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Recent questions tagged gate2006-ec
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GATE ECE 2006 | Question: 1
The rank of the matrix $\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{array}\right]$ is $0$ $1$ $2$ $3$
The rank of the matrix $\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{array}\right]$ is$0$$1$$2$$3$
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GATE ECE 2006 | Question: 2
$\nabla \times \nabla \times \mathrm{P},$ where $\mathrm{P}$ is a vector, is equal to $\mathrm{P} \times \nabla \times \mathrm{P}-\nabla^{2} \mathrm{P}$ $\nabla^{2} \text{P} +\nabla(\nabla \bullet \text{P})$ $\nabla^{2} \mathrm{P}+\nabla \times \mathrm{P}$ $\nabla(\nabla \bullet \mathrm{P})-\nabla^{2} \mathrm{P}$
$\nabla \times \nabla \times \mathrm{P},$ where $\mathrm{P}$ is a vector, is equal to$\mathrm{P} \times \nabla \times \mathrm{P}-\nabla^{2} \mathrm{P}$$\nabla^{2} \text{P...
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GATE ECE 2006 | Question: 3
$\displaystyle{}\iint(\nabla \times \mathrm{P}) \bullet \mathrm{ds},$ where $\mathrm{P}$ is a vector, is equal to $\displaystyle{}\oint \text{P} \bullet d l$ $\displaystyle{}\oint \nabla \times \nabla \times \mathrm{P} \bullet d l$ $\displaystyle{}\oint \nabla \times \mathrm{P} \bullet d l$ $\displaystyle{}\iiint \nabla \bullet \mathrm{P} d v$
$\displaystyle{}\iint(\nabla \times \mathrm{P}) \bullet \mathrm{ds},$ where $\mathrm{P}$ is a vector, is equal to$\displaystyle{}\oint \text{P} \bullet d l$$\displaystyle...
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GATE ECE 2006 | Question: 4
A probability density function is of the form $\qquad p(x)=\mathrm{Ke}^{-\alpha|x|}, x \in(-\infty, \infty)$ The value of $\text{K}$ is $0.5$ $1$ $0.5 \alpha$ $\alpha$
A probability density function is of the form$\qquad p(x)=\mathrm{Ke}^{-\alpha|x|}, x \in(-\infty, \infty)$The value of $\text{K}$ is$0.5$$1$$0.5 \alpha$$\alpha$
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GATE ECE 2006 | Question: 5
A solution for the differential equation $ \qquad \dot{x}(t)+2 x(t)=\delta(t)$ with initial condition $x(0-)=0$ is $e^{-2 t} \; u(t)$ $e^{2 t} \; u(t)$ $e^{-t} \; u(t)$ $e^{t} \; u(t)$
A solution for the differential equation$ \qquad \dot{x}(t)+2 x(t)=\delta(t)$with initial condition $x(0-)=0$ is$e^{-2 t} \; u(t)$$e^{2 t} \; u(t)$$e^{-t} \; u(t)$$e^{t} ...
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GATE ECE 2006 | Question: 6
A low-pass filter having a frequency response $\mathrm{H}(\mathrm{j} \omega)=\mathrm{A}(\omega) \;e^{j{\phi(\omega)}}$ does not produce any phase distortion, if $\mathrm{A}(\omega)=\mathrm{C}\omega^{2}, \phi(\omega)=k \omega^{3}$ ... $\mathrm{A}(\omega)=\mathrm{C}, \phi(\omega)=k \omega^{-1}$
A low-pass filter having a frequency response $\mathrm{H}(\mathrm{j} \omega)=\mathrm{A}(\omega) \;e^{j{\phi(\omega)}}$ does not produce any phase distortion, if$\mathrm{A...
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GATE ECE 2006 | Question: 7
The values of voltage $\left(\mathrm{V}_{\mathrm{D}}\right)$ across a tunnel-diode corresponding to peak and valley currents are $\text{V}_{\text{P}}$ and $\text{V}_{\text{V}}$ respectively. The range of tunnel-diode voltage $\text{V}_{\text{D}}$ for which the ... $\mathrm{V}_{\mathrm{D}} \geq \mathrm{V}_{\mathrm{V}}$
The values of voltage $\left(\mathrm{V}_{\mathrm{D}}\right)$ across a tunnel-diode corresponding to peak and valley currents are $\text{V}_{\text{P}}$ and $\text{V}_{\tex...
