Gate Paper 1

8/4/2019 Gate Paper 1

1/26

Q1. IfA =

-

-

- l

0 1 2

1 0 3

2 2

isasingularmatrix,then l is

(A)0 (B) -2

(C)2 (D) -1

Q2. Let f x ex( ) = in[0,1].Then,thevalueofc ofthemean-valuetheoremis

(A)0.5 (B) ( )e -1

(C) log ( )e -1 (D)None

Q3. If D u u u= + + xy yz zx x y z ,thenthevalueof A S d is,whereSisthesurfaceofthecubedefined

by 0 1 x , 0 1 y , 0 1 z

(A)0.5 (B)3

(C)0 (D)1.5

Q4. Thegradientoffield f y x xyz = +2 is

(A) y y z x y z xy x y z ( ) ( )+ + + +u u u2

(B) y x z x x z xy x y z ( ) ( )2 + + + +u u u

(C) y yx xy x y z 2

2u u u+ +

(D) y y z x y z xy x y z ( ) ( )2 2+ + + +u u u

Q5. Inthecircuitoffig.Q5thevalueofR1

willbe

(A)25 W (B)50 W

(C)100 W (D)2000 W

1 Paper-1

QuestionsQ1.toQ20.carryonemarkeach.

100V

R1

+

20V

+

70V

R2

60 W

FigQ5

PAPER-1

GATEECEByR.K.Kanodia

MCQs : The book contains only solved Multiple choice questions (MCQ) which is the main requirement of the GATE exam.

Each and every problem has its complete solution. We understand the fact that theoretical studies should be done from

the standard book, that one has studied for the semester exams and thus one should use the same material to

understand the concepts of the same. We have deliberately excluded theoretical matter in the book so as not to mislead the

students. However, wherever needed, satisfactory explanation of the formula has been included in the solution.


2/26

Q6. Thevoltage v o infig.Q6isalwaysequalto

(A)1V (B)5V

(C)9V (D)Noneoftheabove

Q7. Epitaxial growthisusedinintegratedcircuit

(A)becauseitproduceslowparasiticcapacitance

(B)becauseityieldsback-to-backisolatingjunctions

(C)togrowsinglecrystal n - dopedsilicononasingle-crystal p - typesubstrate

(D)togrowselectivelysingle-crystal p - dopedsiliconofoneresistivityon p - typesubstrateofa

differentresistivity.

Q8. Thechemicalreactioninvolvedin epitaxial growthinICchipstakesplaceatatemperatureofabout

(A)500 C (B)800 C

(C)1200 C (D)2000 C

Q9. Inthecircuitoffig.Q9theoutputvoltage v o is

(A)2.67V (B) -2.67V

(C) -6.67V (D)6.67V

Q10. Assertion(A) IntheselfbiasCEtransistoramplifierasinglebatteryisused.

Reason(R) Thecollectorbasejunctionisforwardbiasedby VCC

.

Chosethecorrectoption:

(A)BothAandRindividuallytrueandRisthecorrectexplanationofA.

(B)BothAandRindividuallytrueandbutRisnotthecorrectexplanationofA.

(C)AistruebutRisfalse

(D)Aisfalse

2 Paper-1

20kW20kW

40kW

60kW

-1V

+0.5V

+2V

vo

FigQ9

GATEECEByR.K.Kanodia

Adherence to Pattern: All Multiple choice questions are strictly according to the GATE pattern. Every problem selected and

included in the book is a model problem for the preparation of the exam which would thus prepare and equip the students better.

Kindly note, that the standard of Multiple choice questions and their solution in every unit is much better than the ones available

inafamousseriesofproblems&solutionsasfarasGATEisconcerned.

+

vo 5V

1A4 W

FigQ6


3/26

Q11. Theaddressbuswidthofamemoryofsize1024 8bitsis

(A)10bits (B)13bits

(C)8bits (D)18bits

Q12. Considerthe TTL circuitinfigQ12.ThevalueofVH

and VL

arerespectively

(A)5V,0V (B)4.8V,0V

(C)4.8V,0.2V (D)5V,0.2V

Q13. Consideradiscrete-timesystem S whoseresponsetoacomplexexponentialinput e j np 2 isspecifiedas

S e e j n j n: p p2 3 2 .Thesystemis

(A)definitely LTI (B)definitelynot LTI

(C)maybe LTI (D)informationisnotsufficient.

Q14. TheDTFTofsignal 2 4 2d[ ]- n is

(A) 2 2e j- W (B) 2 2e j W

(C)1 (D)Noneoftheabove

Q15. ConsidertheListIandListII

ListI ListII

P.Derivativecontrol 1.Improvedovershootresponse

Q.Integralcontrol 2.Lesssteadystateerrors

R.Ratefeedbackcontrol 3.Lessstable

S.Proportionalcontrol 4.Moredamping

Thecorrectmatchis

P Q R S

(A) 1 2 3 4

(B) 4 3 1 2

(C) 2 3 1 4

(D) 1 2 4 3

3 Paper-1

+5V

Vi

Vo

2kW4kWFigQ12

AllquestionsaredrawnfromthebookGATEECEbyR.K.Kanodia publishedby NODIA&COMPANY.Forfullsolutionreferthesame.


