GATE EXAM Electronics & Communication PREVIOUS YEAR QUESTION PAPERS 1991 - 2009 Compiled by M.Raja radioraja.m@gmail.comGATE EC - 1991 www.gateIorum.com Join discussion of iIis icsi acr ai Iii.//forun.gaicncnior.con JoinAIIIndIaMockGATECIassroomTestSerIes-200?conducicdlyCATEForuninovcr25ciiicsallovcrIndia.Qucsiion Pacrs including scciion icsis and full icsis arc dcsigncd ly IISc alunni according io iIc laicsi syllalus. Pcrccniilc, All India Fanl, inicraciion wiiI IISc alunni in our onlinc discussion foruns, and norc.visii www.gote|orum.com Ihink G/IE Ihink G/IE Fcrum 1.1Anexcitationisappliedtoasystematt=Tanditsresponseiszerofor . t T < 0isascalarvariableparameter.Intherootlocidiagramofthe system the asymptotes of the root locus for large values of K meet at a point in the s-plane whose coordinates are (a)(-3,0)(b)(-2,0)(c)(-1,0)(d) (2,0) 1.12 Alinearsecondordersingleinputcontinuoustimesystemisdescribedbythe following set of differential equations ( ) ( ) ( )( ) ( ) ( ) ( )1 1 22 1 22 42x t x t x tx t x t x t u t= += + Where( ) ( )1 2andx t x t arethestatevariablesand( ) u t isthecontrolvariable. The system is:(a)controllable and stable(b)controllable but unstable(c)uncontrollable and unstable(d)uncontrollable and stable 1.13Alineartime-invariantdiscrete-timesystemisdescribedbythevectormatrix difference equation( ) ( ) ( ) 1 x k F X k Gu k + = +Where( ) X k isthestatevector,Fisannnconstantmatrix,Gisa ( ) n r constant matrix and( ) u kis the control vector. The state transition matrix of the system is given by inverse Z-transform of (a)ZI - F(b)(ZI - F) Z(c)( )1ZI F G (d) ( )1ZI F Z 1.14Asiliconsampleisuniformlydopedwith 1610 phosphorousatoms/cm3and 162 10 boron atoms/cm3. If all the dopants are fully ionized, the material is (a)n-type with carrier concentration of 16 310 / cm (b)p-type with carrier concentration of 16 310 / cm (c)p-type with carrier concentration of 16 32 10 / cm (d) 2Twill get damaged and 1Twill be safe 1.15Ann-typesiliconsample,havingelectronmobility n = twicetheholemobility ,p issubjectedtoasteadyilluminationsuchthattheelectronconcentration doublesfromitsthermalequilibriumvalue.Asaresult,theconductivityofthe sample increases by a factor of . GATE EC - 1991 www.gateIorum.com Join discussion of iIis icsi acr ai Iii.//forun.gaicncnior.con JoinAIIIndIaMockGATECIassroomTestSerIes-200?conducicdlyCATEForuninovcr25ciiicsallovcrIndia.Qucsiion Pacrs including scciion icsis and full icsis arc dcsigncd ly IISc alunni according io iIc laicsi syllalus. Pcrccniilc, All India Fanl, inicraciion wiiI IISc alunni in our onlinc discussion foruns, and norc.visii www.gote|orum.com Ihink G/IE Ihink G/IE Fcrum 1.16Thesmallsignalcapacitancesofanabrupt 1P n junctionis 21 / nF Cmatzero bias. If the built in voltage is 1 volt, the capacitance at a reverse bias voltage of 99 volts is equal to . 1.17Referringtothefigure.TheswitchSisinposition1initiallyandsteadystate conditionsexistfromtimet=0to 0. t t = Theswitchissuddenlythrowninto position 2. The current 1 through the 10K resistor as a function of time t from t = 0,is..(Givethesketchshowingthemagnitudesofthecurrentatt=0, 0 andt t t = = ) 1.18Discretetransistors 1 2andT T havingmaximumcollectorcurrentratingof0.75 amps are connected in parallel as shown in the figure. This combination is treated as a single transistor to carry a total current of 1 ampere, when biased with self bias circuit. When the circuit is switched on, 1Tdraws 0.55 amps and 2Tdraws 0.45 amps. If the supply is kept on continuously, ultimately it is very likely that (a)both 1 2andT Tget damaged(b)both 1 2andT Twill be safe (c) 1Twill get damaged and 2T will be safe (d) 2Twill get damaged and 1T will be safe 20V 20V 10K 1 S 2 T1T2 GATE EC - 1991 www.gateIorum.com Join discussion of iIis icsi acr ai Iii.//forun.gaicncnior.con JoinAIIIndIaMockGATECIassroomTestSerIes-200?conducicdlyCATEForuninovcr25ciiicsallovcrIndia.Qucsiion Pacrs including scciion icsis and full icsis arc dcsigncd ly IISc alunni according io iIc laicsi syllalus. Pcrccniilc, All India Fanl, inicraciion wiiI IISc alunni in our onlinc discussion foruns, and norc.visii www.gote|orum.com Ihink G/IE Ihink G/IE Fcrum 1.19.Thebuilt-inpotentialofthegatejunctionofan-channelJFETis0.5volts.The drain current saturates at4.0DSV =volts when0.GSV =The pinch off voltage is ________. 1.20.In figure, all transistors are identical and have a high value of beta. The voltage DCVis equal to ______. 1.21.In figure, both transistors are identical and have a high value of beta. Take the dc base-emitter voltage drop as 0.7 volt and KT/q = 25 mV. The small signal low frequency voltage gain( )o iVVis equal to _______ Q1 Q2Q3 Q4 5mA1k 10 volts VDC=? Vi ~ 1k 1.2k 10 volts -5.7 volts VO/V=? GATE EC - 1991 www.gateIorum.com Join discussion of iIis icsi acr ai Iii.//forun.gaicncnior.con JoinAIIIndIaMockGATECIassroomTestSerIes-200?conducicdlyCATEForuninovcr25ciiicsallovcrIndia.Qucsiion Pacrs including scciion icsis and full icsis arc dcsigncd ly IISc alunni according io iIc laicsi syllalus. Pcrccniilc, All India Fanl, inicraciion wiiI IISc alunni in our onlinc discussion foruns, and norc.visii www.gote|orum.com Ihink G/IE Ihink G/IE Fcrum 1.22.Infiguretheinput 1V isa100Hztriangularwavehavingapeaktopeak amplitude of 2 volts and an average value of zero volts. Given that the diode is ideal, the average value of the output 0Vis ________. 1.23.Infigure,then-channelMOSFETsareidenticalandtheircurrentvoltage characteristics are given by the following expressions: For( )2, 12DS D GS DSV DSV I V V mA = For( ) ( ) ( )21 , 1 1DS GS GS GSV V V V mA = Where and GS DSV V arethegatesourceanddrainsourcevoltagesrespectively and 0I is the drain current.The current DCI flowing through the transistor `M is equal to _______ 1.24.InorderthatthecircuitofFigureworksproperlyasdifferentiator,itshouldbe modified to _____ (draw the modified circuit) 1.25Two non-inverting amplifiers, one having a unity gain and the other having a gain of twenty are made using identical operational amplifiers. As a compared to the unity gain amplifier, the amplifier with gain twenty has (a)less negative feedback (b)greater input impedance(c)less bandwidth (d)none of the above Vi 1K 1K VO 0.6 volts M 2mA 5 volts -2 volts IDC=? + + R GATE EC - 1991 www.gateIorum.com Join discussion of iIis icsi acr ai Iii.//forun.gaicncnior.con JoinAIIIndIaMockGATECIassroomTestSerIes-200?conducicdlyCATEForuninovcr25ciiicsallovcrIndia.Qucsiion Pacrs including scciion icsis and full icsis arc dcsigncd ly IISc alunni according io iIc laicsi syllalus. Pcrccniilc, All India Fanl, inicraciion wiiI IISc alunni in our onlinc discussion foruns, and norc.visii www.gote|orum.com Ihink G/IE Ihink G/IE Fcrum 1.26Twodimensionaladdressingof2568bitROMusingto1selectorsrequires ____ (how many?) NAND gates. 1.27The CMOS equivalent of the following nMOS gate (in figure) is ______ (draw the circuit). 1.28Infigure,theBooleanexpressionfortheoutputintermsofinputsA,BandC when the clock `CK is high, is given by _______ 1.29An S-R FLIP-FLOP can be converted into a T FLIP FLOP by connecting ______ to Q and _______ to Q. A B C O/P + n-channel CK AB C O/P=? + p-channel GATE EC - 1991 www.gateIorum.com Join discussion of iIis icsi acr ai Iii.//forun.gaicncnior.con JoinAIIIndIaMockGATECIassroomTestSerIes-200?conducicdlyCATEForuninovcr25ciiicsallovcrIndia.Qucsiion Pacrs including scciion icsis and full icsis arc dcsigncd ly IISc alunni according io iIc laicsi syllalus. Pcrccniilc, All India Fanl, inicraciion wiiI IISc alunni in our onlinc discussion foruns, and norc.visii www.gote|orum.com Ihink G/IE Ihink G/IE Fcrum 1.30A bit stored in a FAMOS device can be erased by _______. 1.31Asignalhasfrequencycomponentsfrom300Hzto1.8KHz.Theminimum possible rate at which the signal has to be sampled is _______. 1.32Asequentialmultiplexerisconnectedasshowninfigure.Eachtimethe multiplexer receives the clock, it switches to the next channel (From 6 it goes to 1). If the input signals are ( )( )( )( )33335cos2 4 102cos2 3.8 106cos2 2.2 104cos2 1.7 10A tB tC tD t= = = = he minimum clock frequency should be _____ KHz. 1.33Forthesignalconstellationshowninfigurebelow,thetypeofmodulationis ______. 1.34Tworesistors 1 2andR R (inohms)attemperatures 1 2andT T K respectively,are connected in series. Their equivalent noise temperatures is _____ K. 1.35A binary source has symbol probabilities 0.8 and 0.2. If extension coding (blocks of4symbols)isused.Thelowerandupperboundsontheaveragecodeword length are(a)lower _______ (b)higher _______ 1.36In a reflex Klystron oscillator(a)the maximum possible efficiency is 58% (b)the frequency of oscillation varies linearly with the reflector voltage(c)the power output varies continuously with reflector voltage(d)the power output is maximum at fixed frequency. 1 2 3 4 5 6 D A Clock MUX B C Sampling and quantizingS2 cos2ntTS1 S3 S4 sin2ntTT=symbol durationGATE EC - 1991 www.gateIorum.com Join discussion of iIis icsi acr ai Iii.//forun.gaicncnior.con JoinAIIIndIaMockGATECIassroomTestSerIes-200?conducicdlyCATEForuninovcr25ciiicsallovcrIndia.Qucsiion Pacrs including scciion icsis and full icsis arc dcsigncd ly IISc alunni according io iIc laicsi syllalus. Pcrccniilc, All India Fanl, inicraciion wiiI IISc alunni in our onlinc discussion foruns, and norc.visii www.gote|orum.com Ihink G/IE Ihink G/IE Fcrum 1.37The input impedance of a short-circuited lossless transmission line quarter wave length is (a)purely reactive(b)purely resistive(c)infinite (d)dependent on the characteristic impedance of the line. 1.38Theelectricfieldcomponentofauniformplaneelectromagneticwave propagating in the Y-direction in a lossless medium will satisfy the equation. (a) 2 22 2y yE Ey t = (b) 2 22 2y yE Ex t = (c) 2 22 2x xE Ey t = (d) 2 22 2x zx zE EH H+=+ 1.39A radio wave is incident on a layer of ionosphere at an angle of 30 degree with the vertical. If the critical frequency is 1.2 MHz, the maximum usable frequency is (a)1.2 MHz(b)2.4 MHz(c)0.6 MHz(d) 1.386 MHz 1.40Inabroadsidearrayof20isotropicradiators,equallyspacedatadistanceof ,2the beam width between first nulls is (a)51.3 degrees(b)11.46 degrees (c)22.9 degrees(d)102.6 degrees (a)Find the Laplace transform of the waveform( ) x tshown in figure. (b)Thenetworkshowninfigureis initiallyundersteadystate conditionwiththeswitchin position1.Theswitchismoved from position 1 to position 2 at t 0.Calculatethecurrent ( ) i t through 1Rafter switching. 3.Theopenlooptransferfunctionofa 2 T2T 3T4T5T6T 1 0 -1 -2 z(t) t R1=5 L=2H R2=5 10V 1 2 i(t) GATE EC - 1991 www.gateIorum.com Join discussion of iIis icsi acr ai Iii.//forun.gaicncnior.con JoinAIIIndIaMockGATECIassroomTestSerIes-200?conducicdlyCATEForuninovcr25ciiicsallovcrIndia.Qucsiion Pacrs including scciion icsis and full icsis arc dcsigncd ly IISc alunni according io iIc laicsi syllalus. Pcrccniilc, All India Fanl, inicraciion wiiI IISc alunni in our onlinc discussion foruns, and norc.visii www.gote|orum.com Ihink G/IE Ihink G/IE Fcrum feedback control system incorporating a dead time element is given by( )( ) 1TsKeG ss s=+ Where K > 0, and T > 0 are variable scalar parameters. (a)For a given value of T show that the closed loop system is stable for all value of 0K K ,theelectronconcentrationper 3cm at300Kwill be: (A) in (B) i An N + (C) A iN n (D) 2iAnN 10.Inap n+junctiondiodeunderreversebias,themagnitudeofelectricfieldis maximum at(A)the edge of the depletion region on the p-side(B)the edge of the depletion region on the n-side (C)thep n+ junction (D)the centre of the depletion region on the n-side 11.The correct full wave rectifier circuit is: (A)(B) R C R C iVoV + + Input Output Input Output

