GATE ECE 2006
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## GATE ECE

The input impedance (Zi) and the output impedance (Zo) of an ideal transconductance (voltage controlled current source)
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In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $${\beta _{D View Question In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters:$${\beta _{D
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In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $${\beta _{D View Question An n-channel depletion MOSFET has following two points on its ID - VGS curve: (i)VGS = 0 at Id = 12 mA and (ii)VGS = - View Question A regulated power supply, shown in figure below, has an unregulated input (UR) of 15 volts and generates a regulated out View Question A regulated power supply, shown in figure below, has an unregulated input (UR) of 15 volts and generates a regulated out View Question For the circuit shown in the following figure, the capacitor C is initially uncharged. At t = 0, the switch S is closed. View Question The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the enve View Question A zero-mean white Gaussian noise is passed through an ideal low-pass filter of bandwidth 10 kHz. The output is then unif View Question The following question refer to wide sense stationary stochastic process: It is desired to generate a stochastic p View Question The following question refer to wide sense stationary stochastic process: The parameters of the system obtained in View Question The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the View Question In the following figure the minimum value of the constant “C”, which is to be added to y1(t) such that y1(t) and y2(t) a View Question Let$$g\left( t \right){\mkern 1mu} {\mkern 1mu} \,\,\,\,\,{\mkern 1mu} = {\mkern 1mu} {\mkern 1mu} p\left( t \right){}
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A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming inde
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The unit impulse response of a system is: $$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$For this system, the steady-state v View Question The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec r View Question The unit-step response of a system starting from rest is given by $$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mat View Question The open-loop transfer function of a unity-gain feedback control system is given by$$G(s) = {K \over {(s + 1)(s + 2)}}, View Question In the system shown below, x(t)=(sin t). In steady-state, the response y(t) will be View Question Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s View Question The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through (-1,j0) point in the GH plane. The gain View Question Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$. W View Question Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$T View Question The transfer function of a phase-lead compensator is given by$${G_c}(s) = {{1 + 3Ts} \over {1 + Ts}}$$where T &gt; 0. View Question A linear system is described by the following state equation$$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t
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A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-5 number is represented by its
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The number of product terms in the minimized sum-of-product expression obtained through the following k-map is ( where ,
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The point p in the following figure is stuck- at-1. The output f will be
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Two D-flip-flops, as shown below, are to be connected as a synchronous counter that goes through the following Q1Q0 sequ
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A 4-bit D/A converter is connected to a free-running 3-bit UP counter, as shown in the following figure. Which of the fo
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$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to
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The electric field of an electromagnetic wave propagating in the positive z-direction is given by $$E = {\widehat a_x} View Question A medium of relative permittivityb$${\varepsilon _r} = 2$$forms an interface with free-space. A point source of electr View Question$$\nabla \times \nabla \times P$$, where P is a vector, is equal to View Question A medium is divided into regions$${\rm I}$$and$${\rm I}{\rm I}$$about$$x = 0$$plane, as shown in the Fig. belo View Question When a plane wave traveling in free-space is incident normally on a medium having$${\varepsilon _r} = 4.0,$$the fracti View Question A rectangular waveguide having$$T{E_{10}}$$mode as dominant mode is having a cutoff frequency of 18 GHz for the$$T{E_
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A mast antenna consisting of a 50 meter long vertical conductor operates over a perfectly conducting ground plane. It is
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A transmission line is feeding 1 Watt of power to a horn antenna having gain of 10 dB. The antenna is matched to the tra
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Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentiall
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The concentration of minority carriers in an extrinsic semiconductor under equilibrium is:
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An n-channel depletion MOSFET has following two points on its ID − VGS curve: (i) VGS = 0 at ID = 12 mA and (ii) VGS = -
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For the matrix $$\left[ {\matrix{ 4 &amp; 2 \cr 2 &amp; 4 \cr } } \right].$$ The eigen value corresponding t
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The rank of the matrix $$\left[ {\matrix{ 1 &amp; 1 &amp; 1 \cr 1 &amp; { - 1} &amp; 0 \cr 1 &amp; 1 &amp; View Question The eigen values and the correspondinng eigen vectors of a$$2 \times 2$$matrix are given by Eigen value$${\lambda _1
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For the differential equation $${{{d^2}y} \over {d{x^2}}} + {k^2}y = 0,$$ the boundary conditions are (i) $$y=0$$ fo
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The value of the counter integral $$\int\limits_{\left| {z - j} \right| = 2} {{1 \over {{z^2} + 4}}\,} dz\,\,in\,the\,p View Question For the function of a complex variable w = lnz (where w = u + jv and z = x + jy) the u = constant lines get mapped in th View Question Consider the function$$f(t)$$having laplace transform$$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2
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An I/O peripheral device shown in figure (b) below is to be interfaced to an 8085 microprocessor. To select the I/O devi
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Following is the segment of a 8085 assembly Language program: LXI SP, EFFF H CALL 3000 H 3000H: LXI H, 3CF4H PUSH P
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A 2mH inductor with some initial current can be represented as shown below, where s is the Laplace Transform varia
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In the figure shown below, assume that all the capacitors are initially uncharged. If νi(t) = 10 u(t) Volts, ν0(t) is gi
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In the two port network shown in the figure below, z12 and z21 are, respectively
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A two-port network is represented by ABCD parameters given by $$\left[ {\matrix{ {{V_1}} \cr {{I_1}} \cr } View Question Let x(t)$$ \leftrightarrow $$X($$(j\omega )$$BE Fourier transform pair. The Fourier Transform of the signal x(5t - 3) View Question Consider the function f(t) having Laplace transform$$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}
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If the region of convergence of $${x_1}\left[ n \right]$$ + $${x_2}\left[ n \right]$$ is 1/3&lt; $$\left| {z\,} \right| View Question Let g(t) = p(t) * p(t), where * denotes convolution and p(t) = u(t) - (t-1) with u(t) being the unit step function. The View Question A system with input$$x\left( n \right)$$and output$$y\left( n \right)$$is given as$$y\left( n \right) = \left(
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In the system shown below, x(t) = (sint)u(t). In steady-state, the response y(t) will be
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A low-pass filter having a frequency response $$H(j\omega )$$ = $$A(\omega ){e^{j\Phi (\omega )}}$$, does not product an
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The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without
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A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where $$g(t)\, = \,\,\sum\limits_{k = - \infty View Question A solution for the differential equation$$\mathop x\limits^. $$(t) + 2 x (t) =$$\delta (t)$$with intial condition$$x
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The Dirac delta function $$\delta (t)$$ is defined as
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As x is increased from $$- \infty \,\,to\,\infty$$, the function $$f(x) = {{{e^x}} \over {1 + {e^x}}}$$
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