GATE 2013 Paper Solution: Vector Fields and Divergence

GATE Paper: IGATE 2013 Solution
Ques, on Set: A [26] B [31-] c [36] D [4.::t] Ans: (A) 0 (B) 0 (C) 0 (D) 0

u g V be.. {-t«o lVldefeYIdr?A-t g "d~ht-'i(J))~
d./s hi Iou.+e.d 'l)C(V1d oVVl "0 'rlq b le.

U t. V CiTe. J':1, f)
,___- - - c -_7 _ MokJ no YI
' _ - +0 t'dU/HCQ. t
/:>'(0 bobiG't; dens;'~
J~nc.JI'o., ,

Sl~r "6 JQ~s.s "OV1 d':si"01'b4HCN1
1--- 'Yq V1 dC)IIl1 V CI "61'q '.? Ie... '

- -. PC3 V 22.U)
)1 -t? ~,'" d_ : ~

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Ques, on Set: A [ 2..,h ] B [3+ ] C [36 ] D [4 +] Ans : (A) 0 (B) fl (C) 0 (D) 0

Le. t- deNt 0 te. X :: v- 0
~.

y: u- 0
X.
=- '
1

X 1/ )V (° 1 .:!) .
11 rtO"fYYl.cd/sed d./s M'&..<-ft'an /C.ci4ss/a1
..

Y rJ )'f ( 01 i)
D: n ClfVYI 0 Use.d Ut qc.t5S io..n disk') bC{-/e£t ,

Yo I..{ c...q VI S e..e. L le.a 6' I
d
. h0 '-H -fh d bc-c qm e N o"'fY'VI Q Ct'su::/.

dis f6i ~..f i CNI ' I Os W~ I( VOI#-# ~Q t /1..10 "f'NI.Q (;sed disk; buh 'ov7
f I
Z.~l5O ~ Yf't..eO 11
2,. VQ'tl QlIce .. .L • .
hCtS

EDyll :: E[ )U I
~l-
J :- J- El/ (;0 ;
X 2-
o·

~x..-L ;:: f
E[ J y)j - t [ _, UI.2.] ;. ~ [[I VIJ ;
~ -'
X '1

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1- (0)1(-

GATE Paper: I GATE 2013 Solution
Ques. on Set: A [26] B [~1 ] C [36] D [4':11 Ans: (A) 0 (B) me) 0 (D) 0
$ubH(!'I1 H_kce bo

P lX ZY)'
-;: P( x- Y z 0)

u.s;~ (e.n trol L)m.lt- -fhe..0"fYY) ./ /10 f:e... I,O'€.

rne.oYL vV; II be. . E[jz B-~ 4-'J(j.:t:.£l:~yj [t [j z..O ~ 0~ as me.Rt-1

be (OVYl e. ln' -t;vYI~ ~ "lJClsu_
L./,O '
tjQv0cW Y<A'8' q 'ole. ./ so · (jJure... loOl' t bt..~
J-z.(2.)


Ques. on Set: A [2.b] B £31-] C [%] D [t,::r] Ans: (A) 0 (B)J2J(C) 0 (D) 0

PCz ~o), /~t- IS. e Co) 'v-hJ'cJ" IS

[p Cz- '2 0) ~ o·A
/pC3V i> :w) c t.J
PC3 V~ 2.V ~O)

Z -:=. 3 Y - 2 U ~ ~ Lr' Ve...O"C to VV 0; vc< HOt1 %
JQIt..ss 1
C{ V YC< Vd CIWl va'tl'-Q b l~ k a l 'E:'o ~ q '" s.s " C( V •.

bC06 bo-th rqVd.~ ct;~'a 'ol~ R.o.s
@Col~ 0:5 ]

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GATE Paper: IGATE 201 3 Solution
Ques. on Set: A [;2,b ] B [n] C[3,h] D [4.:t-] Ans: (A) 0 (8) 2f(C) 0 (D) 0

I' CO~~10'V:- Note -ch.;~ ~P~ 1-tAe.s+fOvt ~y~ .I¥Iostt;;.

bose..d Of'!. q,-Jl.<Ylc.' So jlAst do.if. wi-f"h z... ~~bOl -fi"e

(ovlep+- <i Wl.e..O!V g VO~Ovtc..e· -r he..se.. ~~e ~ t:tr 4esnO Y) I??ostf
d
c..o~ ttl1
co
d~
(
Q
,

loj -GI~~s,' -=-", d.,'s~; k Lcd


Ques. on Set: A ["::f- ] B [19] C [ + ] D U9 ] Ans: (A) D (8) D (C) D (D) 121

G1ven :

P~VIS'rru Plan: IOF"C - Ved- r Colcu1o,;:
o

DIVa(JC()CC c(' a vector flc::1d A' f~ 3',ve..n <»S"
--.
dw {:l -

d'lcyu~"C~ of vec+or -Fi~ld FI--
( g Ocr -r
o~

"
0,)(. Clx. <: :i
" "
a'j' CJ..Jt ~ 1.
~ "-
all' 0t =- (.)
" "
o t .0.">< : 0
o.~ 01her dot prDcJJc~ bcc~c Z~(o
dlV R=
OF. 1h~ form dof prodvd bc/oJeel)
+Wo Unit- Vt""clor wh,c- are orlhtJDfla)


Ques. on Set: A [ ro ] B [I~ ] C [ 8 ] D [2.0] Ans: (A) 0 (8) 0'(C) 0 (D) 0
(~t~) (;-;~~-
To a....p fV'-O J I' (Y> aJ--e S; f' e~e w ; ~j "'- l 0 '/
01rwt. .
To ~ n & '. - M Ct x.J mJ t'Y'l vo.1JJs 0 b- e 1hd
scJ; 5 bet- cx1 0 ~ ~ V-0J7. Oh,...,'

SO~Of.. : -

't>O U~ 1 ncr CoJUJ.i~

e •
(}' k-i ~ e
O. I~ 36
10 • D'I1~5

. 6' 2...3 (,
1 ~. o·31 Y O·~O"lO

O''1-bGO 12..-26~

36· 33LJ

Cc h ~ i 0 1').,:- -UnQ t-.a,x.i vn ? M- Va.ivJ 0 lr e = 1 IS 0

I.V~ Lh ~ tD IN i -h. wI eJvw ) v
i5.

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Ques. on Set: A [ 8 ] B [20 ] C [ G ] D [1Z] Ans: (A) D (8) D (C) g (D) D

(1)le.r) - A s~ s+e.m (})hoS'c:... Irnput.6~ QesFon,-<;e hU):::- J.c..o.U)

Input +0 SySkm xU) = UU-I)

To find - Ou~ pUt of the /)'1,M-crn Y(t)

Plof) -
DeVI51
J (:je.-cordl n
lA appl,~d -+0 Linear 11yY)~ Tnvononf
() fa Corvolutl Ol1 theoren'1 , If Inpof x(t)

"'hOM
0
'''' 1'"1M
K<OS pon M :J: OJ
hU) th~n p'f,(krn cd.n produc~
> I
_
h (l J

outpUt yet) 8,veYl a~ '

y(·n =- Jc>O h cr) ::C(:l- c) d-c
-c<>

r
(0.')
( .b )

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Ques. on Set: A [ g] B [20 ] C [b ] D [1.8] Ans: (A) 0 (8) 0 (C) [;Lj (D) 0
Confl(iVed i!
,-..
I
J
0
::J

(() --I
-.1

-::
I
":'-
I
W l.>
I 'V
~
'-..)
":)
:J

~-;1. ~r i ~T.