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 3 of 22 (C)(D) 12. In a transconductance amplifier, it is desirable to have(A)a large input resistance and a large output resistance(B)a large input resistance and a small output resistance(C)a small input resistance and a large output resistance(D)a small input resistance and a small output resistance 13.X=01110andY=11001aretwo5-bitbinarynumbersrepresentedintwos complement format. The sum of X and Y represented in twos complement format using 6 bits is: (A)100111(B)001000(C)000111(D) 101001 14.TheBooleanfunctionY AB CD = + istoberealizedusingonly2-inputNAND gates. The minimum number of gates required is: (A)2(B)3(C)4(D) 5 15.If the closed-loop transfer function of a control system is given as ( )( ) ( )5,2 3sT ss s=+ + then it is(A)an unstable system (B)an uncontrollable system(C)a minimum phase system (D)a non-minimum phase system 16.If the Laplace transform of a signal( ) ytis( )( )1,1Y sss= then its final value is: (A)-1(B)0(C)1(D) unbounded 17.If( ) R istheautocorrelationfunctionofareal,wide-sensestationaryrandom process, then which of the following is NOT true? (A)( ) ( ) R R = (B)( ) ( ) 0 R R (C)( ) ( ) R R = Input Output Input Output

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 4 of 22 (D)The mean square value of the process is( ) 0 R 18.If( ) Sf isthepowerspectraldensityofareal,wide-sensestationaryrandom process, then which of the following is ALWAYS true? (A)( ) ( ) 0 S Sf (B)( ) 0 Sf (C)( ) ( ) S f Sf = (D)( ) 0 Sf df=} 19.A plane wave of wavelength is traveling in a direction making an angle 30 with positive x-axis and 90 with positive y-axis. TheE

field of the plane wave can be represented as( ) is constantoE(A)

30j t x zE yE e | | | |\ .=

(B)

30j t x zE yE e | | | |\ .=

(C)

30j t x zE yE e | |+ +| |\ .=

(D)