4/26

Q16. Thepolezeroplotgiveninfig.Q16isthatofa

(A) PID controller (B) PD controller

(C)Integrator (D)Lagleadcompensatingnetwork

Q17. InTDMnonessentialfrequencycomponentsofthemodulatingsignalareremovedby

(A)sampler (B)attenuator

(C)pre-aliasfilter (C)modulator

Q18. CoherentdemodulationofFSKsignalcanbeaffectedusing

(A)correlationreceiver (B)bandpassfilterandenvelopedetectors

(C)discriminatordetection (C)aboveall

Q19. Twodissimilarantennashavingtheirmaximumdirectivitiesequal,

(A)musthavetheirbeamwidthsalsoequal.

(B)cannothavetheirbeamwidthsequalbecausetheyaredissimilarantenna.

(C)maynotnecessarilyhavetheirmaximumpowergainequal.

(D)musthavetheireffectiveapertureareas(captureareas)alsoequal.

Q20. ThedominantmodeinarectangularwaveguideisTE10

becausethismodehas

(A)noattenuation (B)nocut-off

(C)nomagneticfieldcomponent (D)thehighestcut-offwavelength

4 Paper-1

s

jwFigQ16

Problem

10. v1

= ?

(A)6V (B)7V

(C)8V (D)10V

1 W 1 W 3 W

2 W 6 W8V v1

+

2 W

6 W 18V

Fig.P.1.4.10

Solution

10. (A)By changing the LHS and RHS in Thevenin

equivalent

v1

4

1 1

12

1 21

1 1

1

6

1

1 2

6= ++

+

++ +

+

= V

4V 12V

1 W 1 W

v1

+

2 W

6 W

1 W

Fig.S1.4.10

Consider above problem and its solution from bookGATE ECE by R. K. Kanodia ( chapter 1.4 Circuit Theorems). If problem

is solved using mesh analysis or nodal gives 4 or 3 variables. The solution shown above has only one variable and require less

calculationreducingtimeanderrorsaswell.Thetrickinthisbookarenotnewbutitequipstudentstothinkdifferently.


5/26

Q21. Iftherankofthematrix, A =

-

2 1 3

4 7

1 4 5

l is2,thenthevalueof l is

(A) -13 (B)13

(C)3 (D)Noneofthese

Q22. Ifu exyz= ,then

3 u

x y z isequalto

(A) e xyz x y z xyz [ ]1 3 2 2 2+ +

(B) e xyz x y z xyz [ ]1 3 3 3+ +

(C) e xyz x y z xyz [ ]1 3 2 2 2+ +

(D) e xyz x y z xyz [ ]1 3 3 3 3+ +

Q23. Thevalueof ex

xdxx

1

1

+

+

sin

cosis

(A) ex

cx tan2

+ (B) ex

cx cot2

+

(C) e x cx tan + (D) e x cx cot +

Q24. Thesolutionofthedifferentialequation ( ) x y dx xydy- + =2 2 0 is

(A) ye Ax2 = (B) xe Ay x2

=

(C) xe Ax y2

= (D) ye Ax y2

=

Q25. TheTaylorsseriesexpansionof f z z( ) sin= about z=p4

is

(A)1

21

4

1

2 4

2

+ -

- -

-

z z

p p

!.......

(B)1

21

4

1

2 4

2

+ -

+ -

+

z zp p

!.......

(C)1

21

4

1

2 4

2

- -

- -

-

z zp p

!.......

(D)Noneoftheabove

5 Paper-1

QuestionsQ21.toQ75.carrytwomarkseach.

AllquestionsaredrawnfromthebookGATEECEbyR.K.Kanodia publishedby NODIA&COMPANY.Forfullsolutionreferthesame.


6/26

Q26. Considerthefollowingtable

Diameterofheart

(inmm)Numberofpersons

120 5

121 9

122 14

123 8

124 5

125 9

Themedianoftheabovefrequencydistributionis

(A)122mm (B)123mm

(C)122.5mm (D)122.75mm

Q27. Fordy

dxx y= + 2 ,giventhat y = 0 at x = 0,usingPicardsmethoduptothirdorderofapproximationthe

solutionofthedifferentialequationis

(A)x x x x2 5 8 11

2 40 480 1600+ + +

(B)x x x x2 5 8 11

2 20 160 4400+ + +

(C)x x x x2 5 8 11

2 20 160 2400+ + +

(D)x x x x2 5 8 11

2 40 480 2400+ + +

Q28. Thebilateral laplace transformofcos ( )* ( )3t u t e u t t- - is

(A)-

+ +

s

s s( )( )1 92, Re ( )s > 0

(B)-

+ +

s

s s( )( )1 92, -


7/26

Q29. The z-transformofx n

n

[ ]

| |

=

2

3is

(A)-

- -- < < -

5

2 3 3 2

3

2

2

3

z

z zz

( )( ),

(B)-

- -

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