class_11_sa2

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  • 8/2/2019 Class_11_SA2

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    Dk`mz Oemaadodmkp*s$

    22

    2* 7$

    O

    77 7

    2 7* 7$* 7$

    O O

    6 6 6 62 7 6* $ * 7$* 7$ 6

    O O O

    ?? ? ? ?

    2 7 6 ?* $ * $* 7$ * 7$? ?

    O O O O

    00 0 0 0 0

    2 7 6 ? 0* $ * $ * 7$* 7$ * $0 1 0

    O O O O O

    == = = = = =

    2 7 6 ? 0 =* $ * 72$ * $* 7$ * 72$ * 7$= =

    O O O O O O

    Fdkeldgc pjmevml aev gkt resdpdqm dkpmimv Pjm mzrgksdek ea g fdkeldgc aev gkt resdpdqm dkpmivgc k ds gs aecceys>

    7 6 6 72 7 6 7* $ O O O +++ O Ok k k k k k k k k k kk kg f g g f g f g f f _elm redkps gfe}p Fdkeldgc Pjmevml

    *d$ Pjm kepgpdek2

    Ok

    k k h h

    h

    h

    g f

    spgk`s aev

    2 7 7

    2 7O O +++ O +++ Ok k k k k k v v k k k k

    v kg f g f g f g f

    Jmkom# pjm fdkeldgc pjmevml ogk gcse fm spgpm` gs aecceys>

    2

    * $ Ok

    k k k h h

    h

    h

    g f g f

    *dd$Pjm oemaadodmkps ea Okh

    eoo}vvdki dk pjm fdkeldgc pjmevml gvm hkeyk gs fdkeldgc

    oemaadodmkps+*ddd$Dk pjm mzrgksdek ea *g ( f$k# pjmvm gvm *k ( 7$ pmvls d+m+# ekm levm pjgk pjm dk`mz+

    *dq$Dk pjm s}oomssdqm pmvls ea pjm mzrgksdek ea *g ( f$k# pjm dk`mz eag iems ek `movmgsdkift }kdpt# spgvpdki ydpj k dk pjm advsp pmvl gk` mk`dki ydpj 2 dk pjm cgsp pmvl+ Gcse# pjm

    dk`mz eaf dkovmgsms ft }kdpt# spgvpdki ydpj 2 dk pjm advsp pmvl gk` mk`dki ydpj k dk pjm

    cgsp pmvl+*q$Dk mqmvt pmvl ea pjm mzrgksdek# pjm s}l ea pjm dk`doms eag gk` f ds k+

    Dk pjm fdkeldgc mzrgksdek ea *g ( f$k# pghdki g < z gk` f Fdkeldgc Pjmevml

    > ER I]RPG * (47 , 41 =2 ?= 2 0 :2 $

    ER I]RPG *41=2 ?=2 0:2$

    Ft

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    Ld``cm pmvl dk pjm mzrgksdek ea *g (f$k Dak ds mqmk# pjmk pjm k}lfmv ea pmvls dk pjm mzrgksdek ydcc fm k ( 7+ _dkom k ds mqmk# k (

    7 ds e``+ Pjmvmaevm# pjm ld``cm pmvl ds

    pj

    76

    k

    pmvl+

    Dak ds e``# pjmk k ( 7 ds mqmk+ _e# pjmvm ydcc fm pye ld``cm pmvls dk pjm mzrgksdek+ Pjmt

    gvm

    pj7

    6

    k

    pmvl gk`

    pj7

    76

    k

    pmvl+

    Ojgrpmv 4> _mw}mkoms gk` _mvdms

    G smw}mkom ds gk gvvgkimlmkp ea k}lfmvs dk `madkdpm ev`mv gooev`dki pe selm v}cm+ G smw}mkom lgt fm `madkm` gs g a}kopdek yjesm `elgdk ds pjm smp ea kgp}vgc k}lfmvs ev

    selm s}fsmp ea pjm ptrm x7# 6# ?h|+

    G smw}mkom oekpgdkdki adkdpm k}lfmv ea pmvls ds ogccm` g adkdpm smw}mkom# yjmvmgs gsmw}mkom oekpgdkdki dkadkdpm k}lfmv ea pmvls ds ogccm` gk dkadkdpm smw}mkom+

    Pjm imkmvgc aevl ea g smw}mkom ds g7# g6# g?# gk7 # gk# g7# g6 mpo+ gvm ogccm` pjm pmvls ea pjm smw}mkom+ Pjm kpj pmvl ea pjm smw}mkom# gk#ds ogccm` pjm imkmvgc pmvl ea pjm smw}mkom+

    Gk gvvgkimlmkp ea k}lfmvs s}oj gs 7# 6# 0# 1# 72 jgs ke qdsdfcm rgppmvk+ Jeymqmv# pjmsmw}mkom ds imkmvgpm` ft pjm vmo}vvmkom vmcgpdek idqmk ft7 6 ?

    6 7

    7# 6# 0

    # ?k k k

    g g g

    g g g k

    Pjds smw}mkom ds ogccm` pjm Adfekgood smw}mkom+

    Cmp7 6# # +++

    kg g g # fm g idqmk smw}mkom+ Gooev`dkict# pjm s}l ea pjds smw}mkom ds idqmk ft pjm

    mzrvmssdek7 6 +++ +++kg g g

    Pjds ds ogccm` pjm smvdms gsseodgpm` ydpj pjm idqmk smw}mkom+

    Pjm smvdms ds adkdpm ev dkadkdpm gooev`dki gs pjm idqmk smw}mkom+ G smvdms ds }s}gcct vmrvmsmkpm` dk g oelrgop aevl }sdki sdilg kepgpdek *$+

    Pjds lmgks pjm smvdms 7 6 7+++ k kg g g g ogk fm yvdppmk gs7

    k

    h

    h

    g

    Gvdpjlmpdo rveivmssdekPjm smw}mkom

    7 6# # +++ kg g g ds ogccm` gk gvdpjlmpdo smw}mkom ev gk gvdpjlmpdo rveivmssdek

    *G+R+$ da7 #k kg g ` k K +

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

    Oelrdcm` Ft> ER I]RPG *41=2 ?=2 0:2$

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    Jmvm#7

    g ds ogccm` pjm advsp pmvl gk` `ds ogccm` pjm oellek `daamvmkom ea pjm G+R+

    Dk spgk`gv` aevl# pjm G+R+ ds yvdppmk gs g# g ( `# g ( 6`

    Pjm kpj ev pjm imkmvgc pmvl ea gk G+R+ ds idqmk ft gk < g ( *k7$ `+ Dag ds pjm advsp pmvl# `ds pjm oellek `daamvmkom# c ds pjm cgsp pmvl gk` k ds pjm k}lfmv ea

    pmvls# pjmk c < g ( *k7$ `+

    Pjm s}l eak pmvls ea gk G+R+ *`mkepm` ft _k$ ds idqmk ft_ X6 * 7$ \

    6k

    kg k `

    Gcse# _ * $6

    k

    kg c

    Rvermvpdms ea gk G+R+ Da g oekspgkp ds g``m` ev s}fpvgopm` ev l}cpdrcdm` pe mgoj pmvl ea gk G+R+# pjmk pjmvms}cpdki smw}mkom ds gcse gk G+R+ Da mgoj pmvl ea gk G+R+ ds l}cpdrcdm` ev `dqd`m` ft g kek,~mve oekspgkp# pjmk pjm vms}cpdki

    smw}mkom ds gcse gk G+R+

    Gvdpjlmpdo lmgk Aev gkt pye k}lfmvs g gk` f# ym ogk dksmvp g k}lfmv G fmpymmk pjml s}oj pjgp g# G# f

    ds gk G+R+ Jmvm# G ds ogccm` pjm gvdpjlmpdo lmgk *G+L+$ ea k}lfmvs g gk` f gk`

    6

    g fG

    +

    CmpG7#G6Gk fm k k}lfmvs fmpymmk g gk` f s}oj pjgp g#G7#G6##Gk# f ds gk G+R+Gooev`dkict# oellek `daamvmkom *`$ ds idqmk ft