30j t x zE yE e | | +| |\ .=

20.If C is a closed curve enclosing a surface S, then the magnetic field intensity, H

the current densityJ

and the electric flux densityD

are related by(A). .s cDH ds J dlt| |= +| |\ .}} }

(B). .c sDH dl J d dst| |= +| |\ .} }}

(C). .s cDH ds J dlt| |= +| |\ .}} }

(D). .c sDH dl J dst| |= +| |\ .} }}

Q.21 - Q.75 Carry Two Marks Each 21.It is given that 1 2, ,....MX x X are M non-zero, orthogonal vectors. The dimension of the vector space spanned by the 2M vectors 1 2 1 2, ,... , , ,...M MX X X X X X is: (A)2M(B)M + 1(C)M (D)dependent on the choice of 1 2, ,...MX X X 22.Consider the function( )22. f x x x = The maximum value of( ) f xin the closed interval4, 4 ( is: (A)18(B)10 (C)-2.25(D)indeterminate 23.Anexaminationconsistsoftwopapers,Paper1andPaper2.Theprobabilityof failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is: (A)0.5(B)0.18(C)0.12(D) 0.06

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 5 of 22 24.Thesolutionofthedifferentialequation 2222d yk y ydx= undertheboundary conditions(i) 1y y = at0 x= and(ii) 2y y = atx= ,where, k1y and 2yare constants, is (A)( )( )21 2 2exp y y y x k y = + (B)( ) ( )2 1 1exp y y y x k y = +(C)( ) ( )1 2 1sinh y y y x k y = + (D)( ) ( )1 2 2exp y y y x k y = + 25.Theequation 3 24 4 0 x x x + = istobesolvedusingtheNewton-Raphson method.If2 x= istakenastheinitialapproximationofthesolution,thenthe next approximation using this method will be: (A) 23 (B) 43 (C)1(D) 32

26.Threefunctions( ) ( ) ( )1 2 3,and, f t f t f t whicharezerooutsidetheinterval[0,T], are shown in the figure. Which of the following statements is correct? (A)( ) ( )1 2andf t f t are orthogonal(B)( ) ( )1 3andf t f t are orthogonal(C)( ) ( )2 3andf t f t are orthogonal(D)( ) ( )1 2andf t f t are orthonormal t t t 2 -2 1 2 -1 1 -3 ( )1f t( )2f t( )3f t0 3T

23T

T

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 6 of 22 27.If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral ( )211Ddss } is: (A)j(B)-j(C)-(D) 28.Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth of Filter 1 be 1Band that of Filter 2 be 2. BThe value of 12BB is: (A)4(B)1(C) 12 (D) 14

29.Forthecircuitshowninthefigure,theTheveninvoltageandresistancelooking into X-Y are: (A) 4,23V (B) 24,3V (C) 4 2,3 3V (D) 4V, 2 j j2 D 20 0 -j2 + + 1C 1L oV iV R Filter 1 + + 2 14 C C =124LL =oV iV R Filter 2 + 2i1 X Y 2A 1 i 2

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 7 of 22 30.Inthecircuitshown, CVis0voltsat0 t= sec.Fort>0,thecapacitorcurrent ( ) ,ci t wheretis in seconds, is given by (A)0.50 exp(-25t) mA(B)0.25 exp(-25t) mA (C)0.50 exp(-12.5t) mA(D)0.25 exp (-6.25t) mA 31.In the AC network shown in the figure, the phasor voltage ABV (in Volts) is: (A)0(B)530 (C)12.530 (D) 1730 32.Ap n+junctionhasabuilt-inpotentialof0.8V.Thedepletionlayerwidthata reversebiasof1.2Vis2m.Forareversebiasof7.2V,thedepletionlayer width will be: (A)4 m(B)4.9 m(C)8 m(D) 12 m 33.Group I lists four types of p-n junction diodes. Match each device in Group I with oneoftheoptioninGroupIItoindicatethebiasconditionofthatdeviceinits normal mode of operation.Group IGroup II (P) Zener Diode (1) Forward bias(Q) Solar cell (2) Reverse bias (R) LASER diode(S) Avalanche Photodiode(A)P-1 Q-2R-1S-2 (B)P-2 Q-1R-1S-2 (C)P-2 Q-2R-1S-1 (D)P-2 Q-1R-2S-2 + 20k 20k 10VcV+ 4F cij3 5 5 -j3 530 A A B

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 8 of 22 34.TheDCcurrentgain( ) ofaBJTis50.Assumingthattheemitterinjection efficiency is 0.995, the base transport factor is: (A)0.980(B)0.985(C)0.990(D) 0.995 35.Group I lists four different semiconductor devices. Match each device in Group I with its characteristic property in Group II. (A)P-3 Q-1R-4S-2 (B)P-1 Q-4R-3S-2 (C)P-3 Q-4R-1S-2 (D)P-3 Q-2R-1S-4 36.For the Op-Amp circuit shown in the figure, oVis: (A)-2 V(B)-1 V(C)-0.5 V(D) 0.5 V 37.For the BJT circuit shown, assume that the of the transistor is very large and 0.7.BEV V =The mode of operation of the BJT is: Group IGroup II (P) BJT(1) Population inversion(Q) MOS capacitor (2) Pinch-off voltage(R) LASER diode (3) Early effect(S) JFET(4) Flat-band voltage+ 1k 1k 1k 2k 1V oV + + 1k 10k 2V 10V

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 9 of 22 (A)cut-off(B)saturation (C)normal active (D) reverse active 38.In the Op-Amp circuit shown, assume that the diode current follows the equation ( ) exp .s TI I V V = For 1 22, ,and for4, .i o o i o oV V V V V V V V = = = = Therelationship between 1 2and o oV V is: (A) 2 12o oV V = (B) 22 1 o oV e V =(C) 2 1 ln 2o oV V = (D) 1 2 ln 2o o TV V V = 39. IntheCMOSinvertercircuitshown,ifthetransconductanceparametersofthe NMOSandPMOStransistorsare 240/pnn p n ox p oxn pWWk k C C A VL L = = = = and their threshold voltages are1,THn THpV V V = =the current I is: (A)0 A(B)25 A(C)45 A(D) 90 A 40.FortheZenerdiodeshowninthefigure,theZenervoltageatkneeis7V,the kneecurrent is negligible and the Zener dynamic resistance is 10. If the input voltage( )iV range is from 10 to 16V, the output voltage( )0V ranges from (A)7.00 to 7.29 V(B)7.14 to 7.29 V (C)7.14 to 7.43 V(D)7.29 to 7.43 V + 2k oV iVPMOS NMOS I 5V 2.5V 200 iVoV +

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 10 of 22 41.TheBooleanexpressionY A B C D A B C D A B C D A B C D = + + + canbe minimized to(A) Y A B C D A B C AC D = + +(B)Y A B C D B C D A B C D = + +(C)Y A B C D B C D A B C D = + +(D)Y A B C D B C D A B C D = + + 42.ThecircuitdiagramofastandardTTLNOTgateisshowninthefigure.When 2.5,iV V =the modes of operation of the transistors will be: (A) 1 : Q reverse active; 2 : Q normal active; 3 : Q saturation; 4 : Q cut-off (B) 1 : Q reverse active; 2 : Q saturation; 3 : Q saturation; 4 : Q cut-off (C) 1 : Q normal active; 2 : Q cut-off; 3 : Q cut-off; 4 : Qsaturation (D) 1 : Q saturation; 2 : Q saturation; 3 : Q saturation; 4 : Qnormal active 43.In the following circuit, X is given by 5CCV V =100 1.4k 4k 1 k oV + 3Q 2Q 1QiV+ 4Q D 1S 0S 0I1I 2I3I1 1 0 0 AB 4-to-1 MUX Y 1S 0S 0I1I 2I3I1 1 0 0 C 4-to-1 MUX YX

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 11 of 22 (A)X A B C A B C A B C A B C = + + +(B)X A B C A B C A B C A B C = + + +(C)X AB BC AC = + +(D)X A B B C A C = + + 44.The following binary values were applied to the X and Y inputs of the NAND latch shown in the figure in the sequence indicated below: 0, 1;0, 0; 1, 1. X Y X Y X Y = = = = = =The corresponding stable P, Q outputs will be: (A)P = 1, Q = 0; P = 1, Q = 0;P = 1, Q = 0 or P = 0, Q = 1 (B)P = 1, Q = 0; P = 0, Q = 1; or P = 0, Q = 1; P = 0, Q = 1 (C)P = 1, Q = 0; P = 1, Q = 1;P = 1, Q = 0 or P = 0, Q = 1 (D)P = 1, Q = 0; P = 1, Q = 1; P = 1, Q = 1 45.For the circuit shown, the counter state( )1 0Q Q follows the sequence (A)00, 01, 10, 11, 00 .(B)00, 01, 10, 00, 01 . (C)00, 01, 11, 00, 01 .(D)00, 10, 11, 00, 10 . 46.An 8255 chip is interfaced to an 8085 microprocessor system as an I/O mapped I/O as shown in the figure. The address lines 0Aand 1Aof the 8085 are used by the8255chiptodecodeinternallyitsthreeportsandtheControlregister.The X Y P Q 0D 0Q 1D 1QClock

