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Transcript of MAT Paper-3
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7/29/2019 MAT Paper-3
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Zfln 1 4 @r+ Ldx+ Ldros 1 433
GNKNRDI FK]ZR^MZFHK]
4+ Z`n bhhoint gfvnk fk t`n nxdlfkdtfhk dii fs t`n Tunstfhk Sdpnr+
2+ D stujnkt ds th wrftn fs`nr dkswnrs fk t`n HLR s`nnt by jdronkfkg t`n dpprhprfdtn bubbin wft` t`n nip he
@B Snkmfi ds t`n mhrrnmt dkswnr(s& he t`n qunstfhk dttnlptnj+
=+ Z`n qunstfhk pdpnr mhktdfks 433 qunstfhks+ Ndm` mdrrfns hkn ldro+
:+ Bidko pdpnrs) mifp bhdrjs) ihg tdbins) sifjn ruin) mdimuidthrs) lhbfin hr dky ht`nr ninmtrhkfm gdjgnts fk dky
ehrl fs kht diihwnj+
>+ Wrftn yhur Kdln % Rhii Kh+ fk t`n spdmn prhvfjnj fk t`n bhtthl he t`fs bhhoint+
5+ Z`nrn fs kh kngdtfvn ldrofkg+ Jh kht spnkj thh lum` tfln hk d pdrtfmuidr qunstfhk+
7+ Bnehrn dkswnrfkg t`n pdpnr) efii up t`n rnqufrnj jntdfis fk t`n bidko spdmn prhvfjnj fk t`n dkswnr s`nnt+
0+ Fk mdsn he dky jfsputn) t`n dkswnr s`nnt dvdfidbin wft` t`n fkstftutn s`dii bn efkdi+
DII FKJFD KZ]N (]ZDGN,FF& ZN]Z ]NRFN]
LHMO ZN]Z - =
MID]] ,P
LNKZDI DSZFZ^JN ZN]Z (LDZ&
SMMS @ndj Heefmn 1
Djjrnss 1 Idos`yd) M,0) Kursnry Sihts) Zdiwdkjf) Ohtd (Rdadst`dk&,=2:33>
Zni+ Kh+ 1 /37::,2:=:727)002:370==3) Edx 1 37::,2:274:5 | Wnbsftn 1 www+pmmp+rnshkdkmn+dm+fk
N,ldfi 1 pmmpCrnshkdkmn+dm+fk
http://www.pccp.resonance.ac.in/ -
7/29/2019 MAT Paper-3
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 4
Jfrnmtfhks 1 (4 th =& Fk ndm` he t`n ehiihwfkg qunstfhks t`nrn fs d kulbnr snrfns wft` hkn tnrl lfssfkg) w`fm` fs
s`hwk by qunstfhk ldro (8&+ Efkj t`n lfssfkg tnrl hut he t`n gfvnk ditnrkdtfvns+
4+ >6) 54) 57) 74) 7=) 8
(D& 76 (B& 70 (M& 77 (J& 7>
2+ 5) 7) 7) 43) 6) 8) 42) 45) 8
(D& 42) 45 (B& 42) 4> (M& 4=) 4> (J& 4=) 45
=+ =) 4=) 22) =2) >6) 56) 423) 4=3) 8
(D& 234 (B& 244 (M& 225 (J& 2=2
Jfrnmtfhks 1 (: th >& Fk ndm` he t`n ehiihwfkg qunstfhks t`nrn fs d kulbnr snrfns wft` hkn fkmhrrnmt tnrl+ Efkj hut
t`n fkmhrrnmt tnrl hut he t`n gfvnk ditnrkdtn
:+ 422) 4:>) 473) 467) 225) 2>7) 200
(D& 200 (B& 2>7 (M& 225 (J& 422
>+ 4) 4) 2) :) 0) 44
(D& 2 (B& : (M& 0 (J& 4
Jfrnmtfhks 1(5 th 0& ^kjnrstdkj t`n ehiihwfkg ehur inttnr snrfns mdrneuiiy+
(]nrfns&
(D& DBM) BMJ) MJN) JNE
(B& MJP) JNW) NEU) EG^
(M& MVW) NPU) GW^) FUZ
(J& MNG) JE@) NGF) E@A
Fk t`n ehiihwfkg qunstfhks ) d tnrl fs gfvnk w`fm` bnihkgs th hkn he t`n dbhvn snrfns+ Efkj hut th w`fm`
snrfns ft bnihkgs dkj fkjfmdtn fts hptfhk fk t`n dkswnr s`nnt+
5+ QDB
7+ G@Z
0+ BMV