    7

    f g

    k

    +

    Pjm k}lfmvsG7#G6Gk gvm idqmk gs aecceys>

    7

    6

    7

    6* $6

    7

    +

    +

    +

    * $

    7k

    f g G g ` g

    k

    f g G g ` g

    k

    k f g G g k` g

    k

    Imelmpvdo rveivmssdek

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

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    G smw}mkom ds sgd` pe fm g imelmpvdo rveivmssdek *I+R+$ da pjm vgpde ea gkt pmvl pe dps

    rvmom`dki pmvl ds pjm sglm pjve}ije}p+ Pjds oekspgkp agopev ds ogccm` pjm oellek vgpde gk` dpds `mkepm` ft v+

    Dk spgk`gv` aevl# pjm I+R+ ds yvdppmk gs 6# #g gv gv yjmvm# g ds pjm advsp pmvl gk` vds pjm

    oellek vgpde+

    Pjm kpj pmvl *ev imkmvgc pmvl$ ea g I+R+ ds idqmk ft gk < gvk7 Pjm s}l eak pmvls *_k$ ea g I+R+ ds idqmk ft

    *7 $ * 7$ev # da 7

    _ 7 7

    # da 7

    k k

    k

    g v g v v

    v v

    kg v

    Imelmpvdo lmgk Aev gkt pye resdpdqm k}lfmvs g gk` f# ym ogk dksmvp g k}lfmv I fmpymmk pjml s}oj pjgp

    g# I# f ds g I+R+ I ds ogccm` g imelmpvdo lmgk *I+L+$ gk` ds idqmk ft I < gf

    Cmp

    I7#

    I6# #

    Ik fm

    kk}lfmvs fmpymmk resdpdqm k}lfmvs

    ggk`

    fs}oj pjgp

    g#

    I7#

    I6#

    # Ik# f ds g I+R+ Oellek vgpde ea I+R+#

    7

    7kfv

    g

    Pjmvmaevm# I7< gv# I6 < gv6## Ik< gv

    k

    CmpG gk` I fm pjm vmsrmopdqm G+L+ gk` I+L+ ea pye idqmk resdpdqm vmgc k}lfmvs g gk` f+ G < gk`

    6

    g fI gf

    GI_}l eak,pmvls ea selm srmodgc smvdms _}l ea advsp k kgp}vgc k}lfmvs

    * 7$7 6 ? +++

    6

    k kk

    _}l ea sw}gvms ea pjm advsp k kgp}vgc k}lfmvs6 6 6 6 * 7$*6 7$

    7 6 ? +++1

    k k kk

    _}l ea o}fms ea pjm advsp k kgp}vgc k}lfmvs6

    ? ? ? ? * 7$7 6 ? +++

    6

    k kk

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

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    Ojgrpmv 72> _pvgdijp Cdkms

    _cerm ea g cdkmDa ds pjm dkocdkgpdek ea g cdkm c *pjm gkicm fmpymmk resdpdqmz,gzds gk` cdkm c$# pjmk pgk dsogccm` pjm scerm ev ivg`dmkp ea cdkm c+

    Pjm scerm ea g cdkm ds `mkepm` ft l+

    Pj}s# l < pgk # 42

    Pjm scerm ea g cdkm yjesm dkocdkgpdek ds 42 ds kep `madkm`+ Jmkom# pjm scerm ea pjm qmvpdogccdkm *t,gzds$ ds }k`madkm`+

    Pjm scerm ea pjm jevd~ekpgc cdkm *z,gzds$ ds ~mve+ Pjm scerm *l$ ea g kek,qmvpdogc cdkm rgssdki pjve}ij pjm redkps *z7#t7$ gk` *z6#t6$ ds idqmk

    ft 6 77 6

    6 7

    #t t

    l z zz z

    +

    _}rresm c7 gk` c6 gvm kek,qmvpdogc cdkms jgqdki scerms l7 gk` l6 vmsrmopdqmct c7 ds rgvgccmc pe c6 da gk` ekct dal7 < l6# d+m+# pjmdv scerms gvm mw}gc+ c7 ds rmvrmk`do}cgv pe c6 da gk` ekct dal7l6 < 7# d+m+# pjm rve`}op ea pjmdv scerms ds7+ Gk go}pm gkicm## fmpymmk c7 gk` c6ds idqmk ft

    6 77 6

    7 6

    pgk # 7 2+7

    l ll l

    l l

    Pjvmm redkps G# F gk` O gvm oeccdkmgv da gk` ekct da_cerm ea GF < _cerm ea FO

    Jevd~ekpgc gk` qmvpdogc cdkms Pjm mw}gpdek ea g jevd~ekpgc cdkm gp `dspgkom g avel pjmz,gzds ds mdpjmvt < g *gfeqmz,

    gzds$ evt

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    Pjm redkp *z#t$ cdms ek pjm cdkm ydpj scerm l pjve}ij pjm adzm` redkp *z2#t2$ da gk` ekct da dps

    oeev`dkgpms sgpdsat pjm mw}gpdek+ Pjds lmgkstt2 < l *zz2$+

    Pye,redkp aevl ea g cdkmPjm mw}gpdek ea pjm cdkm rgssdki pjve}ij pjm redkps *z7#t7$ gk` *z6#t6$ ds idqmk ft

    6 77 7

    6 7

    * $t t t t z zz z

    +

    _cerm,dkpmvomrp aevl ea g cdkm Pjm mw}gpdek ea pjm cdkm# ydpj scerm l# yjdoj lghmst,dkpmvomrp o ds idqmk ft

    t < lz ( o+

    Pjm mw}gpdek ea pjm cdkm# ydpj scerm l# yjdoj lghmsz,dkpmvomrp `ds idqmk ftt < l*z`$+

    Dkpmvomrp aevl ea g cdkmPjm mw}gpdek ea pjm cdkm lghdki dkpmvomrps g gk` f ekz,gzds gk`t,gzds vmsrmopdqmct ds

    7z t

    g f

    Kevlgc aevl ea g cdkmPjm mw}gpdek ea pjm cdkm gp kevlgc `dspgkomr avel pjm evdidk gk` gkicmyjdoj pjm kevlgc

    lghms ydpj pjm resdpdqm `dvmopdek ea pjmz,gzds ds idqmk ft oes sdk z t r

    Gkt mw}gpdek ea pjm aevlGz (Ft ( O< 2# yjmvm G gk`F gvm kep ~mve sdl}cpgkme}sct dsogccm` pjm imkmvgc cdkmgv mw}gpdek ev imkmvgc mw}gpdek ea cdkm+