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 12 of 22 address lines 3A to 7Aas well as theIO Msignal are used for address decoding. The range of addresses for which the 8255 chip would get selected is: (A)F8H - FBH(B)F8H - FCH(C)F8H - FFH(D) F0H - F7H 47.The3-dBbandwidthofthelow-passsignal( ) ,te u twhere( ) ut istheunitstep function, is given by(A) 12Hz(B) 12 1 2Hz (C)(D) 1 Hz 48.A Hilbert transformer is a(A)non-linear system (B)non-causal system(C)time-varying system(D)low-pass system 49.The frequency response of a linear, time-invariant system is given by( )5.1 10Hfj f =+ The step response of the system is: (A) ( )( )55 1te u t (B)( )55 1te u t| | | |\ . (C) ( )( )51 15te u t (D)( )5115te ut| | | |\ . 50.A 5-point sequencex n( is given as3 1, 2 1, 1 0, 0 5, 1 1. x x x x x = = = = =((((( Let ( )jXedenotethediscrete-timeFouriertransformof. xn( Thevalueof ( )jXe d} is: (A)5(B)10(C)16(D) 5 + j10 7A 6A 5A4A 3A IO M1A0A 1A0A CS8255

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 13 of 22 51.The z-transformXz( of a sequencex n( is given by 10.5.1 2Xzz=( It is given that the region of convergence ofXz( includes the unit circle. The value of0 x( is: (A)-0.5(B)0(C)0.25(D) 0.5 52.A control system with a PD controller is shown in the figure. If the velocity error constant1000vK = andthedampingratio0.5, = thenthevaluesof and P DK K are: (A)100, 0.09P DK K = = (B)100, 0.9P DK K = = (C)10, 0.09P DK K = = (D)10, 0.9P DK K = = 53.Thetransferfunctionofaplantis( )( )( )25.5 1T ss s s=+ + +Thesecond-order approximation of( ) T susing dominant pole concept is: (A) ( ) ( )15 1 s s + +(B) ( ) ( )55 1 s s + +(C) 251 s s + +(D) 211 s s + + 54.The open-loop transfer function of a plant is given as( )21.1Gss= If the plant is operatedinaunityfeedbackconfiguration,thentheleadcompensatorthatan stabilize this control system is: (A) ( ) 10 12ss+(B) ( ) 10 42ss++(C) ( ) 10 210ss++(D) ( ) 2 210ss++ 55.Aunityfeedbackcontrolsystemhasanopen-looptransferfunction ( )( )2.7 12KGsss s=+ +ThegainKforwhich1 1 s j = + will lieontherootlocus of this system is: (A)4(B)5.5(C)6.5(D) 10 P DK Ks +( )10010 ss + + r

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 14 of 22 56.TheasymptoticBodeplotofatransferfunctionisasshowninthefigure.The transfer function( ) Gscorresponding to this Bode plot is: (A) ( ) ( )11 20 s s + +(B) ( ) ( )11 20 ss s + + (C) ( ) ( )1001 20 ss s + +(D) ( ) ( )1001 1 0.05 ss s + + 57.The state space representation of a separately excited DC servo motor dynamics is given as 1 1 01 10 10a addtui didt ( (((( ( = + ((( ( ( (A) 21011 11 s s + +(B) 2111 11 s s + +(C) 210 1011 11ss s++ +(D) 211 s s + + 58.In delta modulation, the slope overload distortion can be reduced by(A)decreasing the step size (B)decreasing the granular noise(C)decreasing the sampling rate(D)increasing the step size 59.The raised cosine pulse( ) p tis used for zero ISI in digital communications. The expression for( ) p twith unity roll-off factor is given by( )( )22sin4.4 1 16Wtp tWt W t= The value of( )1at 4p t tW= is: (A)-0.5(B)0(C)0.5(D) 0.1 0 20 40 60 110100 20 -40 dB/decade -20 dB/decade -60 dB/decade ( ) ( ) Gj dB

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 15 of 22 60.Inthefollowingscheme,ifthespectrumM(f)of( ) m t isasshown,thenthe spectrum( ) ( ) ofYf ytwill be: (A)(B) (C)(D) 61.Duringtransmissionoveracertainbinarycommunicationchannel,biterrors occursindependentlywithprobability. p TheprobabilityofATMOSTonebitin error in a block of n bits is given by (A) np(B)1np (C)( ) ( )11 1n nnp p p + (D)( ) 1 1np 62.In a GSM system, 8 channels can co-exist in 200 KHz bandwidth using TDMA. A GSM based cellular operator is allocated 5 MHz bandwidth. Assuming a frequency reusefactorof 1,5i.e.afive-cellrepeatpattern,themaximumnumberof simultaneous channels that can exist in one cell is: (A)200(B)40(C)25(D) 5 63.InaDirectSequenceCDMAsystemthechiprateis1.2288 610 chipsper second. If the processing gain is desired to be AT LEAST 100, the data rate (A)must be less than or equal to 12.288 310 bits per sec (B)must be greater than 12.288 310 bits per sec 0-B+B f M(f) m(t) Hilbert transformer + + y(t) ( ) sin 2Bt ( ) cos 2Bt 0 f Y(f) -B+B 0 f Y(f) -B+B-2B+2B 0 f Y(f) -B+B-2B+2B 0-B+B f M(f)

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 16 of 22 (C)must be exactly equal to 12.288 310 bits per sec (D)can take any value less than 122.88 310 bits per sec. 64.Anair-filledrectangularwaveguidehasinnerdimensionsof3cm2cm.The waveimpedanceofthe 20TE modeofpropagationinthewaveguideata frequency of 30 GHz is (free space impedance 0377 = ) (A)308 (B)355 (C)400 (D) 461 65.TheH

field (in A/m) of a plane wave propagating in free space is given by

( )

0 053 5cos sin .2H x t z y t z | |= + + |\ .

The time average power flow density in Watts is: (A) 0100(B) 0100(C) 2050 (D) 050 66.TheE

field in a rectangular waveguide of inner dimensions a b is given by( ) 2022sin sinxE H t zya ah | | | |= ||\ . \ .

Where 0His a constant, and a and b are the dimensions along the x-axis and the y-axis respectively. The mode of propagation in the waveguide is: (A) 20TE (B) 11TM (C) 20TM (D) 10TE 67.A load of 50 is connected in shunt in a 2-wire transmission line of 050 Z = as showninthefigure.The2-portscatteringparametermatrix(S-matrix)ofthe shunt element is: (A) 1 12 21 12 2 ( ( ( ( ( (B) 0 11 0 ( (

(C) 1 23 32 13 3 ( ( ( ( ( (D) 1 34 43 14 4 ( ( ( ( ( 050 Z = 050 Z = 50

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 17 of 22 68.Theparallelbranchesofa2-wiretransmissionlineareterminatedin100and 200 resistors as shown in the figure. The characteristic impedance of the line is 050 Z = and each section has a length of.4 The voltage reflection coefficient at the input is: (A) 75j (B) 57(C) 57j (D) 57

69.A 2dipoleiskepthorizontallyataheightof 02aboveaperfectlyconducting infinitegroundplane.Theradiationpatternintheplaneofthedipole ( )plane E

looks approximately as (A)(B) (C)(D) 4 4 4 050 Z = 050 Z = 050 Z = 100 200 y z y z y z y z

