GATE ECE 2008

## GATE ECE

In the following transistor circuit, VBE = 0.7V, re = 25m/IE, $$\beta $$ and all the capacitances are very large.
T

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In the following transistor circuit, VBE = 0.7V, re = 25m/IE, $$\beta $$ and all the capacitances are very large.

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Consider the following circuit using an ideal Op-Amp. The I-V characteristics of the diode is described by the relation

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The Op-Amp circuit shown above represents a

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Consider the Schmitt trigger circuit shown below.
A triangular wave which goes from -12V to 12V is applied to the inve

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Consider the amplitude modulated (AM) signal $$A_c\cos\omega_ct\;+\;2\cos\omega_mt\;\cos\omega_ct$$. For
demodulating th

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The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is

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Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-d

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Four messages band limited to W, W, 2 W and 3 W respectively are to be multiplexed using Time Division Multiplexing (TDM

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A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Ea

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A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Ea

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A speech signal, band limited to 4kHz and peak voltage varying between +5V and -5V is sampled at the Nyquist rate. Each

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A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n

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Consider a Binary Symmetric Channel (BSC) with probability of error being 'p'. To transit a bit, say 1, we transmit a se

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Step responses of a set of three second-order underdamped systems all have the
same percentage overshoot. Which of the f

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A linear, time-invariant, causal continuous time system has a rational transfer
function with simple poles at s=-2 and s

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The number of open right half plane poles of $$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$

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Group I lists a set of four transfer functions. Group II gives a list of possible step
responses y(t). Match the step re

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A certain system has transfer function $$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where $$\alpha$$
is a parameter.

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The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes t

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The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over {

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The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes t

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The pole-zero plot given below corresponds to a

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Group I gives two possible choices for the impedance Z in the diagram. The
circuit elements in Z satisfy the condition $

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A signal flow graph of a system is given below.
The set of equations that correspond to this signal flow graph is

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For the circuit shown in the following figure $${I_0}$$ - $${I_3}$$ are inputs to the 4:1 multiplexer R(MSB) and S are c

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Which of the follwing Boolean expression correctly represents the relation between P, Q, R and M1?

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For each of the positive edge-triggered J-K flip flop used in the following future, the propagation delay is $$\Delta $$

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The logic function implemented by the following circuit at the terminal OUT is

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In the following circuit, the comparator output is logic “I” if V1 > V2 and is logic “0” otherwise. The D/A conversio

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In the following circuit, the comparator output is logic “I” if V1 > V2 and is logic “0” otherwise. The D/A conversio

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The value of the integral of the function $$\mathrm g\left(\mathrm x,\mathrm y\right)=4\mathrm x^3\;+\;10\mathrm y^4$$ a

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One end of loss-less transmission line having the characteristic impedance of 75 $$\Omega $$ and length of 1 cm is short

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A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant

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A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm ) is to be operated in $$T{E_{11}}$$ mode. The min

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For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is

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At 20 GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70% efficiency is

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Which of the following is true?

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Which of the following is NOT associated with a P-N junction?

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In the following limiter circuit, an input voltage $${\mathrm V}_\mathrm i\;=\;10\sin\left(100\mathrm{πt}\right)$$ appli

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The drain current of a MOSFET in saturation is given by $$I_D\;=\;K\left(V_{GS}\;-V_T\right)^2$$ where 'K'
is a constant

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A silicon wafer has 100 mm of oxide on it and is inserted in a furnace at a
temperature above 1000ºC for further oxidati

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Two identical NMOS transistors M1 and M2 are connected as shown below. Vbias is
chosen so that both transistors are in s

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For the circuit shown in the following figure, transistors M1 and M2 are identical
NMOS transistors. Assume that M2 is i

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The measured transconductance gm of an NMOS transistor operating in the linear
region is plotted against the gate voltag

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All the four entries of $$2$$ $$x$$ $$2$$ matrix
$$P = \left[ {\matrix{
{{p_{11}}} & {{p_{12}}} \cr
{{p_{21

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The system of linear equations $$\left. {\matrix{
{4x + 2y = 7} \cr
{2x + y = 6} \cr
} } \right\}$$ has

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For real values of $$x,$$ the minimum value of function $$f\left( x \right) = {e^x} + {e^{ - x}}\,\,$$ is

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The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line

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Which of the following function would have only odd powers of $$x$$ in its Taylor series expansion about the point $$x=0

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In the Taylor series expansion of $${e^x} + \sin x$$ about the point $$x = \pi ,$$ the coefficient of $${\left( {x = \p

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Consider points $$P$$ and $$Q$$ in $$xy-$$plane with $$P=(1,0)$$ and $$Q=(0,1).$$ The line integral $$2\int\limits_P^Q

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Which of the following is a solution to the differential equation $${d \over {dt}}x\left( t \right) + 3x\left( t \right)

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The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is

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The equation sin(z) = 10 has

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The residue of the function
$$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$ at z = 2 is

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An 8085 executes the following instructions
2710 LXI H, 30A0H
DAD H
PCHL
All addresses and constants are in Hex. L

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The Thevenin equivalent impedance Zth between the nodes P and Q in the
following circuit is

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In the following circuit, the switch S is closed at t=0. The rate of change of
current $$\frac{di}{dt}(0^+)$$ is given b

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The following series RLC circuit with zero initial conditions is excited by a unit
impulse function $$\delta$$(t).
For

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The following series RLC circuit with zero initial conditions is excited by a unit
impulse function $$\delta$$(t).
For

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The circuit shown in the figure is used to charge the capacitor C alternately from
two current sources as indicated. The

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In the following graph, the number of trees (P) and the number of cut-sets (Q)
are

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A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltme

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The driving point impedance of the following network is given by $$Z(s) = {{0.2\,s} \over {{s^2}\, + \,0.1\,s\, + \,2}}$

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A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltme

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{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT)

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In the following network (Fig .1), the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequ

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In the following network (Fig.1), the switch is closed at t = 0 and the sampling starts from t=0. The sampling frequency

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The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptio

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The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\e

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A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 an

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Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with

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The signal x(t) is described by $$x\left( t \right) = \left\{ {\matrix{
{1\,\,\,for\,\, - 1 \le t \le + 1} \cr

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A discrete time linear shift - invariant system has an impulse response $$h\left[ n \right]$$ with $$h\left[ 0 \right]$$

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