    Pjm rmvrmk`do}cgv `dspgkom *`$ ea g cdkmGz (Ft ( O< 2 avel g redkp *z7#t7$ ds7 7

    6 6

    Gz Ft O `

    G F

    +

    Pjm `dspgkom *`$ fmpymmk pye rgvgccmc cdkms d+m+#Gz (Ft ( O7 < 2 gk`Gz (Ft ( O6 < 2 dsidqmk ft

    7 6

    6 6

    O O`

    G F

    Ojgrpmv 77> Oekdo _mopdeks

    Oekdo smopdeks ev oekdos gvm pjm o}vqms pjgp gvm efpgdkm` ft dkpmvsmopdki g rcgkm ydpj g`e}fcm,kgrrm` vdijp odvo}cgv oekm+ Odvocms# mccdrsms# rgvgfecgs gk` jtrmvfecgs gvm mzglrcms

    ea oekdo smopdeks+

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

    Oelrdcm` Ft> ER I]RPG *41=2 ?=2 0:2$

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    OdvocmG odvocm ds pjm smp ea gcc redkps dk g rcgkm pjgp gvm mw}d`dspgkp avel g adzm` redkp dk pjm rcgkm+

    Pjm adzm` redkp ds ogccm` pjm omkpvm ea pjm odvocm gk` pjm adzm` `dspgkom avel pjm omkpvm dsogccm` pjm vg`d}s ea pjm odvocm+

    Mw}gpdek ea g odvocm

    ydpj omkpvm gp *j# h$ gk` vg`d}s vds*zj$6

    ( *th$6

    < v6

    ydpj omkpvm ds gp evdidk gk` vg`d}s vdsz

    6(t

    6< v

    6

    RgvgfecgG rgvgfecg ds pjm smp ea gcc redkps dk g rcgkm pjgp gvm mw}d`dspgkp avel g adzm` cdkm gk` g adzm`

    redkp *kep ek pjm cdkm dk pjm rcgkm$+

    Pjm adzm` cdkm ds ogccm` pjm `dvmopvdz+ Pjm adzm` redkp A ds ogccm` pjm aeo}s+ Pjm cdkm pjve}ij pjm aeo}s gk` rmvrmk`do}cgv pe pjm `dvmopvdz ds ogccm` pjm gzds ea pjm

    rgvgfecg+ Pjm redkp ea dkpmvsmopdek ea rgvgfecg ydpj pjm gzds ds ogccm` pjm qmvpmz ea pjm rgvgfecg+ Pjm cdkm smilmkp pjgp ds rmvrmk`do}cgv pe pjm gzds ea pjm rgvgfecg pjve}ij pjm aeo}s gk`

    yjesm mk` redkps cdm ek pjm rgvgfecg ds ogccm` pjm cgp}s vmop}l ea pjm rgvgfecg+

    _pgk`gv` mw}gpdeks ea rgvgfecg

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

    g$ Oekdo smopdek> G oekdo smopdek ev oekdo ds pjm ceo}s ea g redkp R*j# h$ yjdoj leqms dk s}oj g

    ygt pjgp dps `dspgkoms avel g adzm` redkp A*g# f$ gcygts fmgvs g oekspgkp vgpde pe dps `dspgkom

    avel g adzm` cdkm# gcc fmdki dk pjm sglm rcgkm+

    f$ Aeo}s> Pjm adzm` redkp A ds ogccm` pjm aeo}s ea pjm oekdo smopdek+

    o$ @dvmopvdz> Pjm adzm` spvgdijp cdkm ds ogccm` pjm `dvmopvdz ea pjm oekdo+

    `$ Moomkpvdodpt> Pjm oekspgkp vgpde ds ogccm` pjm moomkpvdodpt ea pjm oekdo smopdek gk` dp ds `mkepm`

    ft pjm ceymv ogsm cmppmv m+

    m$ Gzds> Pjm spvgdijp cdkm rgssdki pjve}ij pjm aeo}s gk` rmvrmk`do}cgv pe pjm `dvmopvdz ds ogccm`

    pjm gzds ea pjm oekdo smopdek+

    a$ Qmvpmz> Pjm redkps ea dkpmvsmopdek ea pjm oekdo smopdek gk` pjm gzds gvm ogccm` qmvpdoms ea pjm

    oekdo+

    i$ Omkpvm> Pjm redkp yjdoj fdsmops mqmvt ojev` ea pjm oekdo rgssdki pjve}ij dp# ds ogccm` pjm

    omkpvm ea pjm oekdo smopdek+

    j$ Cgp}s,vmop}l> Pjm cgp}s,vmop}l ea g oekdo smopdek ds pjm ojev` rgssdki pjve}ij pjm aeo}s gk`

    rmvrmk`do}cgv pe pjm gzds+

    d$ Aeogc `dspgkom> Pjm `dspgkom ea gkt redkp R*z# t$ ek pjm oekdo smopdek avel pjm aeo}s A*g# f$ ds

    ogccm` pjm aeogc `dspgkom ea redkp R+

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    Ermk Peygv`s Vdijp

    _pgk`gv` Mw}gpdek t6 < 0gz# g ; 2

    Oeev`dkgpms ea Aeo}s *g# 2$

    Oeev`dkgpms ea Qmvpmz *2# 2$

    Mw}gpdek ea @dvmopvdz z < g

    Cmkipj ea Cgp}s Vmop}l 0g

    Gzds ea Rgvgfecg Resdpdqmz,gzds

    Ermk Peygv`s Cmap

    _pgk`gv` Mw}gpdek t6

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    Ermk Peygv`s @eykygv`

    _pgk`gv` Mw}gpdek z6

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    _pgk`gv` mw}gpdeks ea mccdrsm_pgk`gv` Mw}gpdek

    6 6

    6 67#

    z tg f

    g f

    Omkpvm *2# 2$

    Qmvpmz *g# 2$

    Mk` redkps ea ldkev gzds *2# f$

    Aeod *o# 2$

    Cmkipj ea lgnev gzds 6g gcekiz,gzds

    Cmkipj ea ldkev Gzds 6f gcekit,gzds

    Cmkipj fmpymmk aeod 6o gcekiz,gzds

    Vmcgpdek fmpymmkg#f gk`o 6 6 6g f o

    Cmkipj ea cgp}s vmop}l6

    6f

    g

    Moomkpvdodpt *m 7$o

    g

    _pgk`gv` Mw}gpdek6 6

    6 67#

    z tg f

    f g

    Omkpvm *2# 2$

    Qmvpmz *2# g$

    Mk` redkps ea ldkev gzds *f# 2$

    Aeod *2# o$

    Cmkipj ea lgnev gzds 6g gcekit,gzds

    Cmkipj ea ldkev Gzds 6f gcekiz,gzds

    Cmkipj fmpymmk aeod 6o gcekit,gzds

    Vmcgpdek fmpymmkg#f gk`o 6 6 6g f o

    Cmkipj ea cgp}s vmop}l6

    6f

    g

    Moomkpvdodpt *m 7$o

    g

    _rmodgc ogsms ea gk mccdrsm Yjmk o < 2# d+m+# fepj pjm aeod lmvim peimpjmv# pjmk pjm mccdrsm fmoelms g odvocm+ Yjmk o < g# pjmk f < 2+ Dk s}oj g ogsm# pjm mccdrsm vm`}oms pe g cdkm smilmkp nedkdki pjm

    aeod+ Pjds lmgks pjm cmkipj ea pjm cdkm smilmkp ds 6o+

    JtrmvfecgG jtrmvfecg ds pjm smp ea gcc redkps dk g rcgkm# pjm `daamvmkom ea yjesm `dspgkoms avel pyeadzm` redkps dk pjm rcgkm ds g oekspgkp+