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 18 of 22 70.A right circularly polarized (RCP) plane wave is incident at an angle of 60 to the normal,onanair-dielectricinterface.Ifthereflectedwaveislinearlypolarized, the relative dielectric constant 2 r is: (A)2 (B)3 (C)2(D) 3 Common Data Questions Common Data for Questions 71, 72, 73: Thefigureshowsthehigh-frequencycapacitance-voltage(C-V)characteristicsofa Metal/Si2O/silicon(MOS)capacitorhavinganareaof 4 21 10 . cm Assumethatthe permittivities( )0r ofsiliconandSi2Oare 121 10 F/cmand 133.5 10 F/cm respectively. 71.The gate oxide thickness in the MOS capacitor is: (A)50 nm(B)143 nm(C)350 nm(D) 1 m 72.The maximum depletion layer width in silicon is(A)0.143 m(B)0.857 m(C)1 m(D) 1.143 m 73.Consider the following statements about the C-V characteristics plot: S1: The MOS capacitor has an n-type substrate.S2: If positive charges are introduced in the oxide, the C-V plot will shift to the left.Then which of the following is true? (A)Both S1 and S2 are true(B)S1 is true and S2 is false (C)S1 is false and S2 is true(D)Both S1 and S2 are false RCP air dielectric Linearly polarized6060 t 2 r11r =C 7pF 1pF 0 V

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 19 of 22 Common Data for Questions 74, 75: Two4-raysignalconstellationsareshown.Itisgiventhat 1 2and constitutean orthonormal basis for the two constellations. Assume that the four symbols in both the constellationsareequiprobable.Let 02Ndenotethepowerspectraldensityofwhite Gaussian noise. 74.TheratiooftheaverageenergyofConstellation1totheaverageenergyof Constellation 2 is: (A) 24a(B)4(C)2(D) 8 75.IftheseconstellationsareusedfordigitalcommunicationsoveranAWGN channel, then which of the following statements is true? (A)Probability of symbol error for Constellation 1 is lower(B)Probability of symbol error for Constellation 1 is higher(C)Probability of symbol error is equal for both the constellations(D)Thevalueof 0Nwilldeterminewhichofthetwoconstellationshasalower probability of symbol error. Linked Answer Questions: Q.76 to Q.85 Carry Two Marks Each Statement for Linked Answer Questions 76 & 77: Consider the Op-Amp circuit shown in the figure. 22a1 0 2a 22a Constellation 1 2a1 0 a a Constellation 2 a+ 1R R C iVoV 1R

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 20 of 22 76.The transfer function( ) ( )o iV s V s is: (A) 11sRCsRC+(B) 11sRCsRC+(C) 11 sRC (D) 11 sRC + 77.If( )1 siniV V t =and( )2 sin ,oV V t = +then the minimum and maximum values of(in radians) are respectively(A) and 2 2 (B)0 and 2(C)- and 0(D) and 02 Statement for Linked Answer Questions 78 & 79: An 8085 assembly language program is given below. Line 1:MVI A, B5H 2:MVI B, 0EH 3:XRI 69H 4:ADD B 5:ANI 9BH 6:CPI 9FH 7:STA 3010H 8:HLT 78.The contents of the accumulator just after execution of the ADD instruction in line 4 will be (A)C3H(B)EAH(C)DCH(D) 69H 79.After execution of line 7 of the program, the status of the CY and Z flags will be (A)CY = 0, Z = 0(B)CY = 0, Z = 1(C)CY = 1, Z = 0(D) CY = 1, Z = 1 Statement for Linked Answer Questions 80 & 81: Consider a linear system whose state space representation is( ) ( ). xt Axt =

If the initial state vector of the system is( )10 ,2x (=( then the system response is( )222ttexte (=(( . Iftheinitialstatevectorofthesystemchangesto( )101x (=( ,thenthesystem response becomes( ) .ttexte (=((

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 21 of 22 80.The eigenvalue and eigenvector pairs( ) ,i i for the system are (A) 1 11, and-2,1 -2| | | |(( || (( \ . \ .(B) 1 11, and2,1 -2| | | |(( || (( \ . \ .

(C) 1 11, and-2,1 -2| | | |(( || (( \ . \ .(D) 1 12, and 1,1 -2| | | |(( || (( \ . \ .

81.The system matrix A is: (A) 0 11 1 ( ( (B) 1 11 2 ( ( (C) 2 11 1 ( ( (D) 0 12 3 ( (

Statement for Linked Answer Questions 82 & 83: An input to a 6-level quantizer has the probability density function( ) f xas shown in the figure. Decision boundaries of the quantizer are chosen so as t maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are `-1, `0 and `1. 82.The values of a and b are: (A) 1 1and 6 12a b = = (B) 1 3and 5 40a b = =(C) 1 1and 4 16a b = = (D) 1 1and 3 24a b = = 83.Assuming that the reconstruction levels of the quantizer are the mid-points of the decision boundaries, the ratio of signal power to quantization noise power is: (A) 1529(B) 643(C) 763(D) 28 -5-1 015 a b f(x) x