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GATE ECE 2006 | Question: 8
The concentration of minority carriers in an extrinsic semiconductor under equilibrium is directly proportional to the doping concentration inversely proportional to the doping concentration directly proportional to the intrinsic concentration inversely proportional to the intrinsic concentration
The concentration of minority carriers in an extrinsic semiconductor under equilibrium isdirectly proportional to the doping concentrationinversely proportional to the do...
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GATE ECE 2006 | Question: 9
Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the diffusion current drift current recombination current induced current
Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially thediffusion currentdrift currentrecombination c...
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GATE ECE 2006 | Question: 10
The phenomenon known as "Early Effect" in a bipolar transistor refers to a reduction of the effective base-width caused by electron-hole recombination at the base the reverse biasing of the base-collector junction the forward biasing of emitter-base junction the early removal of stored base charge during saturation-to-cutoff switching
The phenomenon known as "Early Effect" in a bipolar transistor refers to a reduction of the effective base-width caused byelectron-hole recombination at the basethe rever...
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GATE ECE 2006 | Question: 11
The input impedance $\left(\text{Z}_i\right)$ and the output impedance $\left(\text{Z}_o\right)$ of an ideal transconductance (voltage controlled current source) amplifier are $\text{Z}_i=0, \text{Z}_o=0$ $\text{Z}_i=0, \text{Z}_o=\infty$ $\text{Z}_i=\infty, \text{Z}_o=0$ $\text{Z}_i=\infty, \text{Z}_o=\infty$
The input impedance $\left(\text{Z}_i\right)$ and the output impedance $\left(\text{Z}_o\right)$ of an ideal transconductance (voltage controlled current source) amplifie...
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GATE ECE 2006 | Question: 12
An $n$-channel depletion MOSFET has following two points on its $\mathrm{I}_\text{D}-\mathrm{V}_{\text {GS}}$ curve $\text{V}_{\text{Gs}}=0$ at $\text{I}_\text{D}=12 \mathrm{~mA}$ and $\mathrm{V}_{\mathrm{GS}}=-6$ Volts at $\mathrm{I}_{\mathrm{D}}=0$ Which ... $\text{V}_{\text {Gs }}=0 \; \text{Volts}$ $\mathrm{V}_{\mathrm{Gs}}=3 \; \text{Volts}$
An $n$-channel depletion MOSFET has following two points on its $\mathrm{I}_\text{D}-\mathrm{V}_{\text {GS}}$ curve$\text{V}_{\text{Gs}}=0$ at $\text{I}_\text{D}=12 \math...
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GATE ECE 2006 | Question: 13
The number of product terms in the minimized sum-of-product expression obtained through the following $\text{K}$-map is (where, " $d$ ... $2$ $3$ $4$ $5$
The number of product terms in the minimized sum-of-product expression obtained through the following $\text{K}$-map is (where, " $d$ " denotes don't care states)$$\begin...
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GATE ECE 2006 | Question: 14
Let $x(t) \longleftrightarrow \mathrm{X}(j \omega)$ be Fourier Transform pair. The Fourier Transform of the signal $x(5 t-3)$ in terms of $X(j \omega)$ is given as $\frac{1}{5} e^ - \frac{j 3\omega }{5} \times\left(\frac{j \omega}{5}\right)$ ... $\frac{1}{5} e^{j 3 \omega} \times\left(\frac{j \omega}{5}\right)$
Let $x(t) \longleftrightarrow \mathrm{X}(j \omega)$ be Fourier Transform pair. The Fourier Transform of the signal $x(5 t-3)$ in terms of $X(j \omega)$ is given as$\frac{...
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GATE ECE 2006 | Question: 15
The Dirac delta function $\delta(t)$ is defined as $\delta(t)= \begin{cases}1, & t=0 \\ 0, & \text { otherwise }\end{cases}$ $\delta(t)= \begin{cases}\infty, & t=0 \\ 0, & \text { otherwise }\end{cases}$ ... $\displaystyle{}\int_{-\infty}^\infty \delta(t) d t=1$
The Dirac delta function $\delta(t)$ is defined as$\delta(t)= \begin{cases}1, & t=0 \\ 0, & \text { otherwise }\end{cases}$$\delta(t)= \begin{cases}\infty, & t=0 \\ 0, & ...