(cl) (e)

h Cr)::: -C u C-C )
'XC-c):= COer-I)
C,$ can b~ ;<>e~n fforn (Jroph (cL) for j; ~.i ~erloN"7J oreo
bdw("~t) her) {3roph (O)~ ond u U- r - I ) {jro.ph (ei.)} I~ l~(O
hb !J 0 fot. .:t Y.t. +) == t < :L ~
L:1. · .
...., 0 { -C L D }

~
'-'
::l

i-I


6
Ques. on Set: A [ g ] B [20] C [ . ] D [1 g ] Ans: (A) 0 (8) 0 (C) 0 (D) 0
Co()lln()~d -2
yet)::; jOOhCI) ~(:1-L) de Of, y([.):= 0 {or YJ- 0 Of -* <. )
lJ

'Jt)= jru(r)
o
U(-±--C-I)cLc

yrt) ~ nonz.ifobc.twe..~Y7 "C-o $ "C:=. ,t-- O".{ OVC.'fICl~pI'flJ
arw tn ofJ,er (nkt't/o) ,~zero

fr
j:-I
YrtJ ~ {) en (J (-;i-r- 1)dc
o

LV en:.. r l fr .t'/:1. m- "C:;> D

CJ ( J - L - 1)=' f

1ft) = Jr I>
j-I
c1 L -ft,r f >/

i [-(21;1--1
(J -If (or } "7 I
2. /

fo '10:) == (*-1)'2 (J (± -/ )
2..

Ques. on Set: A [g ] B [20 ] C [ 6 ] D [.Lg ] Ans: (A) 0 (8) 0 (C) g (D) 0
C~f1}r()t)("d -3

Alkrna~lve f)pproach.' 1hs problan (on ol~o be. Aolved bJ
/oo/<"V tS 'jfl 0) $ ~y~f-cl'f) II') fe7vefl:J cJorfJorn

jf )5'f~fun frCJ(l~fe.f fflCho() ~ HCS) the() I()Pot XeS) J:WocWLL
6lJ~ put -yes) o.t .
y(s):: H(S) X(s)

que·H)) S't") U . L ClJ. Ct));. ..1-
.5
c -s {1<~S?o} en
und- ck IOj '1'1 U Cav;1 e mull' P'IC/ll,,,,,
S by (oc-Ior cf e-!:
b('KI~) '" -c
.}ol<"1nJ loplote t-ro()~~rrn of h(-t): tUCI) L(U(}.-I))=- t::.-~

Vi(S)== L(hO)) =: L (tU(f») rRt-S >oJ S

- J-- [R~ $>0 J
S2

~o 1(s) - H(S) )«sJ
e- s {Of (Re s > 0 7
- -$'.3

-
- e-sxC ~) {or~R~S>oy

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Ques. on Set: A [8 ] B [20 ] C[ 6 ] D rig] Ans: (A) 0 (8) 0 (C) I2l (D) 0

y(~) (prJ/IS+- of two +e(t1lS' e-S' J "i3 w~ Or-e (Join) )0 folC~
I nver~~ LoPlo.ce. of ~ on!! $ who kJ/cr r ~;;() (~ W~ Curl I b e
8dj,nj) we WII' de!~ bJ tJnr~ !n+-ervo! ~In(C mu/flpJIc..oHon

Df focl-or c: _S':lo I rJ r e ?U07 0/ cJOrflOln Cov;! (!..J

~rm e aorf'O I ()

'nv~,~e 0rLaploc~ of yes)
L-l [~O;)J:; lor [c_S ?<-:b J

-
- CJ",I ckfj 0/ [:' (h)J
== lm,f de~ of [}'2.. x. utn]
- ~"U(H~
l - :;; R-n~

ConcluSIon ~ j+~ rr{)pcrtClnt to ~t!~p In mind thl!1t (j,()vo/vhof'
~"'e()rem hO)-::.. rCtJ~'fC+) ~
,/es) XCS} if> vO/ldc>nlj In Ca.A~
H(S'):;
of /lflt>Or lime InVOr-lOfH f,y,,+-~rrr, LI:r fJ'IMern 1,.1 VU'J U,Ae{tlJ
f> 'If.. tt!rr1 be coo/e b'j 1« no WI flU 0 lJ~ pu} 0/
1~/I AYlkrn (0 r~~ poncIJ
.Jo SCU , We con de}errnlne ~1!)()f of !?Y/lrern for on; Input
tfl o fhanC1HcoNy (J)'~hool c:>h,-8e,VI V ()6~ptJ+·

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GATE Paper: Ec, IGATE 2013 Solution

Ques. on Set: A [40] B [ !l,q ] c [ Lr4 ] D' [33] Ans: (A) B (8) 0 (C) 0 (D) 0

fop i C :

Fo1rrl ulo. : Y/5) i PI( fj J(
TfQ.,/Ht'l' ~u"C~io"
-
tJ(5)
::.
fj

PI( is fo1t.J0.1 J ao.iY'l of K~ Po. ih

t. K = (I - H in dj " i d 1. Q.I

+Z( pfOJV.c.J. o~

)

loop Oo. i'fl S) - )

JI'lJ ;,,;Juo.l loopS o.n fou..1

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Ques. on Set: A [~o] B [l~ ] C [Lt4] D [33] Ans: (A) 0 (8) 0 (C) 0 (D) 0

ThW. () HI ~ 0 I.l chi '1 ~ 1oopS·

Fot WOo icI po. ~ 5 0. it. ~

Po(Wo.1d po. H, ~ o.411S o.1t. P, :: ,. 2.... l... 1 = is'!.
J

5 5

P'!. : /. Z . , : Y.s
5

~
-
11 - , 1-(0),,' ( . .' No toop is pteSu!l.. WiU, .... ", u.c.hiYlj p~ ,)

~L: 1-
~
(0): I ( ... No loop is ptt..StYlt Wi a,,. h> o.Chil'l9 PaH. i)

4:

: 1- (-~ -i _4) "
SS1.

So 'Its) :

()tS)


Ques. on Set: A (40) B [ 2.q ) c (44) D [.33) Ans: (A) [3 (B) 0 (C) 0 (D) 0

5 +I
-
lJ ( , ) -:7

1(5) S+ I
-
U(S)

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Ques. on Set: A [ iB] B [ ~ ] C [ 2.1] D [ 9 ] Ans : (A) 0 (B) 0 (C) B' (D) 0

Solu1'07L OvenvieH: FIJP 0- ~ amcl stable. L( L -::rsbm~ p,,)er;,
'!"Y UJ:> ~ )i ~ em -thl.- I~ft- ho.J- oj s - r'QJY1 e. .

-Cor... i.l Ul ern' <7f"l W: )n H Ju 'cJ~_ a.d.t.. -fhJ- fO I&.:> lie on.-fk I~ V- Vw
0'71";. I.-l iv:ch.. $C.Hs}J ca.vooQ, s1-o..k.h LI~ Sjsk!tm

9p-h'cm B ~ Fop shhle/ ca.u.Pai ~FI-enn) ~ o..rcu..
0- 110 Pt!Pfr,,-d-,o,-, -jar:,
1h.o.. J'O,/-h'cm ?J- A€/lO.s on. s- 1cvne - r
o pt-icrn 0";' R~h g}- cho.rrru::J-ovs~~ "''t-'-o...},an am QQJ. cJlJs",d_ Itnjr role/.).
1eJt-$'~ <d-..f-N. :)w - IS .
-)hey ~
0...)(
CUrl d a.M. I; e.. an

OpTICTf1 C: )5 ... .1 is 0.. clnelt:. <7Y s-rJo.me.
I---'-t-h.. cem--r>e 0 QrrIJ 'Po..di'-<f.):L -I Iwncst ~Q.. r~
Ii,,- ..j-., -tM. ..,,;<fJ j ::J W a:x i 5· Ibn co. ..-
+1
TRUE ?
-I
.NOT 0. ,;to.ble) c~

L--r.l 5)s-krrn .