All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 22 of 22 Statement for Linked Answer Questions 84 & 85: IntheDigital-to-Analogconvertercircuitshowninthefigurebelow,10 VRV = and 10 . R k = 84.The currentiis: (A)31.25 A(B)62.5 A(C)125 A(D) 250 A 85.The voltage oVis: (A)-0.781 V(B)-1.562 V(C)-3.125 V(D) -6.250 V + RR R i 2R R 2R2R2R2R RV oV EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 1 of 22 Q. 1 to 20 Carry One Mark Each 1.Allthefourentriesofthe22matrix 11 1221 22p pPp p (=( arenonzero,andoneofits eigenvalues is zero. Which of the following statements is true? (A) 11 22 12 21p p p p 1 =(B) 11 22 12 21p p p p 1 = (C) 11 22 12 21p p p p 0 =(D) 11 22 12 21p p p p 0 + = 2.The system of linear equations 4x 2y 72x y 6+ =+ = has(A)a unique solution (B)no solution (C)an infinite number of solutions(D)exactly two distinct solutions 3.The equation( ) sin z 10has =(A)no real or complex solution (B)exactly two distinct complex solutions (C)a unique solution (D)an infinite number of complex solutions 4.For real values of x, the minimum value of the function( ) ( ) ( ) f x exp x exp x is = + (A)2(B)1(C)0.5(D) 0 5.WhichofthefollowingfunctionswouldhaveonlyoddpowersofxinitsTaylor series expansion about the point x=0? (A) ( )3sin x (B) ( )2sin x (C) ( )3cos x (D) ( )2cos x 6.Which of the following is a solution to the differential equation ( )( )dx t3x t 0?dt+ =(A)( )tx t 3e= (B)( )3tx t 2e= (C)( )23x t t2= (D)( )2x t 3t = 7.Inthefollowinggraph,thenumberoftrees(P) andthenumberofcut-sets(Q) are (A)P=2, Q=2 (B)P=2, Q=6 (C)P=4, Q=6 (D)P=4, Q=10 ( ) 4( ) 1( ) 2( ) 3EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 2 of 22 8.Inthefollowingcircuit,theswitchSisclosedatt=0.Therateofchangeof current( )di0dt+is given by (A)0(B) S SR IL(C) ( )S SR R IL+(D) 9.Theinputandoutputofacontinuoustimesystemarerespectivelydenotedby x(t) and y(t). Which of the following descriptions corresponds to a causal system? (A)( ) ( ) ( ) y t x t 2 x t 4 = + + (B)( ) ( ) ( ) y t t 4 x t 1 = +(C)( ) ( ) ( ) y t t 4 x t 1 = + (D)( ) ( ) ( ) y t t 5 x t 5 = + + 10.Theimpulseresponseh(t)ofalineartime-invariantcontinuoustimesystemis described by( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = + where u(t) denotes the unit step function, and and are real constants. This system is stable if (A) is positive and is positive(B) is negative and is negative (C) is positive and is negative(D) is negative and is positive 11.The pole-zero plot given below corresponds to a (A)Low pass filter(B)High pass filter(C)Band pass filter (D) Notch filter 12.Step responses of a set of three second-order underdamped systems all have the samepercentageovershoot.Whichofthefollowingdiagramsrepresentsthe poles of the three systems? SR( ) i tLSRSIjOOX XEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 3 of 22 (A)(B) (C)(D) 13.Which of the following is NOT associated with a p-n junction? (A)Junction capacitance(B)Charge Storage Capacitance (C)Depletion Capacitance(D)Channel Length Modulation 14.Which of the following is true? (A)A silicon wafer heavily doped with boron is a p+ substrate (B)A silicon wafer lightly doped with boron is a p+ substrate (C)A silicon wafer heavily doped with arsenic is a p+ substrate (D)A silicon wafer lightly doped with arsenic is a p+ substrate 15.For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is (A)360(B)180(C)90(D) 45 16.For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of two of Maxwells equations? (A) .E 0B 0 = =(B) .E 0.B 0 = =(C) E 0B 0 = =(D) E 0.B 0 = = j........XXXXXXj X X X X X X jXXX....XXX..jX.XXXXX...........EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 4 of 22 17.In the following limiter circuit, an input voltage iV 10sin100 t = applied. Assume thatthediodedropis0.7Vwhenitisforwardbiased.TheZenerbreakdown voltage is 6.8V. The maximum and minimum values of the output voltage respectively are (A)6.1V, 0.7V (B)0.7V, 7.5V (C)7.5V, 0.7V (D) 7.5V, 7.5V 18.Asiliconwaferhas100nmofoxideonitandisinsertedinafurnaceata temperatureabove1000Cforfurtheroxidationindryoxygen.Theoxidation rate (A)is independent of current oxide thickness and temperature (B)is independent of current oxide thickness but depends on temperature (C)slows down as the oxide grows (D)is zero as the existing oxide prevents further oxidation 19.The drain current of a MOSFET in saturation is given by( )2p GS rK V V = lwhere K is a constant. The magnitude of the transconductance gm is (A) ( )2GS TDSK V VV(B)( )GS T2K V V (C) dGS DSIV V (D) ( )2GS TGSK V VV 20.Considertheamplitudemodulated(AM)signal C c m cA cos t 2cos t cos t. + For demodulating the signal using envelope detector, the minimum value of Ac should be (A)2(B)1(C)0.5(D) 0 Q. 21 to 75 carry two Marks Each 21.TheTheveninequivalentimpedanceZthbetweenthenodesPandQinthe following circuit is (A)1(B) 11 ss+ + (C) 12 ss+ + (D) 22s s 1s 2s 1+ ++ + 1K D10D2 V6.8VZiV+110V1H1 F11 AQPEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 5 of 22 22.The driving point impedance of the following network is given by( )20.2sZ s .s 0.1s 2=+ + The component values are (A)L 5H, R 0.5 , C 0.1F = = = (B)L 0.1H, R 0.5 , C 5F = = =(C)L 5H, R 2 , C 0.1F = = = (D)L 0.1H, R 2 , C 5F = = = 23.The circuit shown in the figure is used to charge the capacitor C alternately from twocurrentsourcesasindicated.TheswitchesS1andS2aremechanically coupled and connected as follows ( ) ( )( ) ( ) ( )For 2nT t 2n 1 T, n 0,1,2,... S1 to P1 and S2 to P2For 2n 1 T t 2n 2 T, n 0,1,2,... S1 to Q1 and S2 to Q2 < + =+ < + = Assumethatthecapacitorhaszeroinitialcharge.Giventhatu(t) isaunitstep function, the voltage Vc(t) across the capacitor is givenbe (A)( ) ( )nn 01 tu t nT= (B)( ) ( ) ( )nn 0u t 2 1 u t nT=+ (C)( ) ( ) ( ) ( )nn 0tu t 2 1 t nT u t nT=+ (D) ( ) ( ) t 2nT t 2nT Tn 00.5 e 0.5e = ( + 24.The probability density function (PDF) of a random variable X is as shown below R( ) Z sL O( )CV t+ 1A 1A1FC1S2 S10.51Q1 P1 Q2 P2111 0 1 xPDFEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 6 of 22 The corresponding cumulative distribution function (CDF) has the form (A)(B) (C)(D) 25.The recursion relation to solve x=e-x using Newton Raphson method is (A) nxn 1x e+= (B) nxn 1 nx x e+= (C)( )nnxn 1 n xex 1 x1 e+ = ++(D) ( )nnx 2n nn 1 xnx e 1 x 1xx e+ + = 26.The residue of the function( )( ) ( )2 21f z at z 2 isz 2 z 2= =+ (A) 132 (B) 116 (C) 116(D) 132 27.Consider the matrix 0 1P .2 3 (=( The value of eP is (A) 2 1 1 22 1 2 12e 3e e e2e 2e 5e e ( ( (B) 1 2 2 11 2 1 2e e 2e e2e 4e 3e 2e ( + ( + (C) 2 1 1 22 1 2 15e e 3e e2e 6e 4e e ( ( + (D) 1 2 1 21 2 1 22e e e e2e 2e e 2e ( ( + + 28.IntheTaylorseriesexpansionofexp(x)+sin(x)aboutthepointx=,the coefficient of( )2x is (A)( ) exp (B)( ) 0.5exp (C)( ) exp 1 + (D)( ) exp 1 11 0 1 xCDF11 01xCDF11 0 1 xCDF11 01xCDF1 EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 7 of 22 29.( ) ( ) ( )xP x M exp 2 x Nexp 3 x = + istheprobabilitydensityfunctionforthereal randomvariableX,overtheentirexaxis.MandNarebothpositivereal numbers. The equation relating M and N is (A) 2M N 13+ = (B) 12M N 13+ = (C)M N 1 + = (D) M N 3 + = 30.Thevalueoftheintegralofthefunction( )3 4g x, y 4x 10y = + alongthestraight line segment from the point (0, 0) to the point (1, 2) in the x-y plane is (A)33(B)35(C)40(D) 56 31.Alinear,time-invariant,causalcontinuoustimesystemhasarationaltransfer function with simple poles at s=-2 and s=-4, and one simple zero at s=-1. A unit stepu(t)isappliedattheinputofthesystem.Atsteadystate,theoutputhas constant value of 1. The impulse response of this system is (A)( ) ( ) ( ) exp 2t exp 4t u t( + (B)( ) ( ) ( ) ( ) 4exp 2t 12exp 4t exp t u t( + (C)( ) ( ) ( ) 4exp 2t 12exp 4t u t( + (D)( ) ( ) ( ) 0.5exp 2t 1.5exp 4t u t( + 32.The signal x(t) is described by ( )1 for 1 t 1x t0 otherwise + = Two of the angular frequencies at which its Fourier transform becomes zero are (A),2 (B)0.5 ,1.5 (C)0, (D) 2 ,2.5 33.Adiscretetimelinearshift-invariantsystemhasanimpulseresponseh[n]with h[0]=1,h[1]=-1.h[2]-2,andzerootherwise.Thesystemisgivenaninput sequencex[n]withx[0]x[2]-1,andzerootherwise.Thenumberofnonzero samples in the output sequence y[n], and the value of y[2] are, respectively (A)5, 2(B)6, 2(C)6, 1(D) 5, 3 34.ConsiderpointsPandQinthex-yplane,withP=(1,0)andQ=(0,1).Theline integral( )QP2 xdx ydy +alongthesemicirclewiththelinesegmentPQasits diameter (A)is -1 (B)is 0 (C)is 1 (D)depends on the direction (clockwise or anti-clockwise) of the semicircle EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 8 of 22 35.