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GATE ECE 2006 | Question: 16
If the region of convergence of $x_1[n]+x_2[n]$ is $\frac{1}{3}<|z|<\frac{2}{3}$, then the region of convergence of $x_1[n]-x_2[n]$ includes $\frac{1}{3}<|z|<3$ $\frac{2}{3}<|z|<3$ $\frac{2}{3}<|z|<3$ $\frac{1}{3}<|z|<\frac{2}{3}$
If the region of convergence of $x_1[n]+x_2[n]$ is $\frac{1}{3}<|z|<\frac{2}{3}$, then the region of convergence of $x_1[n]-x_2[n]$ includes $\frac{1}{3}<|z|<3$$\frac{2}{...
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GATE ECE 2006 | Question: 17
The open-loop transfer function of a unity-gain feedback control system is given by $ \text{G}(s)=\frac{\text{K}}{(s+1)(s+2)} $ The gain margin of the system in $\text{dB}$ is given by $0$ $1$ $20$ $\infty $
The open-loop transfer function of a unity-gain feedback control system is given by $$ \text{G}(s)=\frac{\text{K}}{(s+1)(s+2)} $$ The gain margin of the system in $\text{...
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GATE ECE 2006 | Question: 18
In the system shown below, $x(t)=(\sin t) u(t)$. In steady-steady-state, the response $y(t)$ will be $\frac{1}{\sqrt{2}} \sin \left(t-\frac{\pi}{4}\right)$ $\frac{1}{\sqrt{2}} \sin \left(t+\frac{\pi}{4}\right)$ $\frac{1}{\sqrt{2}} e^{-t} \sin t$ $\sin t-\cos t$
In the system shown below, $x(t)=(\sin t) u(t)$. In steady-steady-state, the response $y(t)$ will be$\frac{1}{\sqrt{2}} \sin \left(t-\frac{\pi}{4}\right)$$\frac{1}{\sqrt{...
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GATE ECE 2006 | Question: 19
The electric field of an electomagnetic wave propagating in the positive $z$-direction is given by $ \left.\text{E}=\hat{a_x} \sin (\omega t-\beta z\right)+\hat{a_y} \sin \left(\omega t-\beta z+\frac{\pi}{2}\right) $ The wave is linearly polarized in the $z$-direction elliptically polarized left-hand circularly polarized right-hand circularly polarized
The electric field of an electomagnetic wave propagating in the positive $z$-direction is given by $$ \left.\text{E}=\hat{a_x} \sin (\omega t-\beta z\right)+\hat{a_y} \si...
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GATE ECE 2006 | Question: 20
A transmission line is feeding $1 \mathrm{Watt}$ of power to a horn antenna having a gain of $10 \mathrm{~dB}$. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is $10$ Watts $1$ Watt $0.1$ Watt $0.01$ Watt
A transmission line is feeding $1 \mathrm{Watt}$ of power to a horn antenna having a gain of $10 \mathrm{~dB}$. The antenna is matched to the transmission line. The total...
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GATE ECE 2006 | Question: 21
The eigenvalues and the corresponding eigen vectors of a $2 \times 2$ ... $\left[\begin{array}{ll}4 & 8 \\ 8 & 4\end{array}\right]$
The eigenvalues and the corresponding eigen vectors of a $2 \times 2$ matrix are given by$$\begin{array}{cc} \textbf{Eigenvalue}& \textbf{Eigenvector} \\ \lambda_1=8 & \t...
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GATE ECE 2006 | Question: 22
For the function of a complex variable $\text{W}=\ln \text{Z}\; ($where, $\mathrm{W}=u+j \mathrm{v}$ and $\mathrm{Z}=x+j y),$ the $u=$ constant lines get mapped in $\text{Z}$-plane as set of radial straight lines set of concentric circles set of confocal hyperbolas set of confocal ellipses
For the function of a complex variable $\text{W}=\ln \text{Z}\; ($where, $\mathrm{W}=u+j \mathrm{v}$ and $\mathrm{Z}=x+j y),$ the $u=$ constant lines get mapped in $\text...
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GATE ECE 2006 | Question: 23
The value of the contour integral $\displaystyle{}\oint_{\mid z-j \mid =2} \;\frac{1}{z^2+4} d z$ in positive sense is $\frac{j \pi}{2}$ $-\frac{\pi}{2}$ $-\frac{j \pi}{2}$ $\frac{\pi}{2}$
The value of the contour integral $\displaystyle{}\oint_{\mid z-j \mid =2} \;\frac{1}{z^2+4} d z$ in positive sense is$\frac{j \pi}{2}$$-\frac{\pi}{2}$$-\frac{j \pi}{2}$$...
