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GATE : Test Paper
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GATE recruitment process and aptitude test
experiences
Paper Type : Quest ion-Paper
Test Locat ion : ECE quest ions
Post ed By : Raj esh V
GATE placement paper
GATE- 2013,comput er sci ence and ECE el ect r oni cs and el ect r i cal engi neer ing quest i ons wit h
answer s and expl anat i ons GATE- 2013 col lect ion of pr evious year s model exami nat i on
paper s,GATE - 2013 st r eamwi se quest i on wi t h answer s,expl anat i ons,t i ps and t r i cks,GATE-
possi ble and f r equent l y asked quest i on t ype and Quest ion pat t er n,GATE commonl y asked
i mpor t ant Quest i ons Pr epar ed based on l at est GATE syll abus, GATE Pr evi ous year quest i ons
f or CSE,EEE,ME,ECE,AE,I T et c.. GATE 2013 model wr i t t en t est examinat ion quest i on paper s
wi t h answer s and expl anat i ons,GETE- 2013 sol ved pr evi ous year s sample quest i on
paper s,GATE 2010,2011,2012,2013 sampl e pl acement paper s wi t h sol ut i ons,GATE gener al
apt i t ude and gener al awar ness quest ions,I mpor t ant Gat e exam quest i ons and answer s wit h
expl anat ion,Gat e 2013 St r eamwi se Syl l abus and Quest i ons pat t er n,Fr equent l y asked gat e
exam quest i ons

GATE MODEL QUTI ON PAPER ( ECE)

1.The elect ron and hol e concent rat i ons in an int rinsic semi conduct or are ni per cm3 at 300k.Now, if
accept or impurit i es are int roduced wit h a concent rat ion of Na per cm3( where Na> > ni) ,t he elect ron
concent rat ion per cm3 at 300k will be
a) ni c) ni+ Na
b) Na-ni d) ni 2/ Na

2.I n a t rans conduct ance amplifier ,it i s desirable t o have
a) a large input resist ance and a large out put resi st ance
b) a large input resist ance and a smal l out put resi st ance
c) a small input resist ance and a l arge out put resi st ance
d) a small input r esist ance and a smal l out put resi st ance

3.The range of signed deci mal number t hat can be represent ed by 6 bit s 1s compl ement number is
a) -31 t o + 31
b) -64 t o + 63
c) -63 t o + 64
d) -32 t o + 31

4.A mast er sl ave f lip-fl op has t he charact eri st ic t hat
a) Change i n t he input immediat ely refl ect ed in t he out put
b) Change i n t he out put occurs when t he st at e of mast er is affect ed
c) Change i n t he out put occur when t he st at e of t he slave is affect ed
d) Bot h t he mast er and t he slave st at es are affect ed at t he same l ine

5.The Fourier t ransform of a conj ugat e symmet ric funct i on is always
a) imaginar y
0
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b) Conj ugat e ant i-symmet ric
c) real
d) conj ugat e symmet ric

6.I f t he Laplace of t he signal y( t ) i s Y( s) = 1/ ( s( s-1) ) t hen i t s fi nal value is
a) 1
b) 0
c) 1
d) Unbounded

7.A l inear syst em is equivalent ly represent ed by t wo set s of st at e equat ions.
X= AX+ BU and W= CW+ DU
The eigenvalues of t he represent at ions, are also comput ed as ( u)and ( ) .whi ch one of t he st at ement is
t rue?

a) [ u] = [ ] and X= W
b) [ u] = [ ] and X =W
c) [ u] = [ ] and X= W
d) [ u] = [ ] and X= W

8.I f t he closed l oop t ransfer funct i on of a cont rol syst em i s given as
T(s)= ( s-5) / (( s+ 2) (s+ 3)) , t hen it is
a) A unst able syst em
b) An uncont roll able syst em
c) A mini mum phase syst em
d) A non-mi nimum phase syst em

9.The i nput t o a coherent det ect or is DSB-SC signal plus noise. The noi se at t he det ect or out put is
a) The in-phase component
b) The quadrat ur e-component
c) Zero
d) The envel ope