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 system relations R1, R2, R3, R4. PropertiesRelations P1: Linear but NOT time-invariantR1:( ) ( )2y t t x t =P2: Time-invariant but NOT linear( ) ( ) R2: y t t x t =P3: Linear and time-invariant( ) ( ) R3: y t x t =( ) ( ) R4 : y t x t 5 = (A)( ) ( ) ( ) P1,R1 , P2,R3 , P3,R4 (B)( ) ( ) ( ) P1,R2 , P2,R3 , P3,R4(C)( ) ( ) ( ) P1,R3 , P2,R1 , P3,R2 (D)( ) ( ) ( ) P1,R1 , P2,R2 , P3,R3 36.A memoryless sourceemits n symbols each with a probability p. Theentropy of the source as a function of n (A)increases as log n(B)decreases as log (1/n) (C)increases as n(D)increases as n log n 37.{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence ( ) ( ) ( )N 1r 01y n x r x n r isN== + (A)( )2X k (B)( ) ( )N 1r 01X r X * k rN=+ (C)( ) ( )N 1r 01X r X k rN=+ (D)0 38.Group I lists a set of four transfer functions. Group II gives a list of possible step responsesy(t).Matchthestepresponseswiththecorrespondingtransfer functions Group I 2 2 2 225 36 36 49P Q R Ss 25 s 20s 36 s 12s 36 s 7s 49= = = =+ + + + + + + Group II (1)(2) ( ) y t1t( ) y t1tEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 9 of 22 (3)(4) (A)P-3,Q-1,R-4,S-2 (B)P-3,Q-2,R-4,S-1 (C)P-2,Q-1,R-4,S-3 (D)P-3,Q-4,R-1,S-2 39.Acertainsystemhastransferfunction( )2s 8G s ,s s 4+=+ isaparameter. Consider the standard negative unity feedback configuration as shown below Which of the following statements is true? (A)The closed loop system in never stable for any value of (B)For some positive values of , the closed loop system is stable, but not for all positive values (C)For all positive values of , the closed loop system is stable (D)Theclosedloopsystemisstableforallvaluesof,bothpositiveand negative 40.A single flow graph of a system is given below ( ) y t1t( ) y t1t( ) G s+1 / s 1 / s1 / s 11 EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 10 of 22 The set of equations that correspond to this signal flow graph is (A) 1 112 223 3x x0 1 0udx 0 x 0 0dtu0 0 1x x| | | | (( || | | ((= +||| ((| ||\ (( || \ \ (B) 1 112 223 3x x0 0 0udx 0 x 0 1dtu0 1 0x x| | | | (( || | | ((= +||| ((| ||\ (( || \ \ (C) 1 112 223 3x x0 1 0udx 0 x 0 1dtu0 0 0x x| | | | (( || | | ((= +||| ((| ||\ (( || \ \ (D) 1 112 223 3x x0 0 1udx 0 x 0 0dtu0 1 0x x| | | | (( || | | ((= +||| ((| ||\ (( || \ \ 41.The number of open right half plane poles of( )5 4 3 210G s iss 2s 3s 6s 5s 3=+ + + + + (A)0(B)1(C)2(D) 3 42.The magnitude of frequency response of an underdamped second order system is 5at0rad/secandpeaksto 10at 5 2rad / sec.3Thetransferfunctionofthe system is (A) 2500s 10s 100 + +(B) 2375s 5s 75 + + (C) 2720s 12s 144 + +(D) 21125s 25s 225 + + 43.Group1givestwopossiblechoicesfortheimpedanceZinthediagram.The circuitelementsinZsatisfytheconditionR2C2>R1C1.Thetransferfunction 0iVV represents a kind of controller. Match the impedances in Group I with the types of controllers in Group II. 1V1R+Z1C0VEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 11 of 22 Group IGroup II P. 1.PID controller 2.Lead compensator 3.Lag compensator Q. (A)Q 1,R 2 (B)Q 1,R 3 (C)Q 2,R 3 (D) Q 3,R 2 44.For the circuit shown in the following figure, transistors M1 and M2 are identical NMOS transistors. Assume that M2 is in saturation and the output is unloaded The current Ix is related to Ibias as (A) x bias sI I I = + (B) x biasI I =(C) x bias sI I I = (D) outx bias DDEVI I VR| |= |\ 45.The measured transconductance gm of an NMOS transistor operating in the linear region is plotted against the gate voltage VG at constant drain voltage VD. Which of the following figures represents the expected dependence of gm on VG? (A)(B) 2R2CERoutVxIDDVbiasIaVM1 M2SImgGVmgGV2R2CEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 12 of 22 (C)(D) 46.Consider the following circuit using an ideal OPAMP. The I-V characteristics of the diode is described by the relation TVV0 T 0I I e 1 where V 25mV, I 1 A| |= | = = |\ and V is the voltage across the diode (taken as positive for forward bias). For an input voltage 1V 1V, = the output voltage V0 is (A)0 V(B)0.1V(C)0.7V(D) 1.1V 47. The OPAMP circuit shown above represents a (A)high pass filter(B)low pass filter (C)band pass filter(D)band reject filter mgGVmgGV4 K DiV 1V =100K+0V+C2R1R LiV0VEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 13 of 22 48.Two identical NMOS transistors M1 and M2 are connected as shown below. Vbias is chosen so that both transistors are in saturation. The equivalent gm of the pair is defined to be outiIV at constant Vout. The equivalent gm of the pair is (A)The sum of individual gms of the transistors (B)The product of individual gms of the transistors (C)Nearly equal to the gm of M1 (D)Nearly equal to gm/g0 of M2 49.An 8085 executes the following instructions 2710 LXI H, 30A0H2713 DAD H2714 PCHL AlladdressesandconstantsareinHex.LetPCbethecontentsoftheprogram counter and HL be the contents of the HL register pair just after executing PCHL. Which of the following statements is correct (A)PC 2715H = (B)PC 30A0H = (C)PC 6140H = (D) PC 6140H =HL 30A0H = HL 2715H = HL 6140H = HL 2715H = 50.An astable multivibrator circuit using IC 555 timer is shown below. Assume that the circuit is oscillating steadily outIoutV2M1M iVbiasV9V( )8Supply ( )4Re set( ) 6 Threshold( ) 2 Trigger( ) Output 3( ) Discharge7( ) Gnd112 K.01 F CV10K30KEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 14 of 22 The voltage VC across the capacitor varies between (A)3V to 5V(B)3V to 6V(C)3.6V to 6V(D) 3.6V to 5V 51.Siliconisdopedwithborontoaconcentrationof41017atoms/cm3.Assuming the intrinsic carrier concentration of silicon to be 1.51010/cm3 and the value of kTq to be 25mV at 300K Compared to undoped silicon, the Fermi level of doped silicon (A)Goes down by 0.13eV (B)Goes up by 0.13eV (C)Goes down by 0.427eV(D)Goes up by 0.427eV 52.The cross section of a JFET is shown in the following figure. Let Va be -2V and let Vpbetheinitialpinch-offvoltage.IfthewidthWisdoubled(withother geometricalparametersanddopinglevelsremainingthesame),thentheratio between the mutual transconductances of the initial and the modified JFET is (A)4 (B) ( )pp1 2 / V121 1/ 2V| | | | | \ (C) ( )pp1 2 / V1 1/ 2V (D) ( )( ) ( )pp1 2 / V1 1/ 2 V 53.Consider the Schmidt trigger circuit shown below. A triangular wave which goes from -12V to 12V is applied to the inverting input of the OPAMP. Assume that the output of the OPAMP sings from +15V to -15V. The voltage at the non-inverting input switches between(A)-12V and +12V(B)-7.5V and +7.5V(C)-5V and +5V(D) 0V and 5V W Drainp+np+GateGVSourceGateGV+10k10kiV10k0V15V +15V EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 15 of 22 54.The logic function implemented by the following circuit at the terminal OUT is (A)P NOR Q (B)P NAND Q (C)P OR Q (D)P AND Q 55.Consider the following assertions S1: For Zener effect to occur, a very abrupt junction is required S2: For quantum tunneling to occur, a very narrow energy barrier is required Which of the following is correct? (A)Only S2 is true (B)S1 and S2 are both true but S2 is not a reason for S1 (C)S1 and S2 are both true