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GATE ECE 2006 | Question: 24
The integral $\displaystyle{}\int_0^\pi \sin ^3 \theta\; d \theta$ is given by $\frac{1}{2}$ $\frac{2}{3}$ $\frac{4}{3}$ $\frac{8}{3}$
The integral $\displaystyle{}\int_0^\pi \sin ^3 \theta\; d \theta$ is given by$\frac{1}{2}$$\frac{2}{3}$$\frac{4}{3}$$\frac{8}{3}$
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GATE ECE 2006 | Question: 25
Three companies $\text{X, Y}$ and $\text{Z}$ ... computer is defective, the probability that it was supplied by $\text{Y}$ is $0.1$ $0.2$ $0.3$ $0.4$
Three companies $\text{X, Y}$ and $\text{Z}$ supply computers to a university. The percentage of computers supplied by them and the probability of those being defective a...
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GATE ECE 2006 | Question: 26
For the matrix $\left[\begin{array}{ll}4 & 2 \\ 2 & 4\end{array}\right]$, the eigen value corresponding to the eigenvector $\left[\begin{array}{l}101 \\ 101\end{array}\right]$ is $2$ $4$ $6$ $8$
For the matrix $\left[\begin{array}{ll}4 & 2 \\ 2 & 4\end{array}\right]$, the eigen value corresponding to the eigenvector $\left[\begin{array}{l}101 \\ 101\end{array}\ri...
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GATE ECE 2006 | Question: 27
For the differential equation $\dfrac{d^2 y}{d x^2}+k^2 y=0$, the boundary conditions are $y=0$ for $x=0$, and $y=0$ for $x=a$ The form of non-zero solutions of $y$ (where $m$ ... $y=\displaystyle{}\sum_m\;\mathrm{~A}_{m} \;e^{-\frac{m \pi x}{a}}$
For the differential equation $\dfrac{d^2 y}{d x^2}+k^2 y=0$, the boundary conditions are$y=0$ for $x=0$, and$y=0$ for $x=a$The form of non-zero solutions of $y$ (where $...
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GATE ECE 2006 | Question: 28
Consider the function $f(t)$ having Laplace transform $ \text{F}(s)=\frac{\omega_0}{s^2+\omega_0^2} \operatorname{Re}[s]>0 $ The final value of $f(t)$ would be $0$ $1$ $-1 \leq f(\infty) \leq 1$ $\infty$
Consider the function $f(t)$ having Laplace transform $$ \text{F}(s)=\frac{\omega_0}{s^2+\omega_0^2} \operatorname{Re}[s]>0 $$ The final value of $f(t)$ would be$0$$1$$-1...
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GATE ECE 2006 | Question: 29
As $x$ is increased from $-\infty$ to $\infty$, the function $ f(x)=\frac{e^x}{1+e^x} $ monotonically increases monotonically decreases increases to a maximum value and then decreases decreases to a minimum value and then increases
As $x$ is increased from $-\infty$ to $\infty$, the function $$ f(x)=\frac{e^x}{1+e^x} $$monotonically increasesmonotonically decreasesincreases to a maximum value and th...
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GATE ECE 2006 | Question: 30
A two-port network is represented by $\text{ABCD}$ ... $\frac{\mathrm{B}+\mathrm{AR}_{\mathrm{L}}}{\mathrm{D}+\mathrm{CR}_{\mathrm{L}}}$
A two-port network is represented by $\text{ABCD}$ parameters given by$$ \left[\begin{array}{c} \mathrm{V}_1 \\ \mathrm{I}_1 \end{array}\right]=\left[\begin{array}{ll} \m...
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GATE ECE 2006 | Question: 31
In the two port network shown in the figure below, $z_{12}$ and $z_{21}$ are, respectively $r_e$ and $\beta r_o$ $0$ and $-\beta r_o$ $0,$ and $\beta r_o$ $r_e$ and $-\beta r_o$
In the two port network shown in the figure below, $z_{12}$ and $z_{21}$ are, respectively$r_e$ and $\beta r_o$$0$ and $-\beta r_o$$0,$ and $\beta r_o$$r_e$ and $-\beta r...
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GATE ECE 2006 | Question: 32
The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by $\text{RL}$ network only $\text{RC}$ network only $\text{LC}$ network only $\mathrm{RC}$ as well as $\mathrm{RL}$ networks
The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero...