10.I n t he PCM syst em ,if t he code word l engt h i s increased from 6 t o 8 bi t es ,t he si gnal t o quant izat i on
rat i o i mproves by t he fact or
a) [ 8/ 6]
b) 12
c) 16
d) 8

11.The dept h of penet rat ion of t he elect romagnet i c wave in a medium having conduct ivit y at a frequency
of 1MHz is 25cm. t he dept h of penet rat i on of frequency of 4MHz wi ll be
a) 6.25cm
b) 12.50cm
c) 50cm
d) 100cm

12.A t ransmissi on line i s feeding 1 wat t of power t o horn ant enna having gai n of 10 db. The ant enna is
mat ched t o t ransmi ssion l ine. The t ot al power radi at ed by horn ant enna t o free space is
a) 10 wat t s
b) 1 wat t s
c) 0.1 wat t s
d) 0.01 wat t s

13.Whi ch of t he foll owing is NOT associat ed wit h a p-n j unct ion?
a) Junct ion capacit ance
b) Charge st orage capacit ance
c) Depl et ion capacit ance
d) Channel lengt h modulat ion

14.For a hert z dipole ant enna ,t he half power beam widt h ( HPBW) i n t he E-plane i s
a) 3600
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b) 1800
c) 900
d) 450

15.I n t he followi ng l i mit er circuit , an input volt age vi= 10si n100 nt is appli ed .assume t he di ode drop is
0.7v when it is forward bi ased .t he zener breakdown volt age i s 6.8v .t he maxi mum values of t he out put
volt age i s 6.8v

a) 6.1v,-0.7v
b) 0.7v,-7.5v
c) 7.5v,-0.7v
d) 7.5v,-7.5v

16.The syst em of linear equat ion
4x+ 2y= 7
2x+ y= 6 has
a) A unique solut ion
b) No solut i on
c) An infi nit e number of solut i ons
d) Exact ly t wo dist inct solut i ons

17.A sili con wafer has 100nm of oxi de on it and is insert ed i n a fur nace at a t emperat ure above 10000c
for furt her oxi dat ion in dry oxygen rat e .t he oxidat i on rat e
a) I s independent of current oxide t hi ckness and t emperat ure
b) I s independent of current oxide t hi ckness but depends on t emperat ure
c) slow down as t he oxi de grows
d) is zero as t he exit i ng oxide prevent s furt her oxi dat ion

18.Whi ch of t he foll owing is a solut ion t o t he different ial equat ion ( dx( t ) ) / dt + 3x( t )= 0?
a) x(t ) = 3e-t
b) x(t ) = 2e-3t
c) x( t ) = 3/ 2 t 2
d) x(t ) = 3t 2

19.The equat ion sin ( z) = 10 has
a) no real compl ex solut ion
b) exact ly t wo dist i nct complex solut i ons
c) a unique sol ut ions
d) an infini t e number of compl ex sol ut ions

20.Consider t he ampl it ude modulat ed ( AM) signal for demodulat ing t he
si gnal envel ope det ect or. The mi nimum value of Ac should be
a) 2
b) 1
c) 0.5
d) 0

Quest ions 21 t o 75 carry t wo mark each

21.The Thevenin equivalent impedance Zt h bet ween t he nodes P and Q i n t he fol lowing cir cuit is
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a) 1
b) 1+ s+ 1/ s

c) 2+ s+ 1/ s

d)

22.The driving point i mpedance of t he foll owing net work
I s given by .t he component values are
a) L= 5H R= 0.5O C= 0.1F
b) L= 0.1H R= 0.5O C= 5F
c) L= 5H R= 2O C= 0.1F
d) L= 0.1H R= 2O C= 5F

23.The ci rcuit in t he figure is used t o charge t he capacit ance C alt ernat ely from t wo current sources as
i ndicat ed .The swi t ch S1 and S2 are mechanical ly coupled and connect ed as follows
For 2nTSt < (2n+ 1) T (n= 0,1,2,3..) S1 t o P1 and S2 t o P2
For ( 2n+ 1)TSt < ( 2n+ 2)T (n= 0,1,2,3..) S1 t o Q1 and S2 t o Q2