Jfrnmtfhks 1 (6 th 43& Ndm` he t`n ehiihwfkg qunstfhks fs bdsnj hk inttnr snrfns fk w`fm` shln inttnrs drn lfssfkg+
Fk t`n gfvnk hptfhks lfssfkg inttnr fs gfvnk fk prhpnr snqunkmn+ ]ninmt t`n mhrrnmt hptfhk he ndm` qunstfhk+
6+ d X b X b b m d X m X b
(D& m b d b (B& d m m d (M& d b b d (J& b b m m
43+ x y X X x y y X x y X x
(D& x y y y (B& x y x x (M& y x x y (J& x y y x
LDZ SDSNR
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 2
Jfrnmtfhks 1 (44 th 4:& Gnt t`n ruin dkj efkj t`n suftdbin hptfhk ehr bidko mnii+
44+ 6 > =:
22 7 74
8 44 4>7
(D& =5 (B& =: (M& =2 (J& 20
42+ : 0 40
43 42 26
45 4> 8
(D& =2 (B& =5 (M& =0 (J& :0
4=+
> =
2
4> 42
=
03 :>
8
(D& 7 (B& 5 (M& > (J& :
4:+4=
45
:6
: 8
2>
5:
6 45 4
=5
04
(D& 45 (B& 4> (M& 4: (J& 42
4>+ W`fm` inttnr mhlns hkiy hkmn fk t`n ifst bnihw,
B J G F A M @ D B J N J G E M A F E G A
(D& G (B& J (M& A (J& D
45+ Detnr indvfkg t`n efrst efvn inttnrs he dip`dbnt snrfns) phfkt hut t`n lfjjin inttnr he rnldfkfkg inttnrs+
(D& S (B& L (M& T (J& I
Jfrnmtfhk 1 (47 th 24& Z`n mdpftdi inttnrs fk ndm` he t`n ehiihwfkg whrjs drn mhjnj dkj wrfttnk fk sldii inttnrs)
but kht fk t`n sdln hrjnr ds t`n inttnrs fk t`n whrj+ Efkj t`n mhjns ehr inttnrs dkj dkswnr t`n
qunstfhk+
] N R F N ] h d n h n p
] M D R N p h o n j
] N N J f h n h
M D R J p f o j
D M Z j k o
47+ RNJ
(D& fhj (B& hnj (M& jkp (J& fhp
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - =
40+ ZNDR
(D& pkhf (B& pnko (M& ohkf (J& pokh
46+ ]NZ
(D& knh (B& fnk (M& koh (J& pko
23+ MFZN
(D& fjhd (B& pohf (M& hdkj (J& jdfk
24+ JFMN
(D& jfho (B& phok (M& dhjk (J& jhdf
22+ ]ukfi wdionj 5 ols thwdrjs t`n Ndst+ Z`nk turknj th fs rfg`t dkj wdionj 43 ols+ Dgdfk n turknj th
`fs rfg`t dkj wdionj 5 ols+ Efkdiiy `n turknj th `fs inet dkj wdionj 4: ols+ @hw edr fs `n erhl t`n
stdrtfkg phfkt dkj fk w`fm` jfrnmtfhk8
(D& 2> ols ]hut` (B& 2: ols ]hut` (M& 2: ols Khrt` (J& 23 ols Khrt`
Jfrnmtfhks 1 (2= th 2>& ]tujy t`n fkehrldtfhk gfvnk bnihw dkj dkswnr t`n qunstfhks t`dt ehiihw 1
Rdau fs d mdrpnktnr+ @n ds efvn thhis wft` w`fm` n whros+ Z`ny drn D) B) M) J dkj N+ Ndm` he t`nl `ds
d jfeenrnkt wnfg`t ds gfvnk bnihw 1
(f& D wnfg`s twfmn ds lum` ds B(ff& B wnfg s ehur dkj d die tflns ds lum` ds M
(fff& M wnfg`s die ds lum` ds J
(fv& J wnfg`s die ds lum` ds N
(v& N wnfg`s inss t`dk D but lhrn t dk M
2=+ W`fm` he t`n ehiihwfkg fs t`n lhst ifg`t fk wnfg`t 8(D& D (B& J (M& B (J& M
2:+ W`fm` he t`n ehiihwfkg fs lhst ndvy fk wnfg`t 8(D& D (B& B (M& M (J& J
2>+ W`fm` he t`n ehiihwfkg rnprnsnkts t`n jnsmnkjfkg hrjnr he wnfg`ts he thhis 8(D& B) J) N) D) M (B& D) B) N) J) M (M& B) J) N) M) D (J& N) M) J) D) B