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GATE ECE 2006 | Question: 33
A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is $0.5 \mathrm{~A}$ $2.0 \mathrm{~A}$ $1.0 \mathrm{~A}$ $0.0 \mathrm{~A}$
A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is$0...
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GATE ECE 2006 | Question: 34
In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by $8 e^{-0.004 t}$ Volts $8\left(1-e^{-0.004 t}\right)$ Volts $8 u(t)$ Volts $8$ Volts
In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by$8 e^{-0.004 t}$ Volts$8\le...
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GATE ECE 2006 | Question: 35
Consider two transfer functions $ \mathrm{G}_1(s)=\frac{1}{s^2+a s+b} \text { and } \mathrm{G}_2(s)=\frac{s}{s^2+a s+b} $ The $3\text{-dB}$ bandwidths of their frequency responses are, respectively $\sqrt{a^2-4 b}, \sqrt{a^2+4 b}$ $\sqrt{a^2+4 b}, \sqrt{a^2-4 b}$ $\sqrt{a^2-4 b}, \sqrt{a^2-4 b}$ $\sqrt{a^2+4 b}, \sqrt{a^2+4 b}$
Consider two transfer functions $$ \mathrm{G}_1(s)=\frac{1}{s^2+a s+b} \text { and } \mathrm{G}_2(s)=\frac{s}{s^2+a s+b} $$ The $3\text{-dB}$ bandwidths of their frequenc...
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GATE ECE 2006 | Question: 36
A negative resistance $R_{\text {neg }}$ is connected to a passive network $N$ having driving point impedance $Z_{1}$ (s) as shown below. For $Z_{2}(s)$ ... $\left|\text{R}_{\text {neg }}\right| \leq \angle Z_{1}(j \omega), \forall \omega$
A negative resistance $R_{\text {neg }}$ is connected to a passive network $N$ having driving point impedance $Z_{1}$ (s) as shown below. For $Z_{2}(s)$ to be positive re...
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GATE ECE 2006 | Question: 37
In the circuit shown below, the switch wa connected to position $1$ at $t<0$ and at $t=0$, it is changed to position $2$. Assume that $y$ the diode has zero voltage drop and a storage time $t_{s}$. For $0 < t \leq t_{s}, \text{V}_{\text{R}}$ is given by ... $\mathrm{V}_{\mathrm{R}}=+5$ $0 \leq \mathrm{V}_{\mathrm{R}}<5$ $-5 < \mathrm{V}_{\mathrm{R}} < 0$
In the circuit shown below, the switch wa connected to position $1$ at $t<0$ and at $t=0$, it is changed to position $2$. Assume that $y$ the diode has zero voltage drop ...
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GATE ECE 2006 | Question: 38
The majority carriers in an $n$-type semiconductor have an average drift velocity $\mathrm{V}$ in a direction perpendicular to a uniform magnetic field $\text{B}.$ The electric field $\mathrm{E}$ induced due to Hall effect acts in the direction $\mathrm{V} \times \mathrm{B}$ $\mathrm{B} \times \mathrm{V}$ along $\text{V}$ opposite to $\mathrm{V}$
The majority carriers in an $n$-type semiconductor have an average drift velocity $\mathrm{V}$ in a direction perpendicular to a uniform magnetic field $\text{B}.$ The el...
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GATE ECE 2006 | Question: 39
Find the correct match between Group $1$ and Group $2$ ... $\text{E - 3, F - 4, G - 1, H - 2}$ $\text{E - 1, F - 3, G - 2, H - 4}$
Find the correct match between Group $1$ and Group $2$$$\begin{array}{ll}\qquad \textbf{Group 1} & \qquad \textbf{Group 2} \\\text{E. Varactor diode} & \text{1. Voltage r...
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40
GATE ECE 2006 | Question: 40
A heavily doped $n$-type semiconductor has the following data Hole-electron mobility ratio : $0.4$ Doping concentration : $4.2 \times 10^{8} \; \mathrm{atoms/m}^{3}$ Intrinsic concentration : $1.5 \times 10^{4} \; \mathrm{atoms/m}^{3}$ The ... that of the intrinsic semiconductor of same material and at the same temperature is given by $0.00005$ $2,000$ $10,000$ $20,000$
A heavily doped $n$-type semiconductor has the following dataHole-electron mobility ratio : $0.4$Doping concentration : $4.2 \times 10^{8} \; \mathrm{atoms/m}^{3}$Intrins...
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