Assume t hat t he capaci t or has zero i nit i al charge, given t hat u(t ) is a unit st ep funct ion , t he volt age Vc
( t ) across t he capacit or is gi ven by
a) _( n= 0)^ ( -t ) nt u(t -nT)

b) u( t ) + 2_(n= 0) ^ ( -t ) nt u( t -nT)

c) t u( t ) + 2 _(n= 0) ^ ( -t ) nt u( t -nT)u( t -nt )

d) _( n= 0) ^ [ 0.5-e-( t -2nT) + 0.5e-( t -2nT-T) ]


24.The probabili t y densi t y funct ion ( PDF) of a random variable X i s as shown below
The corresponding cumulat i ve dist ribut ion (CDF) has t he form

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25.The recursi on relat ion t o solve x= e-x using Newt on-Raphson met hod is
a) xn+ 1= e-xn

b) xn+ 1= xn-e-x0


26.The recursi on of t he funct ion at Z= 2 i s
a) -1/ 32

b) -1/ 16

c) 1/ 16

d) 1/ 32

27.Consider t he mat rix P= (0&1@-2&-3) .The value of ep is

28.I n t he Taylor series expansion of t he exp(x)+ sin( x) about t he point x= n, t he coefficient of (x-n)2 is
a) exp( n)
b) 0.5 exp( n)
c) exp(n)+ 1
d) exp(n) -1

29.Px(x) = M exp ( -2| x| ) + N exp ( -3| x| ) is t he probabili t y densi t y funct i on for t he real random variabl e x,
Over t he ent ire x axis .M and N are bot h posi t ive real numbers . The equat i on relat i ng M ans N is
a) M+ 2/ 3N= 1

b) 2M+ 1/ 3N= 1
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c) M+ N= 1

d) M+ N= 3

30.The value of t he int egral of t he funct i on g( x,y) = 4x3+ 10y4 along t he st rai ght l i ne segment from t he
poi nt (0,0) t o t he point ( 1,2) i n t he x-y plane is
a) 33
b) 35
c) 40
d) 56

31.A li near ,t i me-invariant , casual cont inuous t ime syst em has a rat i o t ransfer funct ion wit h a simple
pol es at s= -2, and s= -4 and one simple zero at s= -1.a unit st ep u( t ) is appl ied at t he point of t he syst em
.at st eady st at e, The out put has const ant value of 1.The impulse response of t he syst em

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
x( t )= { 1 for -1StS+ 1
{ 0 ot herwise
Two of t he angular frequenci es at whi ch it s Fourier t ransform becomes zero are
a) n,2n
b) 0.5 n,1.5n
c) 0, n
d) 2 n,2.5n

33.A discret e t ime l inear shift -invariant syst em has an i mpulse response h[ n] wi t h
h[ 0] = 1,h[ 1] = -1,h[ 2] = 2, and zero ot herwi se . The syst em is given a input sequence ,x[ n] wi t h
x[ 0] = x[ 3] = 1 and ot herwise. The number of nonzero samples in t he out put sequence y[ n] ,and t he value
of y[ 2] are respect ively
a) 5,2
b) 6,2
c) 6,1
d) 5,3

34.Consider point s P and Q in t he x-y plane, wi t h P= ( 1,0) and Q= ( 0,1) . The l ine i nt egral
2j_P^ Q(( xdx+ ydy) @ ) al ong t he semici rcle wit h t he l ine segment PQ as it s diamet er
a) is -1
b) is 0
c) is 1
d) depends on t he direct ion ( clockwise or ant i clockwise) of t he semi circl e

35.Let x(t ) be t he input and y(t ) be t he out put of a cont inuous t ime syst em.Mat ch t he syst em propert ies
P1,P2 and P3 wit h syst ems relat ions R1,R2,R3 and R4