25+ W`fm` kulbnr bntwnnk >3 th 05 fs lfssfkg fk t`n grfj 8
>> 72 >= 74 54 >5
75 56 5: 73 7> 5>
70 >7 04 >3 >0 >6
53 0= 55 0: 7: 57
02 >4 77 >: 03 >2
7= 05 52 0> 5= 76
(D& 50 (B& 74 (M& >4 (J& 0=
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - :
27+ W`fm` inttnr dppndrs efvn tflns fk t`n grfj bnihw8
H D G M N @ J A
D H H K H R K L
E S O J G D E K
S B G L E L G B
F O @ J A M R F
G H K I H H N @R E R L D E H J
(D& D (B& L (M& H (J& E
20+ Jnintn dii t`n kulbnrs t`dt dppndr lhrn t`dk hkmn fk t`n ifst bnihw dkj djj t`n rnldfkfkg thgnt`nr+ W`dt
fs t`n dkswnr+
> 2 = > 4 = : 2 5 : 5 0 7 = 0 > 7 6 2
(D& 43 (B& 4> (M& 6 (J& 44
Jfrnmtfhks 1 (26 th =3& Rndj t`n fkehrldtfhk gfvnk bnihw th dkswnr qunstfhks+
P fs lht`nr he V but V fs kht t`n jdug`tnr he P+ ] fs shk he G dkj brht`nr he Z+ Z fs sfstnr he V+
26+ W`dt fs t`n rnidtfhks`fp bntwnnk G dkj Z 8(D& Edt`nr,Jdug`tnr (B& Lht`nr,Jdug`tnr (M& Brht`nr,]fstnr (J& Mdkt bn ehukj
=3+ W`dt fs t`n rnidtfhks`fp bntwnnk G dkj P 8
(D& @usbdkj , Wfen (B& Brht`nr , ]fstnr (M& kmin , Kfnmn (J& Kh rnidtfhk
=4+ Hk Fkjnpnkjnkmn jdy) m`hmhidtns wnrn th bn nqudiiy jfstrfbutnj dlhkg =53 m`fijrnk fk d sm`hhi+ Dmtudiiy
hk t`dt jdy 423 m`fijrnk wnrn dbsnkt )hk dmmhukt he t`fs ndm` m`fij ght > m`hmhidtns nxtrd+ @hw ldky
m`hmhidtns ndm` stujnkt ght hk t`dt jdy 8
(D& 42 (B& 43 (M& 4> (J& 5
Jfrnmtfhks 1 (=2 th =5& Rndj t`n ehiihwfkg fkehrldtfhk mdrneuiiy dkj dkswnr t`n qunstfhks t`dt ehiihw+
(f& Z`nrn drn sfx stujnkts ( D) B) M) J) N dkj E& fk d grhup+ Ndm` stujnkt mdk hpt ehr hkiy t`rnn m`hfmns
hut he t`n sfx w`fm` drn lusfm) rndjfkg) pdfktfkg) bdjlfkthk) mrfmont dkj tnkkfs+
(ff& D) M dkj E ifon rndjfkg+
(fff& J jhns kht ifon bdjlfkthk) but ifons lusfm+
(fv& Bht` B dkj N ifon pdfktfkg dkj lusfm+
(v& D dkj J jh kht ifon pdfktfkg) but t`ny ifon mrfmont+
(vf& Dii stujnkt nxmnpt hkn ifon bdjlfkthk+
(vff& Zwh stujnkts ifon tnkkfs+
(vfff& E jhns kht ifon mrfmont) lusfm dkj tnkkfs+
=2+ W`fm` pdfr he stujnkts `ds t`n sdln mhlbfkdtfhk he m`hfmns 8
(D& D dkj M (B& M dkj J (M& B dkj N (J& J dkj E
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - >
==+ W`h dlhkg t`n ehiihwfkg stujnkts ifons bht` tnkkfs dkj mrfmont 8
(D& D dkj B (B& M (M& B dkj J (J& J
=:+ @hw ldky stujnkts ifon pdfktfkg dkj bdjlfkthk 8
(D& 4 (B& 2 (M& = (J& :
=>+ W`h dlhkg t`n ehiihwfkg jh kht ifon lusfm 8
(D& D ) M dkj J (B& D) B dkj M (M& D) M dkj E (J& B) J dkj E
=5+ W fm he t`n ehiihwfkg fs t`n lhst phpuidr m`hfmn 8(D& Znkkfs (B& Bdjlfkthk (M& Rndjfkg (J& Sdfktfkg
=7+ Z`n inttnrs I) L) K) H) S) T) R) ] dkj Z fk t`nfr hrjnr drn substftutnj by kfkn fktngnrs 4 th 6 but kht fk t`dt
