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 $$G\left(s\right)\;=\;\frac k{\left View Question For the following feedback system$$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of t View Question Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which one of the following con View Question The phase margin in degrees of G(s)=$${{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 +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline View Question The output F in the digital logic circuit shown in the figure is View Question Five JK flip - flops are cascaded to form circuit shown in figure. Clock pulses at a frequency of 1 MHz are applied as s View Question The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to input A of the XOR gate. View Question A two - port network has scattering parameters given by$$[S] = \left[ {\matrix{ {{s_{11}}} &amp; {{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 $$\theta View Question When the optical power incident on a photodiode is 10μW and the responsivity is 0.8 A/W, the photocurrent generated (in View Question If fixed positive charges are present in the gate oxide of an n-channel enhancement type MOSFET, it will lead to View Question In the ac equivalent circuit shown in the figure, if in is the input current and RF is very large, the type of feedback View Question In the following circuit employing pass transistor logic, all NMOS transistors are identical with a threshold voltage of View Question A depletion type N -channel MOSFET is biased in its linear region for use as a voltage controlled resistor. Assume thres View Question For matrices of same dimension$$M,N$$and scalar$$c,$$which one of these properties DOES NOT ALWAYS hold ? View Question Consider the matrix$${J_6} = \left[ {\matrix{ 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 \cr 0 &amp; 0 &amp; 0 &
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$$A$$ real $$\left( {4\,\, \times \,\,4} \right)$$ matrix $$A$$ satisfies the equation $${A^2} = {\rm I},$$ where $${\rm View Question The Taylor series expansion of$$3sinx+2cosx$$is View Question The volume under the surface$$z\left( {x,y} \right) = x + y$$and above the triangle in the$$xy$$plane defined by  View Question Let$$\,{X_1},\,\,{X_2}\,\,$$and$$\,{X_3}\,$$be independent and identically distributed random variables with the uni View Question Let$$X$$be a real - valued random variable with$$E\left[ X \right]$$and$$E\left[ {{X^2}} \right]$$denoting the mea View Question In a housing society, half of the families have a single child per family, while the remaining half have two children pe View Question$$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 $$h\left( t \right) = \left\{ {\ View Question A system is described by the following differential equation, where u(t) is the input to the system and y(t) is output o View Question Consider a discrete time periodic signal x$$\left[ n \right]$$=$$\sin \left( {{{\pi n} \over 5}} \right)$$. Let ak be View Question Let x$$\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 $$\int_{ - \infty }^\infty {g(t){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2} View Question Consider two real valued signals,$$x\left( t \right)$$band - limited to$$\,\left[ { - 500Hz,\,\,500Hz} \right]$$and View Question A discrete - time signal x[n] =$${\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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