Ques. on Set: A [1.~ ] B [ 6 ] C [20 ] D [ "1- ] Ans: (A) EIlB) 0 (C) 0 (D) 0

S 5

A=

To j;",d ' ..N;n imwrn. E.rrnvo..2c.u. .
50kS,'cm Ovenv;ew D'kL m.Jli"/icoJ-,'''I') 0 ~ erJ=m'r~ ~"l~ -to ~
de.{(f(IYY i n.~ 0- -hv. rn dr>, x A

Iftl % ~ X /I:>. X 1>-3 = 0

Hv.'cl-L if"f'rli~/ ~"~ ~ iN.. Q-bo~ e.;.r v~ ~v.aJ. +0 ~eJlO • .::r+-'rn..~ 'b~
CIne qp 4><0 "ne.na.~iy.e. e ~ ~.

G:mc.ll.l.l> 10( : As o..U.. ihL (!) FO"Il s e-x Ctlfr- ~ ~ o..r...cL (t' e....-krt ~ :<:erto... ~.
'7; et1 ~ Is ~ ty inirn t.uYY e Irm v~ .

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GATE Paper: !;:c IGATE 2013 Solution
Ques. on Set: A [2.9] B [4@] c [3,3] D (44) Ans: (A) D (8) D (C) B (D) D

ope'll loop ~"'(),'Ilsrti' Pll YJC!:ioll of 0. de "10~O( a.S W(S) " 10
V<>.(5) 1+105

R(~) v. . (s) LJ(5)

~)
J
1
I
K... I -10
I fl05
,

fOpi C: P CO'lb'o 1(''1 hl/it 011 a~ Fe e.J bOo CK
fu n ch' 0"11
Fo'fvtlulo. : Fa'l ~i'fH 01de.t &~5hY>'l ~ '0 of lyaY) S ~/, t

IS
---
C(S)
RCs)
~
- l'
K
ItS
CO'll'fQ.ti'l'~ with tJ ts)

vIl.tS)
:
-I0
1 flo 5

l'ore.nloop ::.
10

w(s)

RLS)
1+ Ka. (~ )
If I 0 5

Ko. 10 10 Ko.

Itlo5+KQ.10 105+ (IOKo.+l)

CC&"l ~:",ud)
----------------------~----------------------
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GATE Paper: EC I GATE 2013 Solution
Ques. on Set: A [2..9] B [40] c [33] D [41 ] Ans: (A) 0 (8) 0 (C) [3 (D) 0

IOl~o.+1

wt~)

R(S)
-+( 10 ) 5
1;;:+1

50 ~ -10
'0/(0.+ 1

iv oP loop gif bt.rr)
rV) ~ ll!.& h Ol'l 3 !-Yl Ji.o.,k fiY1!t.. Co Yl S. ~ o.t'l CIOS!-6

Ii V'f) e Co fl S ~o. "'" loop b'rhV>1
i& - I
t i ",!-5 or 0P Opt.fl
100

So A -= ~ ( nJ
I (.1 o.se. J la~f ~ ~
100
1oft-Iftldor)
10Ko.+I 100

101<0.+1::: 100

Ko,::q·q t;,L/o

[Ko. :: / n ] ().pp {oi.:"""o.h vOollte.


Ques. on Set: A [5"2] B [ 54] C [5"~ ] D [ ~.2.] Ans : (A) D (B) D (C) 0' (D) D

b:::'- 600 f'l"rl' .
81.:::-1. Cl ~ ::; ).. t1 _ T1' Lf J)_.J.-
o -;; -"-3 XI 0 "'-1>0- wu.,
----~~~--~~
&-.'1-:::' '-i,~
£;t-

7.J
--tOpiC- '.- F10Xle'-"a..--re. p..op~a.-ttc~ Cale.c.-b(t)""'''2!...,e...+iC.~)

~ gf"s-t "" f 0i~ 8~'11~

-=) s;.; S~" /I ~ ~ ~ 8;,-, Iq.~
~ &~ ::: l..(Y.3 ~ Y 5"" I rh -the... cieoi-(e.cl ~-(1.uolv>tJl.- ~/.L.
'10 bi',..,c1 -hoJe... ~Y1tJd~~ ISLe...c.h ic., ~~
-tl->e. f'--(Of~,,+'O"1l CDy-y'.>+CU.,t lrl-<hT.

the lri~l...:,e...
/<,'l. :: l1-~S~'l&i, ) ~ =:. Kb eMf) L
;:: KO -~-
- IJ
J2- J2-

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GATE Paper: GC IGATE 2013 Solution
Ques. on Set: A [5""2.] B [5"~] C [S"~] D [$"'2.] Ans: (A) 0 (B) 0 (C) K2r(D) 0

-5 C~I . Co t>~~ X +~ S;nf}l"b)
e
• TI)(. 10'-l
e J 3 ['2.- C)( + Z, ) (!)

Cornr0-..el1-t-6 cOVlM;-tu-t-~n3 -the a....,.,.,f-'1~t(.o.ot£L

( A
fto == f~ ~ o.~ _ to'!.> ~ ~

- - (9

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GATE Paper: E.C I GATE 2013 Solution
Ques. on Set: A [531B [ S 5) C [ §.5] D [53 1 Ans: (A) 0"(8) 0 (C) 0 (D) 0

Gf"t-Yl: £ lu.-rvic ~e).o 'If-c-rO"f6 ot; a 'VYlO 770 C):, 'o..-nat-ic 1P1<Vl<' UlwJe

< *' (;-( )., :::- 60 () ~Y>')
z..,::.o
"';
--~~~~-----7~
Y;, ;. 3:!!. == if' X 1 ~ yo..,/,I,"
1'-. l3

- -
JDf->'C. : -

•
obl, <u..te

,

l/l.ul ().1) '0-00 uJ~ .

o
O'Yl 1::.0 ",f.,{'du b' ~3 +h e 'Va hLV) we. ~et /9': ~ ({ ~

"The --( e.b1edion coebtlic1 e.nt tt':»
1 •
r::: ?s Col'-:, 19·'2- - -];- c.o1:>4S
- o· 2-3.
~ COl:> 19· 2.- +- ~ col!.4{
J4'~ J

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GATE Paper: E-C IGATE 2013 Solution
Ques. on Set: A [ 5'3] B ( '5~1 C [SS] D [ 5'3 ] Ans: (A) 0"(8) 0 (C) 0 (D) 0
"10 bi rd. -th e j:>~ b'te..c.:ttol

we. 'Yl e.e.d. -to hi ncJ. in e.
C.O-f'll> to:: 'Ylt, l:ro-< fve..b1,e.t.. u:-~

--rh e p 'n oJ:£- -te.:·{ .....,

-JC ~'lL')l+-~1.>C-:z,))
e-

'- --0
b () '"'( u, or 'I <" '2l f-(
-2"
~~£1JO
fyo
_ '>I. f .... o

---(0

CV> )

E.{:::; o · 2.3 ~ / () -r-2. )
.)1- L.... 2"