hrjnr+ : fs dssfgknj th S+ Z`n jfeenrnkmn bntwnnk S dkj Z fs >+ Z`n jfeenrnkmn bntwnnk K dkj Z fs =+ W`dt
fs t`n fktngnr dssfgknj th K 8
(D& 7 (B& > (M& : (J& 5
=0+ ]fx stujnkts D) B) M) J) N dkj E drn sfttfkg fk t`n efnij+ D dkj B drn erhl Jni`f w`fin t`n rnst drn erhl
bdkgdihrn+ J dkj E drn tdii w`fin ht`nrs drn s`hrt+ D) M dkj J drn gfris w`fin ht`nrs drn bhys+ W`fm` fs t`n
tdii gfri erhl Bdkgdihrn 8
(D& E (B& J (M& N (J& M
Jfrnmtfhks 1 (=6 th :3& Fk t`n ehiihwfkg qunstfhks w`fm` snt he sfgks s`huij mhlpintn t`n dstnrfsos (& snqunktfdiiyfk hrjnr th ldon t`n nqudtfhk ldt`nldtfmdiiy lndkfkgeui 8 Efkj t`n mhrrnmt snt he sfgks ehrl dlhkg t`n
ditnrkdtfvns gfvnk ukjnr ndm` qunstfhk+
=6+ 2: 2 2 43
(D&
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 5
:=+ 23) :2) 63
(D& F (B& FF (M& FFF (J& FU
::+ 42) =5) 03
(D& F (B& FF (M& FFF (J& U
Jfrnmtfhks 1 (:> th :6 & Fk ndm` qunstfhk t`nrn fs shln rnidtfhk bntwnnk t`n efrst twh tnrls+ ]dln rnidtfhks`fp
nxfsts fk t`n knxt twh tnrls+ Z`n lfssfkg tnrl (8& fs hut he t`n hptfhks gfvnk bnihw+ Efkj t`n mhrrnmt
hptfhk+
:>+ 8 1 F R H I 11 H I F R 1 ^ E M P
(D& E M P (B& N M P (M& M P E (J& M P E
:5+ O D U N R F 1 L J Q F ^ O 11 ] F K G N R 1 8
(D& O @ Z I R (B& R O @ Z I (M& I R O @ Z (J& Z @ O I R
:7+ Z D I O 1 T T N W 11 R H S N 1 8
(D& A U U ] (B& O ] (M& A ] ] (J& O A A ]
:0+ 424 1 2 11 654 1 8
(D& 4 (B& = (M& : (J& >
:6+ 44 1 =3 11 8 1 420
(D& 5> (B& 55 (M& 57 (J& 50
Jfrnmtfhks 1 (>3 th >:& Fk ndm` qunstfhk t`nrn drn ehur snts he inttnrswhrjs+ Hkn snt fs jfeenrnkt erhl t`n rnst t`rnn
fk shln wdy hr t`n ht`nr+ Efkj hut t`fs jfeenrnkt snt+
>3+ (D& N L G T Z (B& Z S U R P (M& H P K Q S (J& L ] W T
>4+ (D& M G I R (B& J @ L ] (M& L T U D (J& E A H
>2+ (D& ::4) 42 (B& 2>5) 4= (M& :0:) 45 (J& 206) 46
>=+ (D& 02) 45 (B& 5=) 40 (M& >:) 22 (J& :5) 2:
>:+ (D& 424) 2 (B& 4::) = (M& 456) : (J& 22>) 4
Jfrnmtfhks 1(>> th >5& M`hhsn t`n Unkk jfdgrdl w`fm` bnst jnsmrfbn t`n rnidtfhks`fp dlhkg t`n t`rnn gfvn
midssns (Z`n sfzn he mfrmin jhns kht fkjfmdtn rnidtfvn sfzns he midssns&
>>+ Zrfdkgins) Tudjrfidtnrdis) ]qudrns
(D& (B&(M&
(J&
>5+ Sidynrs) @uldk Bnfkgs) ]tujnkts
(D& (B& (M& (J&
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 7
>7+ Lh`dk wds bhrk hk Dugust 22+ Drvfkj fs yhukgnr t`dk Lh`dk by 43 jdys+ Z`fs yndr fkjnpnkjnkmn jdy
ediis hk Zunsjdy+ Hk w`fm` jdy Drvfkj bfrt`jdy edii 8
(D& Zunsjdy (B& Wnjknsjdy (M& Z`ursjdy (J& Erfjdy
>0+ D erfnkj he lfkn mdln th lnnt ln nvnry ]ukjdy+ Z`n efrst tfln `n mdln dt 42 1 =3 ? t`n knxt tfln dt
4123) t`nk dt 2 1 =3) t`nk dt :+33 w`nk jfj `n turk up t`n tfln detnr t`dt 8
