GATE ECE 2014 Set 1
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GATE ECE

A BJT is baised in forward active mode Assume VBE = 0.7 V, kT/q = 25 mV and reverse saturation current Is = 10-13A. The
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For the amplifier shown in the figure, the BJT parameters are VBE = 0.7 V, $$\beta $$ = 200, and thermal voltage VT = 2
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A good current buffer has
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In the low - pass filter shown in the figure, for a cut - off frequency of 5 KHz, the value of R2 (in k$$\Omega $$ ) is
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In the ac equivalent circuit shown in the figure, if i$${_F}$$ is very large, the type of feedback is
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In the voltage regulator circuit shown in the figure, the op - amp is ideal. The BJT has VBE = 0.7 V and $$\beta $$ = 10
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In the circuit shown, the op-amp has finite input impedance, infinite voltage gain and zero input offset voltage. The ou
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In a code - division multiple access (CDMA) system with N = 8 chips, the maximum number of users who can be assign
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Consider a random process $$X\left( t \right) = \sqrt 2 \sin \left( {2\pi t + \varphi } \right),$$ where the ra
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Let $$Q\left( {\sqrt y } \right)$$ be the BER of a BPSK system over an AWGN channel with two - sided noise power spectra
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The capacity of a Binary Symmetric Channel (BSC) with cross - over probability 0.5 is ______ .
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A fair coin is tossed repeatedly until a 'Head' appears for the first time. Let L be the number of tosses to get this fi
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The forward path transfer function of a unity negative feedback system is given by $$$G\left(s\right)\;=\;\frac k{\left
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For the following feedback system $$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of t
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Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which one of the following con
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The phase margin in degrees of G(s)=$${{10} \over {\left( {s + 0.1} \right)\left( {s + 1} \right)\left( {s + 10} \right)
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Consider the state space model of a system, as given below The system is
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The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to
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Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline
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The output F in the digital logic circuit shown in the figure is
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Five JK flip - flops are cascaded to form circuit shown in figure. Clock pulses at a frequency of 1 MHz are applied as s
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The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to input A of the XOR gate.
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A two - port network has scattering parameters given by $$[S]$$ $$ = \left[ {\matrix{ {{s_{11}}} & {{s_{12}}} \
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For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglect
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In spherical coordinates, let $${{{\widehat a}_{_0}},\,{{\widehat a}_{_\phi }}}$$ denote unit vectors along the $$\theta
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When the optical power incident on a photodiode is 10μW and the responsivity is 0.8 A/W, the photocurrent generated (in
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If fixed positive charges are present in the gate oxide of an n-channel enhancement type MOSFET, it will lead to
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In the ac equivalent circuit shown in the figure, if in is the input current and RF is very large, the type of feedback
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In the following circuit employing pass transistor logic, all NMOS transistors are identical with a threshold voltage of
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A depletion type N -channel MOSFET is biased in its linear region for use as a voltage controlled resistor. Assume thres
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For matrices of same dimension $$M,N$$ and scalar $$c,$$ which one of these properties DOES NOT ALWAYS hold ?
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Consider the matrix $${J_6} = \left[ {\matrix{ 0 & 0 & 0 & 0 & 0 & 1 \cr 0 & 0 & 0 &
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$$A$$ real $$\left( {4\,\, \times \,\,4} \right)$$ matrix $$A$$ satisfies the equation $${A^2} = {\rm I},$$ where $${\rm
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The Taylor series expansion of $$3$$ $$sin$$ $$x$$ $$+2cos$$ $$x$$ is
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The volume under the surface $$z\left( {x,y} \right) = x + y$$ and above the triangle in the $$xy$$ plane defined by $
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Let $$\,{X_1},\,\,{X_2}\,\,$$ and $$\,{X_3}\,$$ be independent and identically distributed random variables with the uni
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Let $$X$$ be a real - valued random variable with $$E\left[ X \right]$$ and $$E\left[ {{X^2}} \right]$$ denoting the mea
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In a housing society, half of the families have a single child per family, while the remaining half have two children pe
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$$C$$ is a closed path in the $$z-$$plane given by $$\left| z \right| = 3.$$ The value of the integral $$\oint\limits_
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A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is
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Consider the configuration shown in the figure which is a portion of a larger electrical network For R = 1 Ω and curr
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A Y-network has resistances of 10Ω each in two of its arms, while the third arm has a resistance of 11Ω in the equivalen
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For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output i
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A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power fa
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In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is _
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A periodic variable x is shown in the figure as a function of time. The root - mean - square (rms) value of x is _______
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A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\
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A system is described by the following differential equation, where u(t) is the input to the system and y(t) is output o
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Consider a discrete time periodic signal x$$\left[ n \right]$$= $$\sin \left( {{{\pi n} \over 5}} \right)$$. Let ak be
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Let x $$\left[ n\right]$$= $${\left( { - {1 \over 9}} \right)^n}\,u(n) - {\left( { - {1 \over 3}} \right)^n}u( - n - 1).
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For a function g(t), it is given that $$\int_{ - \infty }^\infty {g(t){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}
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Consider two real valued signals, $$x\left( t \right)$$ band - limited to $$\,\left[ { - 500Hz,\,\,500Hz} \right]$$ and
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A discrete - time signal x[n] = $${\rm{sin(}}\,{\pi ^2}n)$$, n being an integer is
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General Aptitude

For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all residen
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Find the odd one from the following group: W,E,K,O I,Q,W,A F,N,T,X N,V,B,D
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A train that is 280 meters long, traveling at a uniform speed, crosses a platform in 60 seconds and passes a man standin
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The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the following bar chart. If the t
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You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on
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