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: $${\beta _{D
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In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $${\beta _{D
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In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $${\beta _{D
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An n-channel depletion MOSFET has following two points on its ID - VGS curve: (i)VGS = 0 at Id = 12 mA and (ii)VGS = -
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A regulated power supply, shown in figure below, has an unregulated input (UR) of 15 volts and generates a regulated out
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A regulated power supply, shown in figure below, has an unregulated input (UR) of 15 volts and generates a regulated out
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For the circuit shown in the following figure, the capacitor C is initially uncharged. At t = 0, the switch S is closed.
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The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the enve
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A zero-mean white Gaussian noise is passed through an ideal low-pass filter of bandwidth 10 kHz. The output is then unif
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The following question refer to wide sense stationary stochastic process: It is desired to generate a stochastic p
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The following question refer to wide sense stationary stochastic process: The parameters of the system obtained in
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The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the
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In the following figure the minimum value of the constant “C”, which is to be added to y1(t) such that y1(t) and y2(t) a
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Let $$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
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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
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The unit-step response of a system starting from rest is given by $$$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mat
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The open-loop transfer function of a unity-gain feedback control system is given by $$G(s) = {K \over {(s + 1)(s + 2)}},
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In the system shown below, x(t)=(sin t). In steady-state, the response y(t) will be
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Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s
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The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through (-1,j0) point in the GH plane. The gain
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Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$. W
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Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$ T
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The transfer function of a phase-lead compensator is given by $${G_c}(s) = {{1 + 3Ts} \over {1 + Ts}}$$ where T > 0.
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A linear system is described by the following state equation $$$\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 $$$E = {\widehat a_x}
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A medium of relative permittivityb $${\varepsilon _r} = 2$$ forms an interface with free-space. A point source of electr
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$$\nabla \times \nabla \times P$$, where P is a vector, is equal to
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A medium is divided into regions $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ about $$x = 0$$ plane, as shown in the Fig. belo
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When a plane wave traveling in free-space is incident normally on a medium having $${\varepsilon _r} = 4.0,$$ the fracti
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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 & 2 \cr 2 & 4 \cr } } \right].$$ The eigen value corresponding t
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The rank of the matrix $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & { - 1} & 0 \cr 1 & 1 &
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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
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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
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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 }
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Let x(t) $$ \leftrightarrow $$ X($$(j\omega )$$ BE Fourier transform pair. The Fourier Transform of the signal x(5t - 3)
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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]$$ is 1/3< $$\left| {z\,} \right|
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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
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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
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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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