ if that ball is blue, and $3$ if it is ... $\text{(i), (ii),}$ and $\text{(iii)}$ None of $\text{(i), (ii),}$ or $\text{(iii)}$
Suppose a bag contains $5$ red balls, $3$ blue balls, and $2$ black balls. Balls are drawn without replacement until the bag is empty. Let $X_{i}$ be a random variable wh...
admin
46.4k
points
131
views
admin
asked
Mar 14, 2023
Probability and Statistics
tifrece2023
engineering-mathematics
probability
+
–
Page:
« prev
1
2
3
4
5
6
...
75
next »
GO Electronics
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register