(D& :+=3 (B& >+>3 (M& >+=3 (J& >+23
Jfrnmtfhks 1 (>6 th 5=& D mubn pdfktnj rnj hk twh djadmnkt edmns dkj bidmo hk t`n edmns hpphsftn th t`n rnj edmns
dkj grnnk hk t`n rnldfkfkg edmns fs mut fkth 5: sldiinr mubns he nqudi sfzn+
>6+ @hw ldky mubns dvn kh edmn pdfktnj 8
(D& 3 (B& : (M& 0 (J& 45
53+ @hw ldky mubns dvn hkiy hkn edmn pdfktnj 8
(D& 0 (B& 2: (M& 20 (J& :0
54+ @hw ldky mubns dvn inss t`dk t`rnn edmns pdfktnj 8
(D& 0 (B& 2: (M& 20 (J& :0
52+ @hw ldky mubns drn t`nrn wft` t`n t`rnn edmns pdfktnj 8(D& : (B& 0 (M& 45 (J& 2:
5=+ @hw ldky mubns dvn hkn edmn grnnk dkj dt indst hkn he t`n djadmnkt edmns bidmo hr rnj 8
(D& 0 (B& 45 (M& 2: (J& 20
Jfrnmtfhk 1 (5:&Z`n sfx edmns he d mubn dvn bnnk ldronj wft` kulbnrs 4) 2) =) :) > dkj 5 rnspnmtfvniy+ Z`fs mubnfs rhiinj jhwk t`rnn tflns+ Z`n t`rnn phsftfhks drn gfvnk+ M`hhsn t`n efgurn t`dt wfii bn ehrlnj w`nk t`n
mubn fs ukehijnj+
5:+
(D& (B& (M& (J&
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 0
Jfrnmtfhks 1( 5> th 57& Fk t`n ehiihwfkg qunstfhks ) t`nrn drn efgurns th t`n inet he t`n lfrrhr fkjfmdtnj by ifkns dkj
t`nfr lfrrhr fldgns drn gfvnk fk hkn he t`n ehur efgurn+
5>+
YYYYYYYYYYYYYYYY
(D& (B& (M& (J&
55+
YYYYYY
YYYYYYYYYY
(D& (M& (J&(B&
57+
YYYYYYYYYYYY
YYYY
(D& (M& (J&(B&
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 6
Jfrnmtfhks 1(50 th 56& Fe d squdrn he pdpnr fs ehijnj erhl t`n mnktrn dkj muts drn ldjn ds s`hwk fk t`n prhbinl
efgurn) hw wfii ft dppndr w`nk ft fs hpnknj 8 ]ninmt t`n dpprhprfdtn efgurn erhl t`n m`hfmns+
50+
(D& (B& (M& (J&
56+
(D& (B& (M& (J&
73+ @hw ldky qudjrfidtnrdis drn t`nrn fk t`n efgurn8
(D& = (B& : (M& > (J& 5
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 43
74+ @hw ldky pdrdiinihgrdls drn t`nrn fk t`n efgurn8
(D& 42 (B& 43 (M& 0 (J& 5
Jfrnmtfhks 1 (72 th 7=& Fk ndm` he t`n ehiihwfkg qunstfhks d jnsfgk fs gfvnk+ Hkn sldii snglnkt fs lfssfkg erhl t`n
jnsfgk+ ]ninmt t`n ditnrkdtfvn w`fm` wfii mhlpintn t`n jnsfgk w`nk pidmnj hk t`n lfssfkg drnd+
72+
8(D& (B& (M& (J&
7=+
8
(D& (B& (M& (J&
Jfrnmtfhks 1 (7: th 75& Z`nrn drn twh snts he efgurns+ Hkn fs qunstfhk efgurns dkj t`n ht nr fs dkswnr,efgurns+
Z`nrn fs shln rnidtfhks`fp bntwnnk t`n efrst twh efgurns he t`n qunstfhk,efgurns+ Z`n sdln rnidtfhks`fp
nxfsts bntwnnk t`n t`frj dkj ehurt` efgurns+ ]ninmt t`n hptfhk he t`n mhrrnmt dkswnr,efgurn ehr t`n pidmn he
qunstfhk ldro (8&+
Tunstfhk,Efgurns
7:+
P P
P P P
P PP P
P PP
8
Dkswnr Efgurns
P P P
P P
(D& (B& (M& (J&
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]pdmn Ehr Rhug` Whro
LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 44
7>+ Tunstfhk,Efgurns
8
Dkswnr Efgurns
(D& (B& (M& (J&
75+ Tunstfhk,Efgurns
8
Dkswnr Efgurns
Jfrnmtfhks 1 (77 th 76& Z`nrn drn twh snts he efgurns+ Hkn fs he Srhbinl Efgurns w`fin dkht`nr fs snt he Dkswnr
Efgurns+ Z`nrn fs d snqunkmn dmmhrjfkg th w`fm` t`n Srhbinl Efgurns drn drrdkgnj+ Hkn efgurn he Dkswnr
Efgurns fs th bn sninmtnj w`fm` mdk bn pidmnj fk snqunkmn he Srhbinl Efgurns+ Efkj t`n mhrrnmt hptfhk he
t`n sninmtnj Dkswnr Efgurn+
77+ Srhbinl Efgurns
Dkswnr Efgurns
(D& (B& (M& (J&
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LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 42
70+ Srhbinl Efgurns
Dkswnr Efgurns
(D& (B& (M& (J&
76+ Srhbinl Efgurns
Dkswnr Efgurns
(D& (B& (M& (J&
Jfrnmtfhks 1 ( 03 th 04& Fk ndm` qunstfhk ehur efgurns drn gfvnk+ Hkn he t`nl jhns kht mhrrnidtn wft` t`n rnst+ Efkjhut t`n jfeenrnkt efgurn+
03+
(D& (B& (M& (J&
04+
(D& (B& (M& (J&
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LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 4=
Jfrnmtfhks 1 (02 th 0>& Fk ndm` he t`n ehiihwfkg prhbinls) t`nrn fs hkn qunstfhk dkj t`rnn stdtnlnkts F) FF dkj FFF
gfvnk bnihw t`n qunstfhk+ Vhu `dvn th jnmfjn w`nt`nr t`n jdtd gfvnk fk t`n stdtnlnkts fs sueefmfnkt th
dkswnr t`n qunstfhk+ Rndj dii t`n stdtnlnkts mdrneuiiy dkj efkj w`fm` he t`n stdtnlnkt fsdrn sueefmfnkt th
dkswnr t`n gfvnk qunstfhk+ M`hhsn t`n mhrrnmt ditnrkdtfvn fk ndm` qunstfhk+
02+ @hw ldky shks jhns P dvn 8
F+ T dkj drn brht`nrs he Z+
FF+ R fs t`n sfstnr he S dkj ^+
FFF+ R dkj Z drn jdug`tnrs he P+(D& Hkiy F dkj FF (B& Hkiy FF dkj FFF
(M& Dii F) FF dkj FFF (J& F) FF dkj FFF thgnt`nr drn kht sueefmfnkt+
0=+ Ufiidgn Z fs fk w`fm` jfrnmtfhk wft` rnspnmt th vfiidgn R 8
F+ Z fs th t`n Khrt` he W w`fm` fs th t`n Wnst he ]+
FF+ Z fs th t`n Khrt`,Wnst he ]+
FFF+ W fs th t`n Khrt`,Wnst he R+
(D& Hkiy F dkj FF (B& Hkiy FF dkj FFF
(M& Hkiy F dkj FFF (J& Khkn he t`nsn
0:+ Fk w`fm` yndr wds ]dkady bhrk 8
F+ ]dkady fs sfx yndrs hijnr t`dk Ghpdi+FF+ Ghpdis brht`nr wds bhrk fk 4602+
FFF+ ]dkadys brht`nr fs twh yndrs yhukgnr t`dk Ghpdis brht`nr w`h fs nfg`t yndrs yhukgnr t`dk Ghpdi+
(D& Hkiy F dkj FF (B& Hkiy FF dkj FFF
(M& Hkiy F dkj FFF (J& Dii F) FF dkj FFF
0>+ W`dt fs t`n thtdi lhkt`iy sdidry he Udsu 8
F+ Udsus bdsfm sdidry fs Rs 433 lhrn t`dk Rdadks sdidry w`h dish snrvns fk Udsus mhlpdky+
FF+ Ht`nr diihwdkmns jrdwk by Rdadk bnsfjns fs sdidry drn Rs 2333 pnr lhkt` w`fm` fs Rs >3 inss t`dk
Udsus sdidry+
FFF+ Rdadks bdsfm sdidry fs Rs 4>>3 pnr lhkt`+
(D& Hkiy F dkj FF (B& Hkiy FF dkj FFF