    Pjm pye adzm` redkps gvm ogccm` pjm aeod+

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

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    Pjm oekspgkp# yjdoj ds pjm `daamvmkom ea pjm `dspgkoms ea g redkp ek pjm jtrmvfecg avel pjmpye adzm` redkps# ds gcygts cmss pjgk pjm `dspgkom fmpymmk pjm pye adzm` redkps+

    Pjm ld`,redkp ea pjm cdkm smilmkp nedkdki pjm aeod ds ogccm` pjm omkpvm ea pjm jtrmvfecg+ Pjm cdkm pjve}ij pjm aeod ds ogccm` pjm pvgksqmvsm gzds gk` pjm cdkm pjve}ij pjm omkpvm gk`

    rmvrmk`do}cgv pe pjm pvgksqmvsm gzds ds ogccm` pjm oekn}igpm gzds+

    Pjm redkps gp yjdoj pjm jtrmvfecg dkpmvsmops pjm pvgksqmvsm gzds gvm ogccm` pjm qmvpdoms eapjm jtrmvfecg+

    Pjm moomkpvdodpt ea pjm jtrmvfecg ds pjm vgpde ea pjm `dspgkoms avel pjm omkpvm ea pjm mccdrsmpe ekm ea pjm aeod gk` pe ekm ea pjm qmvpdoms ea pjm mccdrsm+

    G jtrmvfecg ds stllmpvdo ydpj vmsrmop pe fepj pjm oeev`dkgpm gzms+ Pjm cdkm smilmkp pjgp ds rmvrmk`do}cgv pe pjm pvgksqmvsm gzds pjve}ij pjm aeo}s gk` yjesm

    mk` redkps cdm ek pjm jtrmvfecg ds ogccm` pjm cgp}s vmop}l ea pjm jtrmvfecg+

    _pgk`gv` mw}gpdeks ea jtrmvfecg

    _pgk`gv` Mw}gpdek

    6 6

    6 6 7z t

    g f

    Omkpvm *2# 2$

    Qmvpdoms *g# 2$

    Aeod *o# 2$

    Oekn}igpm gzds t,gzds

    Pvgksqmvsm gzds z,gzds

    Cmkipj ea oekn}igpm gzds 6f

    Cmkipj ea pvgksqmvsm gzds 6g

    Cmkipj fmpymmk aeod 6o

    Vmcgpdek fmpymmkg#f gk`o 6 6 6o g f

    Cmkipj ea cgp}s vmop}l66f

    g

    Moomkpvdodpt * m 7$o

    g

    _pgk`gv` Mw}gpdek6 6

    6 67t z

    g f

    Omkpvm *2# 2$

    Qmvpdoms *2# g$

    Aeod *2# o$

    Oekn}igpm gzds z,gzds

    Pvgksqmvsm gzds t,gzds

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

  • 8/2/2019 Class_11_SA2

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    Cmkipj ea oekn}igpm gzds 6f

    Cmkipj ea pvgksqmvsm gzds 6g

    Cmkipj fmpymmk aeod 6o

    Vmcgpdek fmpymmkg#f gk`o 6 6 6o g f

    Cmkipj ea cgp}s vmop}l

    66f

    g

    Moomkpvdodpt * m 7$o

    g

    G jtrmvfecg jgqdki mw}gc cmkipjs ea fepj pjm gzms# d+m+# pvgksqmvsm gk` oekn}igpm *g < f$ dsogccm` gk mw}dcgpmvgc jtrmvfecg+

    Ojgrpmv 76> Dkpve`}opdek pe Pjvmm @dlmksdekgc Imelmpvt

    Oeev`dkgpm gzms gk` oeev`dkgpm rcgkms Dk pjvmm,`dlmksdeks# pjm oeev`dkgpm gzms ea g vmopgki}cgv Ogvpmsdgk oeev`dkgpm stspml gvm

    pjvmm l}p}gcct rmvrmk`do}cgv cdkms+ Pjm gzms gvm ogccm`z#t# gk`~,gzms+

    Pjm pjvmm rcgkms `mpmvldkm` ft pjm rgdv ea gzms gvm pjm oeev`dkgpm rcgkms# ogccm` ZT# T^gk` ^Z,rcgkms+Pjm pjvmm oeev`dkgpm rcgkms `dqd`m pjm srgom dkpe mdijp rgvps hkeyk gs eopgkps+

    Oeev`dkgpms ea g redkp Dk pjvmm,`dlmksdekgc imelmpvt# pjm oeev`dkgpms ea g redkp R gvm gcygts yvdppmk dk pjmaevl ea pvdrcmps d+m+# *z#t#~$+ Jmvm#z#t# gk`~ gvm pjm `dspgkoms avel pjm T^# ^Z gk` ZT,

    rcgkms+

    Gcse# pjm oeev`dkgpms ea pjm evdidk gvm *2# 2# 2$

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

    Oelrdcm` Ft> ER I]RPG *41=2 ?=2 0:2$

  • 8/2/2019 Class_11_SA2

    13/23

    Pjm sdik ea pjm oeev`dkgpms ea g redkp `mpmvldkm pjm eopgkp dk yjdoj pjm redkp cdms+ Pjmaecceydki pgfcm sjeys pjm sdiks ea pjm oeev`dkgpms dk pjm mdijp eopgkps+

    Eopgkps

    Oeev`dkgpms D DD DDD DQ Q QD QDD QDDD

    z ( ( ( (t ( ( ( (

    ~ ( ( ( (

    Oeev`dkgpms ea redkps ctdki ek `daamvmkp gzms*d$ Gkt redkp ek pjmz,gzds ds ea pjm aevl *z# 2# 2$*dd$Gkt redkp ek pjmt,gzds ds ea pjm aevl *2#t# 2$*ddd$Gkt redkp ek pjm~,gzds ds ea pjm aevl *2# 2#~$

    Oeev`dkgpms ea redkps ctdki dk `daamvmkp rcgkms*d$ Oeev`dkgpms ea g redkp dk pjm T^,rcgkm gvm ea pjm aevl *2#t#~$*dd$Oeev`dkgpms ea g redkp dk pjm ZT,rcgkm gvm ea pjm aevl *z#t# 2$*ddd$Oeev`dkgpms ea g redkp dk pjm ^Z,rcgkm gvm ea pjm aevl *z# 2#~$

    @dspgkom fmpymmk pye redkps7 7 7 6 6 6

    R * # # $ gk` W * # # $ z t ~ z t ~ds idqmk ft

    6 6 6

    6 7 6 7 6 7RW * $ * $ * $ z z t t ~ ~

    Pjds ds hkeyk gs pjm `dspgkom aevl}cg+

    _mopdek aevl}cgPjm oeev`dkgpms ea redkp V# yjdoj `dqd`ms pjm cdkm smilmkp nedkdki pye redkps