and S2 is a reason for S1 (D)Both S1 and S2 are false 56.Thetwonumbersrepresentedinsigned2scomplementformare P 11101101 and Q 11100110 = = . If Q is subtracted from P, the value obtained in signed 2s complement form is (A)100000111(B)00000111(C)11111001(D) 111111001 57.WhichofthefollowingBooleanExpressioncorrectlyrepresentstherelation between P, Q, R and M1? (A)( )1M P OR Q XOR R = (B) ( )1M P AND Q XOR R =(C)( )1M P NOR Q XOR R = (D)( )1M P XOR Q XOR R = 58.For the circuit shown in the following figure I0-I3 are inputs to the 4:1 multiplexer R(MSB) and S are control bits ddVOUTP Q PQRXYZ1MEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 16 of 22 The output Z can be represented by(A)PQ PQS QRS + + (B)PQ PQR PQS + +(C)PQR PQR PQRS QRS + + + (D)PQR PQRS PQRS QRS + + + 59.For each of the positive edge-triggered J-K flip flop used in the following figure, the propagation delay isT Which of the following waveforms correctly represents the output at Q1? (A) (B) (C) (D) ZR SPPPQPQ3I2I1I0I4:1 MuxCLK11111Q0Q0J0K1J1KT1tt01CLK2T1t T + 014T1t 2 T + 012T1t 2 T + 014T1t T + 01EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 17 of 22 60.Forthecircuitshowninthefigure,Dhasatransitionfrom0to1afterCLK changes from 1 to 0. Assume gate delays to be negligible Which of the following statements is true? (A)Q goes to 1 at the CLK transition and stays at 1 (B)Q goes to 0 at the CLK transition and stays at 0 (C)Q goes to 1 at the CLK transition and goes to 0 when D goes to 1 (D)Q goes to 0 at the CLK transition and goes to 1 when D goes to 1 61.Arectangularwaveguideofinternaldimensions( ) a 4cmand b 3 = = istobe operated in TE11 mode. The minimum operating frequency is(A)6.25GHz(B)6.0GHz(C)5.0GHz(D) 3.75GHz 62.One of a loss-less transmission line having the characteristic impedance of 75and length of 1cm is short-circuited. At 3GHz, the input impedance at the other end of the transmission line is(A)0(B)Resistive(C)Capacitive(D) Inductive 63.A uniform plane wave in the free space is normally incident on an infinitely thick dielectricslab(dielectricconstant r9 = ).Themagnitudeofthereflection coefficient is(A)0(B)0.3(C)0.5(D) 0.8 64.In the design of a single mode step index optical fiber close to upper cut-off, the single mode operations is NOT preserved if(A)Radius as well as operating wavelength are halved (B)Radius as well as operating wavelength are doubled (C)Radius is halved and operating wavelength is doubled (D)Radius is doubled and operating wavelength is halved 65.At20GHz,thegainofaparabolicdishantennaof1meterdiameterand70% efficiency is(A)15dB(B)25dB(C)35dB(D) 45dB 1010CLKDQQEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 18 of 22 66.Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3dB cut-off frequency of fc. The noise power at the filter output is(A)K(B) cKf (C) cK f (D) 67.Consider a Binary Symmetric Channel (BSC) with probability of error being p. To transitabit,say1,wetransmitasequenceofthree1s.Thereceiverwill interpretthereceivedsequencetorepresent1ifatleasttwobitsare1.The probability that the transmitted bit will be received in error is(A)( )3 2p 3p 1 p + (B) 3p (C)( )31 p (D)( )3 2p p 1 p + 68.FourmessagesbandlimitedtoW,W,2Wand3Wrespectivelyaretobe multiplexedusingTimeDivisionMultiplexing(TDM).Theminimumbandwidth required for transmission of this TDM signal is(A)W(B)3W(C)6W(D) 7W 69.Consider the frequency modulated signal( ) ( )510cos 2 10 t 5sin 2 1500t 7.5sin 2 1000t ( + + withcarrierfrequencyof 510 Hz . The modulation index is(A)12.5(B)10(C)7.5(D) 5 70.The signal c m ccos t 0.5cos t sin t + is(A)FM only(B)AM only (C)both AM & FM(D)neither AM nor FM Common Data Questions 71, 72 & 73 A speech signal, band limited to 4kHz and peak voltage varying between +5V and -5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.71.If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is(A)64kHz(B)32kHz(C)8kHz(D) 4kHz 72.Assumingthesignaltobeuniformlydistributedbetweenitspeakvalues,the signal to noise ratio at the quantizer output is (A)16dB(B)32dB(C)48dB(D) 64dB 73.The number of quantitization levels required to reduce the quantization noise by a factor of 4 would be (A)1024(B)512(C)256(D) 64 EC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 19 of 22 Common Data Questions 74 & 75 ThefollowingseriesRLCcircuitwithzeroinitialconditionsisexcitedbyaunit impulse function( ) t 74.For t > 0, the output voltage( )cV tis (A) 1 3t t2 22e e3| | | |\ (B) 1t22te3 (C) 1t22 3e cos t23 | | | |\ (D) 1t22 3e sin t23 | | | |\ 75.For t > 0, the voltage across the resistor is(A) 3 1t t2 21e e3 | | | |\ (B) 1t23t 1 3te cos sin2 23( | | | |(|| || (\ \ (C) 1t22 3te sin23 | | | |\ (D) 1t22 3te cos23 | | | |\ Linked Answer Questions: Q.76 to 85 Carry Two Marks Each Statement for Linked Answer Questions: 76 & 77 A two-port network shown below is excited by external dc sources. The voltages andthecurrentsaremeasuredwithvoltmetersV1,V2andammeterA1,A2(all assumedtobeideal),asindicated.Underfollowingswitchconditions,the readings obtained are: i) 1 2 1 1 2 2S Open, S Closed A 0A, V 4.5V, V 1.5V, A 1A = = = =ii) 1 2 1 1 2 2S Closed, S Open A 4A, V 6V, V 6V, A 0A = = = = +( ) t 1H11F( )cV t1A6V++ 1S1V+2V+2S2A +1 22 11.5V+Two PortNetworkEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 20 of 22 76.The z-parameter matrix for this network is(A) 1.5 1.54.5 1.5 ( ( (B) 1.5 4.51.5 4.5 ( ( (C) 1.5 4.51.5 1.5 ( ( (D) 4.5 1.51.5 4.5 ( ( 77.The h-parameter matrix for this network is(A) 3 31 0.67( ( (B) 3 13 0.67 ( ( (C) 3 31 0.67 ( ( (D) 3 13 0.67 ( ( Statement for Linked Answer Questions: 78 & 79 Inthefollowingnetwork,theswitch isclosedatt=0-and thesamplingstarts from t = 0. The sampling frequency is 10Hz. 78.The samples( ) ( ) x n n 0, 1, 2, ... =are given by(A) ( )0.05n5 1 e (B) 0.05n5e(C) ( )5n5 1 e (D) 5n5e 79.The expression and the region of convergence of the z-transform of the sampled signal are(A) 555z, z ez e (D) 555z, z ez e> +( )sSamplerf 10Hz =z transform ( ) X z5Vs10 F 200k( ) x nEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 21 of 22 Statement for Linked Answer Questions: 80 & 81 Inthefollowingtransistorcircuit BE c EV 0.7V, r 25mV / I , and = = andallthe capacitances are very large 80.The value of DC current IE is(A)1mA(B)2mA(C)5mA(D) 10mA 81.The mid-band voltage gain of the amplifier is approximately(A)-180(B)-120(C)-90(D) -60 Statement for Linked Answer Questions: 82 & 83 In the following circuit, the comparator output is logic I if V1 > V2 and is logic 0 otherwise. The D/A conversion is done as per the relations ( ) ( )3n 2DAC 3 2 1 0n 0V 2 Volts, where b MSB ,b , b and b LSB are the counter outputs== The counter starts from the clear state 82.The stable reading of the LED display is (A)06(B)07(C)12(D) 13 20k10kC1CccV 9V =3kc2C3kEC 2.3kEI+inV 6.2VClock=4 bitUp Counter5V +ClkClr4 bitUp CounterBinarytoBCD2 DigitLEDDisplayEC GATE Paper 2008www.gateforum.com All rights reserved by GATE Forum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com.Page 22 of 22 83.The magnitude of the error between DAC inV and Vat steady state in volts is(A)0.2(B)0.3(C)0.5(D) 1.0 Statement for Linked Answer Questions: 84 & 85 Theimpulseresponseh(t)ofalineartimeinvariantcontinuoustimesystemis given by( ) ( ) ( ) h t exp 2t u t = , where u(t) denotes the unit step function 84.Thefrequencyresponse( ) H ofthissystemintermsofangularfrequencyis given by( ) H(A) 11 f2 + (B) ( ) sin(C) 12 j + (D) j2 j+ 85.The output of this system to the sinusoidal input( ) ( ) x t 2cos 2t =for all time t, is(A)0(B)( )0.252 cos 2t 0.125 (C)( )0.52 cos 2t 0.125 (D)( )0.52 cos 2t 0.25 GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. GATE PAPERECGATE-2009www.gateforum.com All rights reserved by Gateforum Educational Services Pvt. Ltd.No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com.