(M& Hkiy F dkj FFF (J& Dii F) FF dkj FFF
Jfrnmtfhk 1( 05 th 07& Z`nrn fs shln rnidtfhks`fp bntwnnk t`n twh tnrls hk t`n inet sfjn he t`n sfgk (11&+ ]ninmt t`n
sdln rnidtfhks`fp bntwnnk t`n twh tnrls hk t`n rfg`t sfjn+
05+ Ifhk 1 Mub 11
(D& Edt`nr 1 M`fij (B& Dukt 1 M`fij (M& Lht`nr 1 M`fij (J& Edt`nr 1 Lht`nr
07 Snrshk 1 ]hmfnty 11
(D& ]tujy 1 Okhwinjgn (B& Ifbrdry 1 Sdgns (M& Bhho 1 Ifbrdry (J& Mhpy 1 ]tujy
00+ Z`rnn yndrs dgh Rdau wds 0 yndrs yhukgnr t`dk ]dkau+ W`dt wfii bn jfeenrnkmn bntwnnk t`nfr dgns detnr
> yndrs
(D& 0 yndrs (B& 7 yndrs (M& 42 yndrs (J& 4> yndrs
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LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 4:
Jfrnmtfhks 1 (06 th 63& Gfvnk qunstfhks drn bdsnj hk t`n drrdkgnlnkt he inttnrs 'd th z' fk t`n ehrl he d pyrdlfj+
Fk ndm` qunstfhk twh snts he inttnrs gfvnk hk t`n inet he sfgk (1 1& w`fm` drn rnidtnj fk shln wdy hr ht`nr+
]dln rnidtfhks`fp fs bntwnnk twh snts hk t`n rfg`t wft` hkn bidko tnrl+ ]ninmt t`n mhrrnmt hptfhk ehr t`n
bidko tnrl+
db m j
n eg
` fa o i l k h p
q r s t u v w x yz
06+ meo 1 otz 1 1 8 1 hvz
(D& jfp (B& m`h (M& glu (J& `kv
63+ neg 1 glu 1 1 nos 1 8
(D& `lk (B& stu (M& noa (J& for
Jfrnmtfhks (64 th 6:& 1 ]tujy t`n ehiihwfkg fkehrldtfhk mdrneuiiy dkj dkswnr t`n gfvnk qunstfhks1
D whrj dkj kulbnr drrdkgnlnkt ldm`fkn w`nk gfvnk dk fkput ifkn he whrjs dkj kulbnrs rndrrdkgns
t`nl ehiihwfkg d pdrtfmuidr ruin fk ndm` stnp+ Z`n ehiihwfkg fs dk fiiustrdtfhk he fkput dkj rndrrdkgnlnkt+
Fkput 1 qufmo efrn 4> 20 =6 wdr 46 yniihw
]tnp F 1 yniihw qufmo efrn 4> 20 =6 wdr 46
]tnp FF 1 yniihw 4> qufmo efrn 20 =6 wdr 46
]tnp FFF1 yniihw 4> wdr qufmo efrn 20 =6 46
]tnp FU1 yniihw 4> wdr 46 qufmo efrn 20 =6
]tnp U 1 yniihw 4> wdr 46 qufmo 20 efrn =6
Dkj ]tnp U fs t`n idst stnp he t`n dbhvn fkput+
Ds pnr t`n ruins ehiihwnj fk t`n dbhvn stnps) efkj hut fk ndm` he t`n ehiihwfkg qunstfhks t`n dpprhprfdtn
stnp ehr t`n gfvnk fkput+
64+ ]tnp FF he dk fkput fs 1 znbrd 42 bdko mdrrfdgn :5 =4 26 jusoW`fm` he t`n ehiihwfkg stnps wfii bn t`n idst but hkn 8
(D& U (B& UF (M& UFF (J& UFFF
62+ Fkput 1 dgn jfn 72 >= => hij ghdi 25
@hw ldky stnps wfii bn rnqufrnj th mhlpintn t`n rndrrdkgnlnkt8
(D& Ehur (B& Efvn (M& ]fx (J& ]nvnk
6=+ ]tnp FF he dk fkput fs 1 wfk 42 62 ehr 04 diwdys =5 hln
W`fm` he t`n ehiihwfkg wfii bn ]tnpUFF 8
(D& wfk 42 `hln =5 62 ehr 04 diwdys
(B& wfk 42 `hln =5 ehr 62 diwdys 04
(M& wfk 42 `hln 62 ehr 04 diwdys =5(J& Khkn he t`nsn
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LDZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 4>]DZXKZ]N ]ZDGN,FF LHMO ZN]Z SDSNR,=XSDGN - 4>