    7 7 7 6 6 6R * # # $ gk` W * # # $ z t ~ z t ~

    dkpmvkgcct dk pjm vgpde l> k gvm6 7 6 7 6 7# #

    lz kz lt kt l~ k~

    l k l k l k

    mzpmvkgcct dk pjm vgpde l> k gvm6 7 6 7 6 7# #

    lz kz lt kt l~ k~

    l k l k l k

    Pjm oeev`dkgpms ea pjm ld`,redkp ea pjm cdkm nedkdki pjm redkps7 7 7 6 6 6

    * # # $ gk` * # # $z t ~ z t ~gvm

    7 6 7 6 7 6# #6 6 6

    z z t t ~ ~

    +

    Pjm oeev`dkgpms ea pjm omkpved` ea g pvdgkicm yjesm qmvpdoms gvm7 7 7 6 6 6

    * # # $# * # # $z t ~ z t tgk`

    ? ? ?* # # $ z t ~

    gvm 7 6 ? 7 6 ? 7 6 ?# #

    ? ? ?

    z z z t t t ~ ~ ~

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

  • 8/2/2019 Class_11_SA2

    14/23

    Ojgrpmv 7?> Cdldps gk` @mvdqgpdqms

    Cdldp ea g a}kopdek cdl * $

    z g

    a z

    ds pjm mzrmopm` qgc}m eaagpz < g# idqmk pjm qgc}ms eaakmgvz pe pjm cmap eag+

    Pjds qgc}m ds ogccm` pjm cmap jgk` cdldp eaa*z$ gp g+

    cdl * $z g

    a z

    ds pjm mzrmopm` qgc}m eaagpz < g# idqmk pjm qgc}ms eaakmgvz pe pjm vdijp eag+

    Pjds qgc}m ds ogccm` pjm vdijp jgk` cdldp eaa*z$ gp g+

    Da pjm vdijp gk` cmap jgk` cdldps oedkod`m# ym ogcc pjgp oellek qgc}m pjm cdldp eaa*z$ gpz< g# gk` `mkepm dp ft cdl * $

    z ga z

    +

    Aev g a}kopdekagk` g vmgc k}lfmv g# cdl * $z g

    a z

    gk`a*g$ lgt kep fm pjm sglm+

    Gcimfvg ea cdldpsCmpagk` i fm pye a}kopdeks s}oj pjgp fepj cdl * $z g a z gk` cdl * $z g i z mzdsp+ Pjmk#

    cdl X * $ * $\ cdl * $ cdl * $ z g z g z g

    a z i z a z i z

    cdl X * $ * $\ cdl * $ cdl * $ z g z g z g

    a z i z a z i z

    cdl X* $* $\ cdl * $ z g z g

    a z a z

    # yjmvm ds g oekspgkp

    cdl * $* $cdl* $ cdl * $

    z g

    z g

    z g

    a za z

    i z i z

    # yjmvm cdl * $ 2z g

    i z

    _elm spgk`gv` cdldps Aev g rectkeldgc a}kopdeka*z$# cdl * $ * $+z g a z a g Daa*z$ ds g vgpdekgc a}kopdek ea pjm aevl * $* $

    * $

    i za z

    j z # yjmvm i*z$ gk` j*z$ gvm rectkeldgc

    a}kopdeks# s}oj pjgp j*z$ 2# pjmk* $

    cdl * $* $z g

    i ga z

    j g +

    7cdl k k kz g

    z gkg

    z g

    # yjmvm k ds g resdpdqm dkpmimv ev gkt vgpdekgc k}lfmv gk` g ds resdpdqm

    2

    sdkcdl 7z

    z

    z

    2

    7 oescdl 2z

    zz

    Cmpagk` i fm pye vmgc,qgc}m` a}kopdeks ydpj pjm sglm `elgdk# s}oj pjgpa*z$ i*z$ aev gcczdk pjm `elgdk ea `madkdpdek+ Aev selm g# da fepj cdl * $

    z ga z

    gk` cdl * $

    z gi z

    mzdsp# pjmk cdl * $

    z ga z

    cdl * $z g

    i z

    +

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

    Oelrdcm` Ft> ER I]RPG *41=2 ?=2 0:2$

  • 8/2/2019 Class_11_SA2

    15/23

    _gk`ydoj pjmevmlCmpa# i# gk` j fm vmgc a}kopdeks s}oj pjgpa*z$ i*z$ j*z$ aev gccz dk pjm oellek `elgdk ea

    `madkdpdek+ Aev selm vmgc k}lfmv g# da cdl * $ cdl * $ z g z g

    a z c j z

    #pjmk cdl * $z g

    i z c

    +

    @mvdqgpdqms _}rresmads g vmgc,qgc}m` a}kopdek gk` g ds g redkp dk dps `elgdk ea `madkdpdek+ Pjm

    `mvdqgpdqm eaagp g X`mkepm` fta*g$\ ds `madkm` gs

    2

    * $ * $)* $ cdl

    j

    a g j a ga g

    j

    # rveqd`m` pjm cdldp mzdsps+

    @mvdqgpdqm eaa*z$ gp g ds `mkepm` fta*g$+

    _}rresmads g vmgc,qgc}m` a}kopdek+ Pjm `mvdqgpdqm eaax`mkepm` ft * $a z ev X * $\` a z`z

    |

    ds `madkm` gs

    2

    * $ * $

    X * $\ * $ cdlj

    ` a z j a z

    a z a z`z j

    # rveqd`m` pjm cdldp mzdsps+Pjds `madkdpdek ea `mvdqgpdqm ds ogccm` pjm advsp rvdkodrcm ea `mvdqgpdqm+

    Gcimfvg ea `mvdqgpdqms ea a}kopdeksAev pjm a}kopdeks } gk` q *rveqd`m` } gk` q gvm `madkm` dk g oellek `elgdk$#

    * $ ) ) )} q } q * $ ) ) )}q } q }q

    6

    ) )} } q }q

    q q

    _elm spgk`gv` `mvdqgpdqms 7* $ #k k` z kz

    `z

    aev gkt resdpdqm dkpmimv k

    7 7 77 7 2 7 7* +++ $ * 7$ ++++k k k kk k k k` g z g z g z g kg z k g z g`z

    *sdk $ oes` z z`z

    *oes $ sdk` z z`z

    6*pgk $ smo` z z`z

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

  • 8/2/2019 Class_11_SA2

    16/23

    Ojgrpmv 70> Lgpjmlgpdogc Vmgsekdki

    G smkpmkom ds ogccm` g lgpjmlgpdogcct goomrpgfcm spgpmlmkp da dp ds mdpjmv pv}m ev agcsm# f}p kepfepj+ _pgpmlmkps gvm `mkepm` ft slgcc cmppmvsr# w# v# s# mpo+

    Mzglrcm> Oeksd`mv pjm aecceydki smkpmkoms>

    Pjm qgc}m ea depg ds 7+Dp ds g spgpmlmkp+ _dkom ym hkey pjgp d < 7 # pjm idqmk smkpmkom ds agcsm+

    Pjm k}lfmv 2 ds pjm slgccmsp yjecm k}lfmv+Dp ds g spgpmlmkp gs pjds smkpmkom ds gcygts pv}m+

    @e te} jgqm dkpmvkmp gp te}v jelm5Dp ds kep g spgpmlmkp gs dp ds g w}mspdek+

    Vmlmlfmv _mkpmkoms dkqecqdki qgvdgfcm pdlm s}oj gs pe`gt# pelevvey gk` tmspmv`gt gvm kep

    spgpmlmkps+ _mkpmkoms dkqecqdki gk mzocglgpdek# g w}mspdek ev gk ev`mv gvm kep spgpmlmkps+ _mkpmkoms dkqecqdki rveke}ks s}oj gs jm ev sjm# }kcmss g rgvpdo}cgv rmvsek ds vmamvvm` pe#

    gvm kep spgpmlmkps+

    _mkpmkoms dkqecqdki rveke}ks aev qgvdgfcm rcgoms s}oj gs jmvm gk` pjmvm gvm kepspgpmlmkps+