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Ques. on Set: A [44] B [33] C [40] D [2.3] Ans: (A) 0 (8) 0 (C) 0'(0) 0
LeE pJ.oV W &DIve. p~b 1e.-wJ
G; ; r<:qpl~I'~tl~ fr~~~]
. iv~:." C1 J.o.(.(r- loV
If Yak"e,s,
C2. 5..t..{ r- 5v

B

~ -7.~ We.. Jj"f~+ c.alwtak.. UVt.Jvq(en+-
w;l
LQ~u'+aV(e ~ (J'Ve.v J I'~r-.l"fe •
g) BJ C>l.l tJ...( Cl. +r'd c..O! po U+0 V t e. (AI e. CJJ.v7

c..-t.-ec..K v-f~;~ OIlS WUl COV't be..-ft-tQ.
WuiJ'a-n /1-1:- '"6'ea..u(e. yOU?! e..JJ06"t.i.V
%0/1" pyoloewJ .

g.()It~·1 Ques. on Set: A [44 ] B [33] C[ 40] D [29] Ans: (A) 0 (B) 0 (C),e((D) 0

fJ l' "'-eM ~-r ?Id ~ '('~ WI w' ",-1' d
"fUlYQ l"u 0 Offi 0 lS '

Je"6l'e.s, ollld we.. KlI.ov-l ~o.t "'-I~ c..q~c.i.f.etIlCE? O~
.l.Vl S~lI1'~S. 9- tV vqle.-vt+- ~pqc.; k,,,,1:f =: C2- G
(2-. + C3
~ w~e.v -two ~pClcJ+O'(" ao~ til. perrolled ~

c;;:. C. I -t C.2.. (.3
C2....--t-(:,

- 100..4 ~ -t 5~ F X 2...u F
S-tlF-t ~ F·
-::: ! .1.t1.'8 5~ F

optiOIl1 co.)
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(0(11-.

forJ:.J Ques, on Set: A [Lr't ] B [ ~ ] C [ 40] D ['-.9] Ans: (A) 0 (8) 0 (C) ¢O) 0

~VI{e. Ie' op+ioV C,Crv be.. ~id~t'

Now W~e..t'I -r y
W 1 V X lf1~85~ F ?- 80kl C

,
~ Now QPpl(j IV t:-;.st '00 d;lCY c.J~'L
'H~U1 Vo~e... QC.'!SOs,s A-B ls 1 V ~~
C, (QV ~C(Vdle..l+ bC.0h MeAX" B.eal(ck)wV',

vol~e.. Qt'fO'>.'" ;~ .io y,
cJ r.....v.:) <vs )
c.2.... C) B
~'I ~ Q t "'(OSS Ac> IH t.l..--""-'O

-, y .

a. c -ross fuevv- wi II Ix. So VVe. .

L"L V'L -:;. (.3 V 3 .
C'2- V :: (3-1'3>
L
L Y2--tV::,::: 7Vj.
C2-'V2-= ~Ll-V2.)
[2... Y'L -:. 1 (3 - (3 Y2. ,


~ GATE
Q Paper: I GATE 2013 Solution
~ __u_es_._on_s_e_t:~A~[244~~]B:~[~~3~]~C~~~~~~~~~~~~~~
[40 ] D [.2.3] Ans'. (A) 0 (8) 0 (C)~ (D) 0
. r/:.

V2-":- 1 (..3
----
::. 2V

V3 :; 1- V2,
-:; 1 - 2

&5 ~ 5~
y '> ~ S V I f,.,o" 10 Ll t "",,~. vol t<;J'- C"''' V~
Q '-'M b<

l.. V L beO} 0 100 v <- OM j, iGl>.it "..-eo ""d o",~J .
as 6==-= "L VJ
e, cet, ) 'AI "'..., .... e- tq I<e. 1V fke.n V,!> '" O~e to b.,
5Y w~i~ ../-s 1 0+ P05>g-; b Ie. ~e.v1.l<? d' l's q 1m

wWV.j '
)
c
OlltJ Opt-iOVl
[3u.:t J 1. y..;

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(0",1: 1

Ques. on Set: A [441 B ['3~ 1C [401 D [231 Ans: (A) D (8) D (C) LY(O) D

(3
A r-..--..----1 I-_---"l~ C---T--o
t
1_--1t---
c.,
volk..qe... CI -::.2.: 0V [posti ble.. 05:. 5'e.a K..dO1-JII! vottc!. is fo VJ,
o.c:~.s.s.

V2- ~ C; X 2·(3
eLf c~
[_V-=-2._-::::_._B_V--,J [po~~ be. Q~ boe.q k.dowv V'C?> Uc~r ~CKJ.ls
C'l- IS. ~YJ .

y~ =-( L~ ,>(2-8
~~-t C; )
~ Zv LPo.s.~~le C<~ 6oeak.doVJIA vo(l'Cr-ClC~J.s
(3 is LY]

t, ey t e.

NooV<2
I
e.1~e.-


Quesoo on Set: A [44 ] B [3:;] C [40] D [23] Ans: (A) 0 (8) 0 (C) 0'(D) 0
He3t-oo
Vol t. QCWS.S c.!U pou'+OVlce LS VlOt

,.
de.bwU Ve Vo (~t- CLe,ms.c:. oet1'StCMc..~ v-{e J vs+ do %

W e. ~ Q V t- +0 Oe.:kA.Yli1./ VI. ce ~ ems s R, g R~

(1-
G
, 1t- 0
Bu.t- ,'" c...a ):>0. c.,; I-v"i Cr H: ..B
p..
VAf!,r 7
~.

L')...
~) -
VAf)

L,-+ (2.-

&eJ I dCM'+ o ppO Ttlf'sfflVlte. (0 (+cJ e me...ft10d .L"'V1 tc.J.

CA /?CJU fv( O"'~I ld 'j Ot( do "*,ct+ ~e..I/ y04. u.:>ill ob~'LI)

0 I
05 ClV"~t0.Q.A1
bu l
..
, ...
",-,W
,1:J:c..1- IS W'("O~oo
J

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Con} .

Ques, on Set: A [iLl B [2. '!> 1C [ .3 1D [1S'l Ans: CA) 0 CB) [3"CC) 0 CD) 0

«c.. D.u1f-.1 o ~ VI' '7l
14, (4, -'> y'tt"""o~ IYI "'1>')

,'V) Sklr C4n nuN 0'"1) .
R.A, f4" P-~ ~ (U 1>1'", h;6-t>

To
- -RA ' , f<6,
h'n../
' In 6~Y' U; 'I? YI e.Jt '<>'7') /f
fYJ 0 .) " j1
<!.c.} Rc.. ~
«c. ~ ..joy I<
~c.m ¥'(/ /:>,'D hnr 1<0., (4, a",~ ~~A' ~CSAJ~ -bJ q

Co Y1'1 ,.....h' ~ ~ b C fa tl-tr k. a '1 d S~ w), eJ-
e f4 ~ OY'I ~ Mo !-<:r6' iJ- S /-<1. r c- 'l?YJ u-h' 6"r) ,

~
PO----;;~IIM---..,.---
~ /
........ ,..." c<c.
(..A

s

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1

Ques. on Set: A [1-1] B [:<. 3] C [ 3 ] D [is'] Ans: (A) 0 (B) me) 0 (D) 0

-
- R.b R.c. - ~ . ({c.
Rg -
~-I'R.b-tf«: R.....tPt,-t-f4
~.(4,
~

~+ ~+ Rc.
,
~c..h ~o., Pt; ~ ~ II:> ,,!coJlt(.oj P..;J f'Hfn- "
/o-It.W '('no ,,0' .ft.{CJ «.,A

U' Rb) CJ<S(c) K'].( f2..- b ~ '- -:z <.. R~
~

l<~ 0- )<:.~ + 'K~ )( ~ -r RIo1- Rc

f<.B' K ROo' )<. R<!. _ K f2-B
!<:. «,. -t 1< Qb t k ~

0c'
l' = I< 1'(.
0

Ap ~<- C9'" A~ ~
((,,' ~ <(4, ~cN1 "r (1:$).> -C'f' 1.if<! or
..