Propert ies Relat ions
P1: l inear but NOT t i me-invari ant R1: y( t ) = t 2x(t )
P2: Time-invarient but NOT l inear R2: y(t )= t | x(t )|
P3: linear and t ime i nvariant R3: 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,R3)
d) ( P1,R1) ,( P2,R2),( P3,R3)

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36.A memory l ess sources emit s n symbols each wit h a probabil it y p. The ent ropy of t he source as a
funct ion of n
a) increase as log n
b) decrease as l og (1/ n)
c) increase as n
d) increase as n l og n

37.{ x( n) } is a real -valued periodi c sequence wi t h a peri od N. x(n) and X( k) from N-poi nt . Discret e
Four ier t ransform ( DFT) pairs . The DFT Y(k) of t he sequence
Y( n) = 1/ N _( r= 0) ^ ( N-1) x( r) x( n+ r) is
a) | X( k) | 2

b) 1/ N _( r= 0) ^ ( N-1) X( r) X'( k+ r )

c) 1/ N _( r= 0) ^ (N-1) X( r) X( k+ r)

d) 0


38.Group 1 l ist a set of t ransfer funct ions. Group 2 gi ves a l ist of a possible st ep response y( t ) .mat ch t he
st ep response wit h corresponding t ransfer funct ions
Group 1
Group 2


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.A cert ain syst em has t ransfer funct ion where is t he paramet er .Consider t he
st andard negat i ve unit y feedback configurat i on as shown below

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Which of t he following st at ement are t rue?
a) t he closed l oop syst em i s never st able for any values of
b) For some posit i ve values of ,t he cl osed loop syst em i s st able , but not for al l posi t ive val ues
c) For all posit ive values of ,t he closed l oop syst em i s st able
d) The closed loop syst em is st able for al l values of ,bot h posit i ve and negat ive

40.A signal flow graph of a syst em is given below.
The set of equat ions t hat correspond t o t his signal fl ow graph is
FI G 16
41.The number of open ri ght half plain pol es of G( s) = 10/ ( s^ 5+ 2s^ 4+ 3s^ 3+ 6s^ 2+ 5s+ 3) is
( a) 0 ( b) 1
( c) 2 (d) 3

42.The magni t ude of frequency of an under damped second order syst em is 5 at 0 rad/ sec and peaks t o
10/ V3 at 5V2 rad/ sec. The t ransfer funct ion of t he syst em is
( a) 500/ ( s^ 2+ 10S+ 100) (b) 300/ (s^ 2+ 5S+ 75)

( c) 720/ ( s^ 2+ 12S+ 144) (d) 1125/ ( s^ 2+ 25S+ 225)




43.Group I gi ves t wo possi ble choices for t he i mpedance Z in t he diagram. The ci rcuit el ement s in Z
sat i sfy t he condit i on R2C2> R1C1. The t ransfer f unct ion V0/ V1 represent s a kind of cont roller. Mat ch t he
i mpedances in Group I wit h t he t ypes of cont roll ers in Group I I
1. PI D cont roll er
2. Lead compensat or
3. Lag compensat or

( a) Q-1, R-2 ( b) Q-1, R-3
( c) Q-2, R-3 ( d) Q-3, R-2
44.For t he circuit shown in t he fol lowing figure, t ransi st ors M1 and M2 are ident i cal NMOS t ransi st ors.
Assume t hat M2 is in sat urat ion and t he out put i s unloaded
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The current I x is relat ed t o I bias as
( a) I x= I bias+ I s ( b) I x= I bi as
( c) I x= I bi as- I s ( d) I x= I bias-[ VDD-(Vout / / RE) ]
45.The measured t ransconduct ance gm of an NMOS t ransist or operat ing in t he linear region is pl ot t ed
agai nst t he gat e vol t age Vg at a const ant drain volt age VD. Which of t he fol lowing figures represent s t he
expect ed dependence of gm on Vg?
( a) . ( b) .
( c) . (d) .
46.Consider t he followi ng circui t usi ng an ideal OPAMP. The I -V charact eri st ics of t he diode is described by
t he relat ion I = I _( 0 ) ( e^ (v/ v_r )-1) where Vr= 25mV, I o= 1A and V is t he volt age across t he di ode (t aken
as posi t ive for forward bi as)
For an input volt age Vi= -1V, t he out put volt age V0 i s.
( a) 0 V ( b) 0.1 V
( c) 0.7 V ( d) 1.1 V