    Pjm `mkdgc ea g spgpmlmkp ds ogccm` pjm kmigpdek ea pjm spgpmlmkp+ Dar ds g spgpmlmkp# pjmk pjm kmigpdek ear ds gcse g spgpmlmkp# gk` ds `mkepm` ft r# gk` ds

    vmg` gs kepr+

    Yjdcm yvdpdki pjm kmigpdek ea g spgpmlmkp# rjvgsms s}oj gs Dp ds kep pjm ogsm ev Dp dsagcsm pjgp gvm }sm`+

    Mzglrcm> Yvdpm pjm kmigpdek ea pjm aecceydki spgpmlmkp>

    r> Pjm sw}gvm veep ea mqmvt resdpdqm k}lfmv ds resdpdqm+

    _ec}pdek>

    Pjm kmigpdek ea pjm idqmk spgpmlmkp ogk fm yvdppmk gs>Pjm sw}gvm veep ea mqmvt resdpdqm k}lfmv ds kep resdpdqm+

    Ev

    Dp ds agcsm pjgp pjm sw}gvm veep ea mqmvt resdpdqm k}lfmv ds resdpdqm+Ev

    Dp ds kep pjm ogsm pjgp pjm sw}gvm veep ea mqmvt resdpdqm k}lfmv ds resdpdqm+

    EvPjmvm mzdsps g resdpdqm k}lfmv yjesm sw}gvm veep ds kep resdpdqm+

    G oelre}k` spgpmlmkp ds ekm pjgp ds lg`m }r ea pye ev levm spgpmlmkps+ Mgoj slgccmv spgpmlmkp ds ogccm` pjm oelrekmkp ea pjm oelre}k` spgpmlmkp+ Pjmsm oelrekmkps gvm nedkm` ft yev`s s}oj gs Gk` gk` Ev+ Pjmsm gvm ogccm`

    oekkmopevs ev oekkmopdki yev`s+

    Mzglrcm> Pjm spgpmlmkp 69 ds g l}cpdrcm ea 4 gk` dp ds mqmk ds g oelre}k` spgpmlmkp+

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

    Oelrdcm` Ft> ER I]RPG *41=2 ?=2 0:2$

  • 8/2/2019 Class_11_SA2

    17/23

    Dps oelrekmkp spgpmlmkps gvm>r> 69 ds g l}cpdrcm ea 4+w> 69 ds mqmk+

    Jmvm# pjm oekkmopdki yev` ds Gk`+

    G spgpmlmkp ydpj Gk` ds kep gcygts g oelre}k` spgpmlmkp+Mzglrcm> Ygpmv ogk fm rvmrgvm` ft pjm ldzp}vm ea jt`veimk gk` eztimk dk g omvpgdkvgpde+

    Pjds spgpmlmkp ds kep g oelre}k` spgpmlmkp+

    V}cms vmigv`dki pjm oekkmopev Gk` Pjm oelre}k` spgpmlmkp ydpj pjm oekkmopev Gk` ds pv}m da gcc dps oelrekmkp spgpmlmkps

    gvm pv}m+

    Pjm oelre}k` spgpmlmkp ydpj pjm oekkmopev Gk` ds agcsm da gkt%fepj ea dps oelrekmkpspgpmlmkps ds%gvm agcsm+

    V}cms vmigv`dki pjm oekkmopev Ev G oelre}k` spgpmlmkp ydpj pjm oekkmopev Ev ds pv}m yjmk ekm oelrekmkp spgpmlmkp ds

    pv}m# ev fepj pjm oelrekmkp spgpmlmkps gvm pv}m+

    G oelre}k` spgpmlmkp ydpj pjm oekkmopev Ev ds agcsm yjmk fepj pjm oelrekmkpspgpmlmkps gvm agcsm+

    Ptrms ea Ev Mzoc}sdqm Ev> G oelre}k` spgpmlmkp ydpj pjm oekkmopev Ev dk yjdoj mdpjmv ea pjm

    oelrekmkp spgpmlmkps lgt fm pv}m# f}p kep fepj

    Mzglrcm> G sp}`mkp ogk pghm jelm sodmkom ev rgdkpdki gs jds%jmv g``dpdekgc s}fnmop dk

    ocgss ZD+

    Dkoc}sdqm Ev>G oelre}k` spgpmlmkp ydpj pjm oekkmopev Ev dk yjdoj mdpjmv ea pjmoelrekmkp spgpmlmkps ev fepj lgt fm pv}m+Mzglrcm> Dk gk mw}dcgpmvgc pvdgkicm# gcc pjm pjvmm sd`ms gvm ea mw}gc cmkipj ev gcc pjm pjvmm

    gkicms gvm ea mw}gc lmgs}vm+

    _elm spgpmlmkps lgt oekpgdk srmodgc rjvgsms s}oj gs Pjmvm mzdsps# Aev gcc# Aev mqmvt+Pjmsm gvm ogccm` w}gkpdadmvs+

    Dlrcdogpdek spgpmlmkp da,pjmk> Pjm smkpmkom dar# pjmk w sgts pjgp dk pjm mqmkp dar ds pv}m#pjmk w l}sp fm pv}m+ Dp `ems kep sgt gktpjdki aev w yjmkr ds agcsm+

    G smkpmkom dar# pjmk w ogk fm yvdppmk dk pjm aecceydki ygts>*d$r dlrcdms w *`mkepm` ftrw$*dd$r ds g s}aadodmkp oek`dpdek aev w*ddd$r ekct daw

    *dq$w ds g kmomssgvt oek`dpdek aevr*q$w dlrcdms r

    Oekpvgresdpdqm gk` oekqmvsm ea g spgpmlmkp Pjm oekpvgresdpdqm ea pjm spgpmlmkprw ds pjm spgpmlmkp wr+

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

  • 8/2/2019 Class_11_SA2

    18/23

    Pjm oekqmvsm ea g spgpmlmkprw ds pjm spgpmlmkp wr+Mzglrcm> Yvdpm pjm oekqmvsm gk` pjm oekpvgresdpdqm ea pjm aecceydki spgpmlmkp>

    Da gk efnmop ds lg`m }r ea ekct cdkm smilmkps# pjmk dp ds g rectiek+

    _ec}pdek>

    Pjm oekqmvsm ea pjm idqmk spgpmlmkp ogk fm yvdppmk gs aecceys>Da gk efnmop ds g rectiek# pjmk dp ds lg`m }r ea ekct cdkm smilmkps+

    Pjm oekpvgresdpdqm ea pjm idqmk spgpmlmkp ogk fm yvdppmk gs aecceys>

    Da gk efnmop ds kep g rectiek# pjmk dp ds kep lg`m }r ea ekct cdkm smilmkps+

    Pjm mw}dqgcmkp aevls ea pjm spgpmlmkp r da gk` ekct daw *`mkepm` ftrw$ gvm gs aecceys> w da gk` ekct dar r da gk` ekct daw r ds g kmomssgvt gk` s}aadodmkp oek`dpdek aev w gk` qdom,qmvsg