~' - <.~ Cc'1Yv.h' ~ "" ~o
f<c' ~ " ~ &~ kt ~T K


Ques. on Set: A [,1.2.] B [ J1 .r] C [ 2. ] D [13 ] Ans: (A) [3"(8) D (C) D (D) D
61'v~y '.
A S;'')p~ ~ 0 6>~ )fh rr,( vw r-o c..tM>~ rJ'rq Y»"" WYI'ttJ
'(' {-j"-~ ~ '(' A 1'> (3 .

/0 ~'n~ _'.

W~ c:U-- to ~ ~+v+ 1- A WAn-J<ALcJ--r;r- A oJ- ~ e/n.4
~ ~ro,Jr ... '>V) .

A"'''''dJ'~ ,
"lI"lP }-r'<.. J,' r:JV)6 l.U~ 1"1 h.,. pr..,J r-q.., .

R~J4kr("
A ov R..~ ~ 'To- u:>i 1/ o,ec -hi CO"'-~.eJn .l-
t
" c,w"" uJ ~ A q'rl~
«.:3 'I»i~ c..v"t-t * 1
A (,..(.M "'" LoLl ~ A
........ Y~6U..'r 'n
~ -h>1"~

:J N'Z_

., '

A D:L D~
.n. (, ., k '" ~ -1 01 GV'("'" W ~
c...A,j ~ l"J 1- D~


1.

Ques. on Set: A [1.2_] B [ .... ] C [2.. ] D [1.3] Ans: (A) [3"(8) D (C) D (D) D
G..,h''''<~

f1LT '2) Sj-b P ~ fmj rQ.","",

PT fZ. ... ~JN~ j..Dc.W1 ' ~ .
~ I1<N f~ ID 0'1

Mv'l- «~ , Dak 9 MoV" ~ ~ ~ I<-efJI J~ ~ tr ~
S6l r-Ji OV) Oll~!'(' ",'{' W
,

~Y~ Yt.J jJN:l' B c;J- -e.A~ ~"'<f'

Jv, v.o ""I dl ~ .)- ""'-< ~ cb> of ,0 €-I(~,

frw Jrt:f.,.., "1

So I v..h' ""J :

Mv;...A, (!)JH~ CI4J =- 0'> 11

/IIIv 1-- 13, b> 11 [61:= OJ YJ

AoO 6 :u-- ",,;1 ~eI.t ~ C9~n.r 4 ~i-*'" G
V> i IrY c..lnlrt.~ "'1 ct u.lJ-'YVvJ.~ A·

t.A J ~ l A.3 1- .B)

LP.:»:: or 11

c..e,) - tB]-1 :: 0)--1:::. olf i1

LA) :: oA l1

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Ques. on Set: A [1.2..] B [~r-] C [ 2. ] D [13] Ans: CA) B-'CB) 0 CC) 0 CD) 0

LA) ::.. oA ,..,

lr..l :: 0'1 H

tp1 ::- t~1 -t U~J ~ bA+o'1 ' - oE H

L€>J =- 0 Lf h

(J2,] -=- LB) - -::... 0 Y -I ~ 0'3 >J
[.fol :: 0 ~ H

ttJ =- t>~ 1
LI1J =- 0"1 11

(A 1 =- LM <'" ~ 11') - of- +03:;: " 1

U~1 = o~ 1
tJSj =- l BJ - ::
Lt..~ :: II 11

Af) lJ33 ::f ~

eM - I 11
lf3J = ol-11

~ lAl ~ (11 t ~Q,) - n -1-02- =- l~"

Ce.1 =- o:l- H

I

Ques. on Set: A £1.2.] B [2S] C [ :2 ] D [L.3] Ans: (A) L1(B) D (C) D (D) D

tf>1 ~ (1l.J -1 =: -I
(!)2- =: 0' H
( J4J -
- 13 H

jNz. f1R. -~ A~ LBJ f 0 ::J ~ Yr1)? to f'1iZ
[.AJ ~
13 11

LB'J -
- 01 '1

P,tZ: A-Oo e, Lllj - lAl -t Li3J :: 1'2, -t 01 - 14 J7
-
Li3') -
- 01 /1

,'t>::'.u-)
t €>J ~ U'3J- - or -I - 00 H (%.(')"0

t A1 -
- ILj H

"1101- j4""~ IrD
L BJ -:::- 1»0 l}-- (pill
~ OD 0

(/1iZ. 0. v,,' ~ ~' ~'f:) u WI", .",0 awl ao
}tJ "nL..... .- ~~
UU =- 14 h
t e,j = 00 n

A O:L 0'.) =:9 (M -::. t!j t 03. = 1.4. -t 03 - ,~I-t

lr31 ~ co 11

11 L -r J> !-or Hv fh"J ..-0 M ,.,.,

tA.! -;: I't- 11
LB] ;:.. co ~

I
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Ques. on Set: A li2] B [ "- r] C [l:2-] D [13] Ans: (A) 8'(8) 0 (C) 0 (D) 0

A- ,'c>

WJ;.s~O' .

~ tA~~~
,
l trOp (0

4 h'mto ~
h'mA.
~ "::l N z.. Crn J) 11' ""'J
'J 1'1'2- 0"'-"'"1',,) ·
No f .b CA}f'of1'~
oS O-}i .l Hu! 8 S I<-t'f' ~ •

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Ques. on Set: A [33 ] B [ 22>] C [451 D [Y, ] Ans: (A) 0cB) D (C) D (D) D