47.The OPAMP circui t shown above represent s a
( a) hi gh pass filt er ( b) Low pass filt er
( c) band pass fi lt er ( d) band rej ect fi lt er

48.Two ident ical NMOS t ransist ors M1 and M2 are connect ed as shown bel ow Vbi as is chosen so t hat bot h
t ransi st ors are in sat urat i on. The equi valent gm of t he pai r is defined t o be ( dI _(out )) / (dV_i ) at const ant
Vout .
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The equival ent gm of t he pair i s
( a) The sum of i ndividual gms of t he t ransist or s
( b) The product of indi vidual gms of t he t ransi st ors
( c) Nearly equal t o t he gm of M1
( d) Nearly equal t o gm/ go of M2
49.An 8085 execut es t he foll owing inst ruct ion
2710 LXI H,30A0H
2713 DAD H
2714 PCHI L
All addresses and const ant s are in Hex. Let PC be t he cont ent s of t he program count er and HL be t he
cont ent s of t he HL regist er pai r j ust aft er execut ing PCHL

Which of t he foll owing st at ement is correct ?
( a) PC = 2715H (b) PC = 30A0H
HL = 30A0H HL = 2715H

( c) PC = 6140H ( d) PC = 6140H
HL = 6140H HL = 2715H
50.An ast able mul t ivibrat or ci rcuit using I C 555 t imer is shown bel ow. Assume t hat t he circui t is osci llat ing
st eadily
The volt age Vc across t he capacit or varies bet ween
( a) 3V t o 5V ( b) 3V t o 6V
( c) 3.6V t o 6V ( d) 3.6V t o 5V
51.Sil icon is doped wit h boron t o a concent rat ion of 4 1017 at oms/ cm3.Assume t he int rinsi c carrier
concent rat ion of sili con t o be 1.5 1010 at oms/ cm3and t he value of kT/ q t o be 25 mV at 300K. Compared
t o undoped sili con, t he Fermi level of doped si licon
( a) goes down by 0.13 eV
( b) goes up by 0.13 eV
( c) goes down by 0.427 eV
( d) goes up by 0.427 eV
52.The cross sect i on of a JFET is shown in t he followi ng fi gure. Let VG be -2V and let VP be t he i nit i al
pi nch-off vol t age. I f t he widt h W is doubled ( wit h ot her geomet rical paramet ers and doping levels
remai ns t he same) , t hen t he rat i o bet ween t he mut ual t ransconduct ances of t he init ial and t he modi fies
JFET is
( a) 4 (b) 1/ 2(( 1-V( 2/ V_P ) )/ ( 1-V( 1/ ( 2V_P) ))
( c) (1-V( 2/ V_P ) ) / ( 1-V( 1/ (2V_P) ) ) ( d)( 1-( 2/ V(V_P )) ) / ( 1-( 1/ (2V( V_P )) ) )
53.Consider t he Schmidt t ri gger circuit shown below
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A t riangul ar wave whi ch goes from -12V t o 12V is appli ed t o t he invert ing input of t he OPAMP. Assume
t hat t he out put of t he OPAMP swings from + 15 V t o -15V. The vol t age at t he non-invert ing input swit ches
bet ween
( a) -15V and + 12V (b) -7.5V and + 7.5 V
( c) -5V and + 5V (d) 0V and 5V
54.The l ogic funct ion implement ed by t he followi ng circui t at t he t erminal OUT is