    Qgcd`gpdki spgpmlmkps Dk ev`mv pe sjey pjgp pjm spgpmlmkp r gk` w ds pv}m# pjm aecceydki spmrs gvm aecceym`>

    7+ _jey pjgp spgpmlmkpr ds pv}m+6+ _jey pjgp spgpmlmkp w ds pv}m+

    Dk ev`mv pe sjey pjgp pjm spgpmlmkp r ev w ds pv}m# pjm aecceydki ogsms gvm pe fmoeksd`mvm`+7+ Gss}ldki pjgpr ds agcsm# sjey pjgp w l}sp fm pv}m+6+ Gss}ldki pjgp w ds agcsm# sjey pjgpr l}sp fm pv}m+

    Dk ev`mv pe rveqm pjm spgpmlmkp dar# pjmk w# ym kmm` pe sjey pjgp gkt ekm ea pjmaecceydki ogsms ds pv}m+

    7+ Gss}ldki pjgpr ds pv}m# rveqm pjgp w l}sp fm pv}m+ *@dvmop lmpje`$6+ Gss}ldki pjgp w ds agcsm# rveqm pjgpr l}sp fm agcsm+ *Oekpvgresdpdqm lmpje`$

    Dk ev`mv pe rveqm pjm spgpmlmkp r da gk` ekct daw# ym kmm` pe aeccey pjm aecceydki spmrs>7+ Dar ds pv}m# pjmk w ds pv}m+6+ Daw ds pv}m# pjmkr ds pv}m+

    Lmpje` ea oekpvg`dopdekPe ojmoh yjmpjmv g spgpmlmkpr ds pv}m# ym gss}lm pjgpr ds kep pv}m# d+m+# r ds pv}m# gk`pjmk ym gvvdqm gp selm vms}cp yjdoj oekpvg`dops e}v gss}lrpdek+ Pjmvmaevm# ym oekoc}`m

    pjgpr ds pv}m+Pjds lmpje` ea rveqdki g idqmk spgpmlmkp pe fm pv}m ds ogccm` pjm oekpvg`dopdek lmpje`+

    ]sdki g oe}kpmv mzglrcmDk ev`mv pe `dsrveqm g spgpmlmkp# ym idqm gk mzglrcm ea pjm sdp}gpdek yjmvm pjm spgpmlmkp

    ds kep qgcd`+ _}oj gk mzglrcm ds ogccm` g oe}kpmv mzglrcm+ Dk lgpjmlgpdos# oe}kpmv

    mzglrcms gvm }sm` aev `dsrveqdki g spgpmlmkp+ Jeymqmv# imkmvgpdki mzglrcms dk agqe}v eag spgpmlmkp `ems kep rveqd`m qgcd`dpt pe pjm spgpmlmkp+

    Mzglrcm> Pjm spgpmlmkp * 7$

    6* 7$ 7

    k k

    # k K ds pv}m aevk < 7# 6# f}p dp ds kep pv}m aev

    k < ?# 0+ Jmvm# k < ? gk` 0 gvm pjm oe}kpmv mzglrcms ea pjm idqmk spgpmlmkp+ _dkom pjm

    spgpmlmkp ds kep pv}m aev mgoj k K# pjm idqmk spgpmlmkp ds agcsm+

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

  • 8/2/2019 Class_11_SA2

    19/23

    Ojgrpmv 7=> _pgpdspdos

    Pjm lmgs}vms ea omkpvgc pmk`mkot# lmgk# lm`dgk gk` le`m idqm }s g ve}ij d`mg yjmvm `gpgredkps gvm omkpmvm`+

    Pjm `dsrmvsdek ev sogppmv dk g `gpg ds lmgs}vm` ek pjm fgsds ea efsmvqgpdeks gk` pjm ptrms ealmgs}vm ea omkpvgc pmk`mkot }sm`+ Pjm lmgs}vms ea `dsrmvsdek gvm gs aecceys>

    Vgkim W}gvpdcm `mqdgpdek Lmgk `mqdgpdek _pgk`gv` `mqdgpdek

    Vgkim ea g smvdms < Lgzdl}l qgc}mLdkdl}l qgc}m

    Lmgk `mqdgpdek gfe}p lmgkX L+@+ * $z \

    Aev }kive}rm` `gpg>7

    7L+@+* $

    k

    d

    d

    z z zk

    # yjmvm z ds pjm lmgk idqmk ft

    7

    7 k

    d

    d

    z zk

    Aev ive}rm` `gpg>7

    7L+@+ * $

    K

    k

    d d

    d

    z a z z

    # yjmvm z ds pjm lmgk idqmk ft

    7

    7

    K

    k

    d d

    d

    z a z

    gk`7

    Kk

    d

    d

    a

    Lmgk `mqdgpdek gfe}p lm`dgk XL+@+*L$\ Aev }kive}rm` `gpg>

    7

    7L+@+* $

    k

    d

    d

    L z L k

    # yjmvmLds pjm lm`dgk

    Aev ive}rm` `gpg>7

    7L+@+* $

    K

    k

    d d

    d

    L a z L

    # yjmvmLds pjm lm`dgk gk`7

    Kk

    d

    d

    a

    Pjm lmgk ea pjm sw}gvms ea pjm `mqdgpdeks avel lmgk ds ogccm` pjm qgvdgkom gk` dp ds `mkepm`ft

    6 +

    Qgvdgkom ea `gpg Aev }kive}rm` `gpg> 6 6

    7

    7* $

    k

    d

    d

    z zk

    *Dk `dvmop lmpje`$ ev 6 6 67

    7* $

    k

    d

    d

    z zk

    *Dk

    sjevpo}p lmpje`$# yjmvm z ds pjm lmgk+

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

    Oelrdcm` Ft> ER I]RPG *41=2 ?=2 0:2$

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    Aev `dsovmpm avmw}mkot `dspvdf}pdek> 6 67

    7* $

    K

    k

    d d

    d

    a z z

    *Dk `dvmop lmpje`$ ev6

    6 6

    67 7

    7K

    K

    k k

    d d d d

    d d

    a z a z

    *Dk sjevpo}p lmpje`$# yjmvm z ds pjm lmgk

    gk`7

    Kk

    d

    d

    a

    +

    Aev oekpdk}e}s avmw}mkot `dspvdf}pdek> 6 67

    7* $

    K

    k

    d d

    d

    a z z

    ev6

    6 6

    67 7

    7K

    K

    k k

    d d d d

    d d

    a z a z

    *Dk `dvmop lmpje`$ ev

    666 6

    67 7

    KK

    k k

    d d d d

    d d

    j a t a t

    *Dk sjevpo}p lmpje`$# yjmvm

    zd _pgk`gv` @mqdgpdek Qgvdgkom

    Oemaadodmkp ea qgvdgpdekPjm lmgs}vm ea qgvdgfdcdpt# yjdoj ds dk`mrmk`mkp ea }kdps# ds ogccm` pjm oemaadodmkp ea

    qgvdgpdek+ Pjm oemaadodmkp ea qgvdgpdek *O+Q+$ ds `madkm` gs

    O+Q+ 722# 2zz

    Yjmvm# gk` z gvm spgk`gv` `mqdgpdek gk` lmgk ea pjm `gpg vmsrmopdqmct+

    Aev oelrgvdki pjm qgvdgfdcdpt ev `dsrmvsdek ea pye smvdms# ym advsp ogco}cgpm pjm O+Qs eamgoj smvdms+ Pjm smvdms jgqdki jdijmv O+Q+ ds sgd` pe fm levm qgvdgfcm pjgk pjm epjmv gk`pjm smvdms jgqdki ceymv O+Q+ ds sgd` pe fm levm oeksdspmkp pjgk pjm epjmv+