() F=, l Oi .b c 01 J (0< r f6]
Cl 10 c. <9.j

01 <l1 b c.
LP ~ ~bJ - [Ci Jo c e/] c ~ 0<- 1;,

b c Ii>f q

To lJihet '.

~~~: I.o~ I~ ~

tP F- I [ ';{ I en) (i) ?(2.-Cy,? ] - XI (k) . Xl. (I, )

XI (I~) =- /)f2T [ "4(Yl)) - - 6)

/(2-~)=- /JJ:T C ')(2(nJ] - -@

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~. _ .
Ques. on Set· A_[ 33 ] _ [ 2- B) C [4 51 0 [3'r ] Ans: (A) 13'(8)
. _B D (C) D (D) D

-;;(2- (0 ) 7(J ~ ) 'X-').. I N- J) - - X L
( I)

~2(1 ) ~'- (I!I ? 7( .... (N)

';1(2- (I ) ?t )..CO)

~(I)
1''1

- ---(0

':t l en} * Xz..-CY» =-

(~61~ ~'K M. ~ t.<S.1'(r ~
2-, Pi'Aoi ~~&WJ1M'- Wi'if .eq~.~!fj

&nMo/
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Ques. on Set: A [3.1 ] B [:2. j;] C [ 4s1 D [3t, ] Ans: (A) [Y(B) 0 (C) 0 (D) 0
~.

C. Mh if ~ (Mr pnllW'
Vcsf~ ~ [. C beat J eA 0~ r 'YlMlJ:Jr.l ( M

JJ-~ef 5. ~ c. b ~
::'f"
~cJJ ® [0
:or
bc..alJ :::
'h" ~ 61/ c.. l:>
[CI 10 c.. b 0 a! c
eI c. b -c.. 0)

Di Bl c. b
b ~ G/ <!.

C. b ~ ej
GI c b ~

@

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Ques. on Set: A [33 ] B [l.!] C [45'] D [Yr ] Ans: (A) g (8) 0 (C) 0 (D) 0
~. ~.

- [ 0< r r 'bJ . [p< f3 f~J

l ~ f2-
)" f
Ir- P~ ~s J 2..J
- 5 iU@~
[ f
L t#tbF!yu.dtT'f1i &(""(,
0< '1-
L
f L c..
0
1
---------------------------~ ~ -

~J.uB(~ ~ ~ .iwfcAt~ ~I;if JE .A?e ~A
v/WttJ: Mq~ ~ CCUA Ax ~~'f::teAA ~ ~s.

~ V0J-ei ~ AeJf ~ ~ £>Ct,frW M1-

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Ques. on Set: A [ 1 ] B [1~] c [ 13] D [ 2.4] Ans: (A) 0 (8) 0 (C)f.1(D) 0

c,t'ven: A bulb Op!yo.,ted. b -two slAlitct,e.s .
e,o~ swift k~ CC1-1.
dopeY<A{-e iVld..efev-Jt!/A,:-tti .
7h~ Lo.3 ic of S/,AJ it~''(j of bl-{ Ih ,

D i" it-", f Lo(J"~

Soiu.-fjo':,.: L.ef c.u c01A.S;d~v -t!,.e ~w;tckea A ~ B ~
hulb Y. ~vvjicl-v?s CCUA be r'1A. "Duo J>t>.siti<:J~ v<.p(o) ~
dowII (I) .

,stO:ftiYlJ witk bo-tt--- A o.t..d }3, ,'.. '1 r()~ib'o "'. Le:t ~e

bu.lb be ofF . Now , ~;lIce & ~IA.. 0r·Yo..f.~ ;vtdefeL<ti.elA,t'o-
~k", g jOe!.. dowl/ / ~ {'uJb '()ou oN.

A (3, '
up (0) "pro) 01' F
lApr..) ...... (,) ON

Now/ tA-fjo.i", stt>.'Yti~ witk hoit- A OI...Jg iv. '1 feS.;f,O>1 0."'"
bu.l!:> oFF. wkev. A Boe~ dow"" blAlb Vol;" be 0 N . N(/V" ),~e.f i (f-

Ai" d6 1<.Jv. po:' i tiov. t.AJ ke v. !3 30 eE. Jo w '" , -ft,..e.. b lA) J., IN ii' J0
o Fr-.
B ,
urlo' ON

'*0"' ..(I) oF F

F I , ty....fI-.
,,,,,,, ~ble. CJ>'Y"f'e&r· ... d.s -n xo F... (J0<.t-e .

So I c.c1'Y'Ye eK ofc.'c>Yl is W. ( c.)

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Ques. on Set: A [SO ] B [ l.j8 ] C [ n.] D [ 43 ] Ans : (A) 0 (B) 0 (C) 0 (D) 16'
(cg~Z) crV'tJL,~- C1mmon j)~ cgV~-biOV'L

loy r J2.-

To Flhc.l :-
' I :s i n A-rnp s i l1.-- +I.-u... VOlh:t.je.. !So Wce a" cL
V 5> Ih Volt5 Ctlr u:>s s 'th.t ~ So lJ,rtt-e.

10 V IJL

-
-CUI. c..l K c.. L. cd- no cLt 'A ---b 1)
:I. $ 7l ~ s peJ,~ .

ct' eta 'yYV ~

C-C. n ;i-e. e. .>" 0 L+--tAJ-e. r". O eli ~/
V1 = I0 V .
Le(;t I-q VI. vi 'S l v0.-
~r CLfP2;-iYJo- ~VL
P OF')

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Ques. on Set: A [50] B [ Lj g] C [st.] D [4 g] Ans: (A) 0 (8) 0 (C) 0 (D).JLr
C<IJ 0 CO nb; 1 v € cL
Vs - S- )( 'L - VIt

Vs - 10 - to

I Vs LO V)
A5 0:; .IS(j 0 h Y") ~ .!:> ..tcu...J?
~ 'f+v-wJjVL Jl }l~Sj?::;-c:IhLe lS-,

:I-IJL = VA - 10 A-lYlp 5 .

I
UVvu.n.:t- ~ V,.9 L-t.

I'l-Sl. = Vrt
l-
KCL cd-

I:I S


Ques. on Set: A [51. ] B [ Lj't ] C [ §V ] D [ 4g] Ans : (A) 0 (8) 0 (C) f f(D) 0

To Irl".cL~- ~ 'fV-wJj h I JL ~ij~
I n ..ft-rn p ::. .

5 0 JJ-.ti 0 I1r '.-

f)'<.LV' i 0 UJ:::, ~ v'tJ.) DOh ~ 60 ~. 0 ~
~ V~ h..... Jl-. )U.D).) j-9""L I ~

10 A-I"rp 51

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Qu es. on Set: A [ 3 ] B [ 15 ] C[ H ) D [ 23 ] Ans: (A) 0 (B) 0 (C) rnD) 0
G..;vem: 'THO Sj~S kiTh... irnruJr.,~ 'Y'fY>rOrl>(.. hi l:.t-) ~ hl.. (t) I'). G:lr> c«..<Jz.

0 jind ~ ::rTf1 "u.Q"e.. Y>er.>fOfY:> e oj 0 Yen a..Q.Q.. ~s-krm .

FPam fPofentJ OJj- U:rrlVO I..&,o.-. <j- eon.-f-inuCTt.tr.> -h'rne :;sbr,.,s,
nlt)= hi (t-) *" h. l:-)
d

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Ques. on Set: A [ ~ ] B [11 ] C [ 3 ] D [2.t] Ans: (A) 0 (8) 0 (C) 0 (D) ~

~'verr. ~ Tn D.. Ie -kchnoloaj, dl'>J oX'fdo..-f,"on ~d Hd- ClxiJa..-h6n
To ::J-in d '" Cotnpr:u-tir:>cm 1- dr>.:J 0 X I' da:l,',m am d he. t- ox i Ja.+r"m.