( a) P NOR Q ( b) P NAND Q
( c) P OR Q ( d) P AND Q
55.Consider t he foll owing assert ions.
S1: For Zener effect t o occur, a very abrupt j unct ion is requi red.
S2: For quant um t unnell ing t o occur, a very narrow energy barri er is required.
Which of t he foll owing is correct ?
( a) Only S2 i s t rue
( b) S1and S2 are bot h t rue but S2 is not a reason for S1
( c) S1 and S2 are bot h t rue but S2 is a reason for S1
( d) Bot h S1 and S2 are fal se
56.The t wo numbers represent ed i n signed 2s complement form are
P= 11101101 and Q= 11100110. I f Q is subt ract ed f rom P, t he value obt ai ned i n si gned 2s compl iment
form is
( a) 100000111 ( b) 00000111
( c) 11111001 (d) 111111001
57.Whi ch of t he foll owi ng Bool ean Expressions cor rect ly represent s t he relat i on bet ween P,Q,R and M1?
( a) M1 = (P OR Q) XOR R ( b) m1 = ( P AND Q) XOR R
( c) m1 = (P NOR Q) XOR R ( d) m1= (P XOR Q) XOR R
58.For t he circui t shown in t he foll owing figure, I 0-I 3 are input s t o t he: mult i plexer. R( MSB) and S are
cont rol bit s
The out put Z can be represent ed as
( a) PQ + P QS + Q R S
( b) P Q + PQ R + P Q S
( c) P Q R+ P QR+ PQRS + Q R S
( d) PQ R + PQR S + Q R S
59.For each of t he posit i ve edge-t riggered J-K fli p flop used i n t he foll owing fi gure, t he propagat ion del ay
i s LT
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Which of t he foll owing wavefor ms correct l y represent s t he out put at Q1
( a)

( b)

( c)

( d)

60..For t he circuit shown in t he figure, D has a t ransi t ion from 0 t o 1 aft er CLK changes from 1 t o 0.
Assume gat e delays t o be negligi ble

Which of t he foll owing st at ement s is t rue?
( a) Q goes t o 1 at t he CLK t ransi t ion and st ays at 1
( b) Q goes t o ) at t he CLK t ransit ion and st ays at 0
( c) Q goes t o 1 at t he CLK t ransi t ion and goes t o 0 when D goes t o 1
( d) Q goes t o 0 at t he CLK t ransi t ion and goes t o 1 when D goes t o 1
61.A rect angular wavegui de of int ernal dimensions ( a = 4 cm abd b= 3 cm) is t o be operat ed in TE11
mode. The mini mum operat i ng frequency is
( a) 6.25GHz ( b) 6.0GHz
( c) 5.0 GHz (d) 3.75GHz
62.One end of a loss-less t ransmissi on line having t he charact erist i c impedance of 75O and lengt h 1 cm is
short-circui t ed. At 3GHz, t he input impedance at t he ot her end of t he t ransmission li ne i s
( a) 0 (b) Resist ive
( c) Capaci t ive ( d) I nduct ive
63.A uni form plane wave in t he free space is normall u i ncident on an infinit ely t hick di elect ric slab
( diel ect ri c const ant r = 9) . The magnit ude of t he reflect ion coefficient i s
( a) 0 (b) 0.3
( c) 0.5 ( d) 0.8
64. I n t he desi gn of a single mode st ep index opt ical fiber close t o upper cut-off, t he singl e mode
operat i on is NOT preserved if
( a) radi us as well as operat ing wavelengt h are halved
( b) radi us as wel l as operat ing wavelengt h are doubled
( c) radi us is halved and operat ing wavelengt h i s doubled
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( d) radi us is doubled and operat i ng wavel engt h is hal ved
65.At 20 GHz, t he gain of a paraboli c dish ant enna of 1 met er diamet er and 70% effici ency i s
( a) 15 dB ( b) 25 dB
( c) 35 dB ( d) 45 dB
66.Noise wit h doubl e-sided power spect ral densi t y of K over al l frequencies is passed t hrough a RC low
pass fil t er wit h 3 dB cut-off frequency of fc. The ni ose power at t he filt er out piut i s
( a) K ( b) Kfc
( c) K
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