6:+ ]tnp FFF he dk fkput fs 1 trdfk 2= stdr 54 =2 edii drj >=
W`fm` he t`n ehiihwfkg fs jnefkftniy t`n fkput8
(D& 2= stdr 54 trdfk =2 edii `drj >=
(B& stdr trdfk 54 2= =2 edii `drj >=
(M& 54 stdr 2= trdfk =2 edii `drj >=
(J& Mdkkht bn jntnrlfknj
6>+ Z`nrn drn >3 stujnkts djlfttnj th d kursnry midss+ ]hln stujnkts mdk spndo hkiy Nkgifs` dkj shln mdk
spndo hkiy @fkjf+ Znk stujnkts mdk spndo bht` Nkgifs` dkj @fkjf+ Fe t`n kulbnr he stujnkts w`h mdk
spndo Nkgifs` fs 24) t`nk hw ldky stujnkts mdk spndo @fkjf) hw ldky mdk spndo hkiy @fkjf dkj hw
ldky mdk spndo hkiy Nkgifs` 8
(D& =6) 26 dkj 44 rnspnmtfvniy (B& =7) 27 dkj 4= rnspnmtfvniy
(M& 20) 40 dkj 22 rnspnmtfvniy (J& 24) 44 dkj 26 rnspnmtfvniy
Jfrnmtfhks (65 th 433& 1 Fk ndm` he t`n ehiihwfkg qunstfhks) twh stdtnlnkts drn gfvnk ehiihwnj by t`rnn hr ehur
mhkmiusfhks kulbnrnj F) FF) FFF dkj FU+ Vhu dvn th tdon t`n gfvnk stdtnlnkts th bn trun nvnk fe t`ny snnl
th bn dt vdrfdkmn erhl t`n mhllhkiy okhwk edmts dkj t`nk jnmfjn w`fm` he t`n gfvnk mhkmiusfhks ihgfmdiiy
ehiihws erhl t`n gfvnk stdtnlnkts jfsrngdrjfkg mhllhkiy okhwk edmts+
65+ ]tdtnlnkts 1 Dii phiftfmfdks drn hknst+ Dii hknst drn edfr+
Mhkmiusfhks 1F+ ]hln hknst drn phiftfmfdk+
FF+ Kh `hknst fs phiftfmfdk+FFF+ ]hln edfr drn phiftfmfdk+ FU+ Dii edfr drn phiftfmfdk+
(D& Khkn ehiihws (B& Hkiy F ehiihws
(M& Hkiy F dkj FF ehiihw (J& Hkiy F dkj FFF ehiihw
67+ ]tdtnlnkts 1 ]hln bhhos drn pnks+ Kh pnk fs pnkmfi+
Mhkmiusfhks 1 F+ ]hln pnks drn bhhos+ FF+ ]hln pnkmfis drn bhhos+
FFF+ ]hln bhhos drn kht pnkmfis+ FU+ Dii pnkmfis drn bhhos+
(D& Hkiy F ehiihws (B& Hkiy FF dkj FFF ehiihw
(M& Hkiy F dkj FFF ehiihw (J& Hkiy F dkj FF ehiihw
60+ ]tdtnlnkts 1 ]hln tdbins drn ZUs+ ]hln ZUs drn rdjfhs+
Mhkmiusfhks 1 F+ ]hln tdbins drn rdjfhs+ FF+ ]hln rdjfhs drn tdbins+
FFF+ Dii rdjfhs drn ZUs+ FU+ Dii ZUs drn tdbins+
(D& Khkn ehiihws (B& Dii ehiihws
(M& Hkiy F dkj FFF ehiihw (J& Hkiy FF dkj FU ehiihw
66+ ]tdtnlnkts 1 ]hln husns drn heefmns+ ]hln heefmns drn sm`hhis+
Mhkmiusfhks 1 F+ ]hln sm`hhis drn husns+ FF+ ]hln heefmns drn husns+
FFF+ Kh husn fs sm`hhi+ FU+ ]hln sm`hhis drn heefmns+
(D& Hkiy FF dkj FFF ehiihw (B& Hkiy F dkj FU ehiihw
(M& Hkiy nft`nr FFF hr FU) dkj F ehiihw (J& Hkiy FF dkj FU dkj nft`nr F hr FFF ehiihw
433+ ]tdtnlnkts 1 Dii tfgnrs drn aukgins+ Kh aukgins drn bfrjs+ ]hln bfrjs drn rdfks+
Mhkmiusfhks 1 F+ Kh rdfk fs aukgin+ + FF+ ]hln rdfks drn aukgins+
FFF+ Kh bfrjs fs tfgnr+ FU+ Dii bfrjs drn tfgnrs+
(D& Hkiy F dkj FF ehiihw (B& Hkiy FFF ehiihws
(M& Hkiy nft`nr F hr FF) dkj FFF ehiihw (J& Hkiy FF ehiihws