-%. dar.,"f'e. d c.harc.ru::b..v:.-hcs <Vn J "l'X.'lor>-e-m err,+s qj--ft....a. juJ,.,., i ce<":.fc <:!
ox i .La. Can be. 'rna..in!J I n:f1uun 07...d ~ -th..... ~ d 0)( i c:knJ. ~r ee,&-, .

N;+h dr:r OXiJo..-t10'Yl. 1 'l1omno..M) hif - ~u..aQ;~ '' ;n OX Ic1P.. ';'" ~
'rns
pnoA.u..a.d.- J)u..rt.<'''d Hd- OX,"JC11," , -k S1/,cort
oy> H~ is £'dH",J -h, 'Z

t-'lcxkn va.rou.n. ~f't:na..~. He.+- oxidv:, (tw r>"'-~ :f= j..... Carnf=d ..f",

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Ques. on Set: A [~] B [ i6 ] C [ 10 ] D [ :u.. ] Ans : (A) B1B) 0 (C) 0 (D) 0
()u:a?nt: For.>t<o.J1Cl. biat>~ f-n. JlU'(tc1t'oY. d.IOde. ,

To jif'd : ..:Jh.a.. se."l~~ ?f- €Y€n+S ~ b+- dQnc~lb i k TT)Cchevnf'sm oj
~j1ow ,

v
In 0- ~HanJ kw,d. fr. Jl.(J'rcm"on Jiack, -fu.. ~0Sd. voHt>..cr-:for-.az- is
o..pplie.d/ o.9:-:fnsf-- -!hJL minoniiJ earoUEJtr.> cutL inje.d.d -tilr>cf'- ~ depk-fil7Yl
~'dY./ -W- di~ -thr>cu~ 1h.L J"f1e-n'on. 'n(f'on- As, 1hz minOVl!!;

autrtA' eJif.l diJtw:>e., -tn,,? ~ d",pldan 'O([iO'Y ' 'Th'j Mil 'Y>~cambrn~
H'f+h. e.=:, h. crthen ,

Gm..cll<r>I·Of'I :
Hem01.. C!lf-h'CTfL ~J (5 (0'r>fU"(~ .

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Ques. on Set: A [ ] B [ 2(; ] C [ ] D[ ] Ans: (A) D (B) D (C) D (D) S

T w-o .PttIAA&.evn vetA..i~~.Jt ~.v) U./2)uA.~ V; Tdltudi·(.MAo-
&VioSth-lkuteJ .

Cu'MU JaA-lve oM·~.t!Jbu..h'(W> i)tLN1Gt-fo-n c ( 0 ~) :

FV (:x) =- F (-x )

F (x) = Gj (:><.)
2,v

J: (9(~'~ ~'gt.9t./Alureel F. J. u~v

~ p.hO~'U~ ot~i~ -t~M.Ltt01A(r
r
'Y1Ae0ut8

wA LA. ..1e SCI WQ . A'vtoJ.. C /) F JJ.;t;/,u .iuJ;{
t9f) fa15 $ 0 ctM.V. h L DF w>l;{J ~80 ~ gQ~

I. ~ihU HIA.~ p~)-6<x') ~Tk.eA... c.J"..~ );k5

f'VbitlV'+ct e-'t. Vt.e1an:l~ .

2. 8e.c»l<PoI ~ P-iV~ (r-e><-)- Uc)()) X;' T~ ~
its FSlt-i V1 1 6l~ lLeOa.t1'V1~ .

~.
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-
Ques. on Set: A [ ] B [ 2-b ] C [ ]D[ ] Ans: (A) D (8) D (C) D (D) if
AU as ~ 4

Le-we.l.
CClM111 rM,J- raM ~

_--J@

F-C~) - LS) 0<-)

1t9UJ Pc 2 V ~ x) =0 P Cv::: ~)

lJ~ ~ h~..&uft ~ ~~ e~e8r2 trwv

--®

Fy ( ~) = Fu ( ;,) --®
9Jr~@ ~ © ~ @
-C2t) -G/CX) = Fve x ) - Fy (~)
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Ques. on Set: A [ ]B[ 2,(' ] C[ ]D[ ] Ans: (A) 0 (8) 0 (C) 0 (D) ~

&1AhPl.

12(2<..) - ~C-X) = Fv (x) - Fu ( ~)

Fc~? - &~) - FCx) - F C'XI':J.) - - 0

C<U-e L 'Z. ..u. +V€ C ")(>0)

~ .> x/2-

r- ex) ;::::> jC ( )(/2.) l' -.' tJ8r> - cj~Cf) et.<S i 1
~(I!»' ~

=:> F 8-) - F ~) :> ()

&tJ b It(fWI 0 I F-c"C) - c" (i<.) "> 0
- -_ _ _-1-l -@

-ve C x<.o)

'Z/2

F<?J :=: F ("'72) "'7'
-&.or ~~ @ IF(?(} - 6Te?c) s. ~ _@
----------------------,-------------------~~~+~.
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Ques, on Set: A [ ] B [ 2-b] C [ ] D[ ] Ans: (A) 0 (8) 0 (C) 0 (D) g"

go 1J1t.91NI (. IU-{ -L A.u. tU c.~ 2. ) h e~ 0 u...t ~wdt-

~eMe1.J, Or-v rul9$1C1)1~ ~eJ "M-rrdi1Jl'~ l' X. ~
~f!t x.;> 0 Q-tAA ~ ~ ,b, ()fh' ()1/1 C
13) ; /Ju::J r ?( <0
OWl ~ lMVl ~ r'Gf/! (A-) , 8u:t- lA-&t ~~ (A) ~ ce )
&0 W<' JL~ ~ ~ ;two ~'/9M..,

NOIAJ [,v'{( ~ .b9 1jVL&t ):,fYWll ~tUf bD'c 1M.

~fPl Dun ~YtS~ wfM'tk. u.91'U .h -j)w<. 1r ~

VtV.u e ~ rx , i, f. If ~ to!> Ttl've vttM sJ ~'Vf X,

II.J1.u.lj-f~ ~ ~ J vv"{ rr
) (F~) -61 (A)) ~ ;;.. 0 f
~------------~~~--~

b't01M. © Fex.) - CnC~) ::.- 0
---;::----:::-:---~

~'~ ~ X/ ~ ~ l (f~)-0J~))X?: 0 ~
- -Wei;;it.;;-:
Web s,te
' ;w w.~A-rEC;~u~s;ejjlo:; l;r.;co:m~E-::m=a7.iI:":ue:'r:'i:-s-::@:-g"at-c-o-n=se=lI=r=,-c--=~
w;; G AT Co n ;: 9:-:-: e ": e u o om ~.

Ques. on Set: A [ ] B [ 2-" ] C [ ]D[ ] Ans: (A) 0 (8) 0 (C) 0 (D) Er
~.

~ ~ (f5j ~01 @ c,.ve ~

,
) ~. t:I1t1 CKJ ? h w tt flt eff ~g wVt }

EK()~~·. A Gr~OAA ha.AMJfhVV venJ~ U9f"tf, ~ Z~RO

1'x CX ) == _1_
-.}.2.TI r

. ~
-L-
.fZi!..... I' 1

-', ,~ <"l....'
.'

------3>7' ?t..

~x.i'(YleitetJ
'X.
)
FI( CX) =.J
- ....
ix(l(.) <3t«..

-i. - - .... .... - - - . -=:::==~ __ '> f.
::. ->-

______________________
Website : www.GATECounsello r.com
~----------------------~~t~.
E-mail : gueries@gateco.unsellor.com

.5

Ques. on Set: A [ ] B [;2.b] C [ ]D[ ] Ans: (A) 0 (8) 0 (C) 0 (D) ~

~ .

%.e 4o<z*:cu.,.d Fr~ .;t:& je'W~
q""~(WI A ~ "cf){: ~.~ ~


Ques. on Set: A [/1-] B [4- ] C [2..2.] D [..9 ] Ans: (A) 0 (8) 0 (C) 0 (D) 0'

G,'J(n - Mo~ FET Opoal'~ If) $afvyo~or> reJlon

10 Find - Ca.()/)e~ of Channel kr1(Jfh rnodulolion

Sol IJHon-