    Aev pye smvdms ydpj mw}gc lmgk qgc}ms# pjm smvdms ydpj ivmgpmv spgk`gv` `mqdgpdek *evqgvdgkom$ ds levm qgvdgfcm ev `dsrmvsm` pjgk pjm epjmv+ Gcse# pjm smvdms ydpj ceymv qgc}m ea

    spgk`gv` `mqdgpdek *ev qgvdgkom$ ds sgd` pe fm levm oeksdspmkp ev cmss sogppmvm` pjgk pjmepjmv+

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

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    Ojgrpmv 71> Rvefgfdcdpt

    Gk mzrmvdlmkp ds ogccm` g vgk`el mzrmvdlmkp da dp sgpdsadms pjm aecceydki pye oek`dpdeks> Dp jgs levm pjgk ekm ressdfcm e}poelm Dp ds kep ressdfcm pe rvm`dop pjm e}poelm dk g`qgkom

    G ressdfcm vms}cp ea g vgk`el mzrmvdlmkp ds ogccm` dps e}poelm+ Pjm smp ea gcc ressdfcm e}poelms ea g vgk`el mzrmvdlmkp ds ogccm` pjm sglrcm srgom

    gsseodgpm` ydpj pjm mzrmvdlmkp+ Dp ds `mkepm` ft _+Mgoj mcmlmkp ea pjm sglrcm srgom d+m+# mgoj e}poelm ea pjm vgk`el mzrmvdlmkp ds ogccm` pjm

    sglrcm redkp+

    Gkt s}fsmp *M$ ea g sglrcm srgom ds ogccm` gk mqmkp+ Pjm mqmkp *M$ ea g sglrcm srgom *_$ ds sgd` pe jgqm eoo}vvm` da pjm e}poelm *$ ea pjm

    mzrmvdlmkp ds s}oj pjgp M+

    Da pjm e}poelm *$ ds s}oj pjgp M# ym sgt pjgp pjm mqmkp *M$ jgs kep eoo}vvm`+ Ptrms ea mqmkps

    Dlressdfcm mqmkp> Gk mlrpt smp *$ ds ogccm` gk dlressdfcm mqmkp+ _}vm mqmkp> Pjm yjecm sglrcm srgom *_$ ds ogccm` g s}vm mqmkp+ _dlrcm mqmkp> Da gk mqmkp *M$ jgs ekct ekm sglrcm redkp ea g sglrcm srgom# pjmk dp ds

    ogccm` g sdlrcm *ev mcmlmkpgvt$ mqmkp+

    Dk g sglrcm srgom oekpgdkdki k `dspdkop mcmlmkps# pjmvm gvm mzgopct k sdlrcm mqmkps+

    Oelre}k` mqmkp> Da gk mqmkp jgs levm pjgk ekm sglrcm redkp# dp ds ogccm` g oelre}k`mqmkp+

    Mzglrcm> Oeksd`mv gk mzrmvdlmkp ea smcmopdki k}lfmvs avel advsp =2 kgp}vgc k}lfmvs# pjmkpjm sglrcm srgom *_$ ds idqmk gs

    _ < x7# 6# ?# 0# 04# =2|

    Dk pjds ogsm#

    *d$ Pjm mqmkp Imppdki g k}lfmv pjgp ds g l}cpdrcm ea fepj 9 gk` 4 ds gk dlressdfcm mqmkp gspjmvm ds ke e}poelm vmcgpm` pe dp+

    *dd$Pjm mqmkp Imppdki g rmvamop sw}gvm pjgp ds levm pjgk 02 ds g sdlrcm mqmkp sdkomM Aev mqmvt mqmkpG# pjmvm oevvmsrek`s gkepjmv mqmkpG ogccm` pjm

    oelrcmlmkpgvt mqmkp peG+ Dp ds gcse ogccm` pjm mqmkp kepG+

    G < x> _ gk` G| < _G+

    Mqmkp G evF> Yjmk smpsG gk`F gvm pye mqmkps gsseodgpm` ydpj g sglrcm srgom# pjmkpjm smpGFds pjm mqmkp mdpjmvG evFev fepj+

    Pjgp ds# mqmkp G evF G ev F|

    ER I]RPG *41=2 ?=2 0:2$

    ER I]RPG *41=2 ?=2 0:2$

    Oelrdcm` Ft> ER I]RPG *41=2 ?=2 0:2$

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    Mqmkp G gk`F> Yjmk smpsG gk`F gvm pye mqmkps gsseodgpm` ydpj g sglrcm srgom# pjmkpjm smpGFds pjm mqmkp G gk`F+

    Pjgp ds# mqmkp G gk`F G gk` F|

    Mqmkp G f}p kepF> Yjmk smpsG gk`F gvm pye mqmkps gsseodgpm` ydpj g sglrcm srgom#pjmk pjm smpGFds pjm mqmkp G f}p kepF+

    Pjgp ds# mqmkp G f}p kepF Oeksd`mv pjm mzrmvdlmkp ea pessdki 6 oedks+ CmpGfm pjm mqmkp imppdki gp cmgsp ekm jmg` gk`Ffm pjm mqmkp imppdki mzgopct pye jmg`s+ Adk` pjm smps vmrvmsmkpdki pjm mqmkps

    *d$ oelrcmlmkp ea G evF*dd$G gk`F*ddd$G f}p kepF

    _ec}pdek>

    Jmvm# _ < xJJ# JP# PJ# PP|G < xJJ# JP# PJ|#F < xJJ|

    *d$G evF

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    * $R* $

    * $

    k GG

    k _ #

    Yjmvm# k*G$ < K}lfmv ea mcmlmkps dk smpG gk` k*_$ < K}lfmv ea mcmlmkps dk smp _

    DaG gk`F gvm pye mqmkps# pjmkR *GF$ < R *G$ ( R *F$R *G F$

    DaG gk`F gvm l}p}gcct mzoc}sdqm mqmkps# pjmkR *GF$ < R *G$ ( R *F$

    DaG ds gkt mqmkp# pjmkR *G$ < 7 R *G$

    ER I]RPG *41=2 ?=2 0:2$

    P jds `eo}lmkp jgs fmmk rvmrgv m ft ER I}rp g+ J m ds w}gc d a d m gs M cmopv ekdos ! O ell}kdogp deks

    mkidkmmv+ J m jgs yvd p pmk lgkt sp}`t, kepms# w}mspd ek, feehc mps gk` lgkt }sma}c sp}a a s aev p jm i}d`gkomea sp}`mkps dk L gpjmlgpd os+ J ds yevhs ek L gpjmlgpd os ogk fm ae}k` ek yyy+ sov df`+ oel% pjmeri}rpg+

    F mdki g p jdkhmv # jm jgs rmkkm `eyk lgkt gv p d ocms yjdoj jgs fmmk fmkmamodgc aev lgkt ea jds sp}`mkps#

    qdsd p jd s fcei aev p jmsm gv pd ocms> yyy+ pjmeri}rp g+ fceisrep+ oel+

    O ekpgop ke+ , 41=2 ? =2 0:2# m, d`> pjmeri}rpgB ilgdc+ oel