1"1 tl~rn C) per-o Hj (() %o/v ro~tJn r'1/fOr) ()()cJer t" e
chonnel Jefljlh eJred ~en draIn crnrenf I'D It rJ1ven by frfll

a.1D =-),I(~ W (Vens- 1/+J2 -(2)
C)Vps L I -(3)
10 - 3-rD!dVDS - ,A ~h~CV(nr-Vt-)l..
-fr Ideol (!olie (wlf~()()l Chonnf) le?Jfh l'Yle>cIv)()/-!o,,)

"It>=- "~(~){VCnJ-Vf)1
Or!) - 0

- (4-)


Ques. on Set: A [1'1-] B [4- ] C[22-] D [ ..5 ] Ans: CA) D CB) D CC) D CD) 0

So MoSFf"T operof-lr.) In ~ Qfvral10n Y'(i lOr) () naJe .. Chan nd
eI'J~h rn6do/a/ion elf-e c} hCl;<> I~ S'S re;<:ll!-onc.- 0' {ornpore -It?
ld~ct) Morrr-"f Wh'C0 ho.)'I C)ufpu~ r~Vf-oYlc~ f"f'nl~ q,(: ,AhoWI
preYI ~1/

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Ques. on Set: A [31-1 B ['2..1 1C [ 4;1 D [% 1 Ans: (A) 0 (8) 0 (C) 0 (D) W

~ A JJ 'V e.ct:r1 c c) 'f ~ ~ C0 t<...jh'Ci' ~'14- I JVI *
C~ ~ c:l)f~'NI'c.J. ~4 01 !jlt')

~> ~dl~ t'" 'I.C.h'o l- - il..lt)

- 2..';J l!t), b~ c. ~C't''}iV~ ~

J~ " ~~) &. 'je)

•
lLts ~ eM}leN....h'0 ~h '.1

d 'a --
ell-
rd -::. -ntx)


Ques. on Set: A [3 r-] B [27- ] C [41] D [3.b ] Ans: (A) 0 (3) 0 (C) 0 (D)la'"

~ 0 ~'" ~ - '-- '<1 ~) I C Y.C Y.}Q- ~ l ~) b~ - z.~'k)
&. ~ (g) <41 1Xh. - 2.. --: ~ )


GATE Paper: I GATE 2013 S I .

. C) 0 CD) 0
Fyo'f'f --HIe... A bov-e.. <5(ue.di o f} .

-rt.<- 6pHmv", -K,,,,oDI'( 'S -+'L Tnt<i~e<-li"" of--I<Z
PAf aJ- ~ 1(e.Leiw.a ~', j n.t,ls .
~6/ -H-..~ .:::rnr-~y.sediol i> l!!5 /~ )
. '. '1l.e.. orhmulI? -H,'teShold;o- 1/s
wif+> -1k~ opfil""()lJtY) -t!-¥dl,o Id. / ~ 2,E..R. I~
B'E-R.-;.. p(rea,iveJ......." PCo) T
L-rr~rtt~o)
rLY~oUv-eJ..<:> )
-rYa,,~~i/"t-«lf
pu)

~ (i-x~ ~ )i-t- L±x *)( ~J'~
; t lli -t1:5)
-
~
,
--
S-o IV€- &1) CroSS cJ.e.e.l(
./
6 pt-11Yl u"" --f-!,r~h.o 1,,( .

Website: www .GATEeounsellor.com E-mail: gueries@gatecounsellor.com

GATE Paper: 0
Qu". on SoC A [ 1, BI IGATE 2 13 Solution
B[so]C(43]D
yWV> : [5"11 An" CAJ 0 C8J 0 C

I p.u 1-,5i.jl).J Joy b,'cD
receive.L
0'5 FtiJ 4- y~~i~
; 1- ~ijll..,:fo~ b; b I
,

~"
-/
__,'- !:YA"",;tTd- w:r~ q,,,.J. pYo~.b;l;ry
... 1'(1) ~ P (0) ::. Y2-

10 Fi VIe{: Bi r Eft"' RAt~ of.JiL Di.ji bo.l c.o~~U";","'" 51'''''

Det~ot) -n,l'~ ~D)el..
y~'~;Y"'"
'i> I,.)
f.","V =" ,,"'" I'K- TVA""'; t o " " ......

o ",e...
CqioJ-e.T> ~ -H-e- ~"I'dho'.:L ~ ;~ lo.s.b .
~ Y/D c,M1')CL- ~ ~e.. dj1}"J Joy P; r D

Pel. f of- 'Yue.:,v-e.ei
'p ilDt- cYD£. ,jYl:J -fi,.e.... -thye.cno 1tL ,,' .
S;O''- -ti-< Pd.., of- y.,u;veA- >d",1 .toy tir I UD«'''j
doT b;)- r·
I;~ 4oj- ""~" AY"":'
.fJ-<- ""uholJ." ,', /:0 -H.eft- ;< "- eJfdY

e.YY0Y -do, bi Ie , ;<
1~
1<- f'Yob. bi
at .-I"<.- flJj- -ik y,co"''';' ';ij •• (yoU'''j

~ optimlJrt) cte.rec.bor) poi()-' I ·

Website'. ww w.GATECounsellor.com E-mal'" . ~~~g~allte~co~Uilln~seillll~oru.c~om
gueries@

Ques. on Set: A [L,g] B [50] C[ 4~ ] D [.s-l] Ans: (A) D (8) D (C) D (D) g--

- ----
-
e
)

O
4-
I gJ .J-
2-

)
J-b

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Ques. on Set: A (4).] B [ 3l] C [42..] D [31] Ans: (A) 0 (8) 0'(C) 0 (D) 0

Y CESQf. = 0 V

>W f(-l' c: V~ Jah,..e

oV

'
0
, -- 5 Y

.

PJWA " I. r- ,. 9z. St- :t&k.e X'1'- 00 cA-v-e1 ~ ~::J::lA). u'{uU-t-

2. ~1A~ -;t:&/c.t X¥=ol ~Gf ~ ~ Ah-e Un';;
3. IL1i "d~ ~<.e )( Y ::: 0 ~~" " "l.-o

,, L ,

x 0_-

Ty

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Ques. on Set: A [42-] B [61.] C [42-] D [31.] Ans: (A) 0 (8) G"(C) 0 (D) 0

C~~l D-u.t Pliw :
C~:L' fx: Y = 0 0

+..5 Y

'< ::. 0 I(

z:: OV

+5v
+-51
f
~_,...---C z:= +5 I
Z- >
I
C>
Y==+Sy

x y 10

+-5Y
1---...,-0 Z =- 0 V

y=ov

I

Ques. on Set: A [ 4 2...] B [ 31] c [4 2-] D [31.] Ans : (A) 0 (8) 5r(C) 0 (D) 0

C&vt+-cl :

t-oV
R,

T
'( =-+sV

,
- -
'f-- '1 z ?~', ~ ~at"e-

0 D tt» G'ij ( OFfL)
6

0 )
1
I I
lu;t-*fr C ()12~)

I 0 0 &:tb~ CaN)

S~ CDN)
I I 0
,
-, 1
,
¥ D<A (3 Ud!" cmt'eQ1 ~J
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Ques. on Set: A [35l B [4:,r:] C [!2.:1] D [38] Ans: (A),%CS) 0 (C) 0 (D) 0

- ~m-= 1 mA/V
Nt'-10S , eor(l{'(lon &;u.J1u.. AmPI,'r'e)J·
~ P-ffed ~ Ow1ne/ ~/-J) m~'on
CtJ7e n~~.

,
).,

,
.L2- - - QD
- d V/
m

RD -t RL -f _I
Sc.

V" - ~
J..''L RL

Vi> - Ro e dm V,,'
l

~-+ R/... + 1.
Sc..
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GATE 2013 Paper Solution: Vector Fields and Divergence

GATE 2013 Paper Solution: Vector Fields and Divergence

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