गणित कक्षा २

;~rf/ k|ljlw / ahf/ *

kf7 !$ lrquf| km / tflnsf

tflnsfaf6 hfgsf/L

5nkmn ug'{xf];\ M

k"0f{sf] k;naf6 Ps xKtfdf laj|mL ePsf ;fdu|Lx¿sf] ljj/0f tnsf]

tflnsfdf lbOPsf] 5 M

laj|mL ePsf ;fdu|Lx¿

;fduL| l;;fsnd O/]h/ sfkL ?n/

;ª\Vof $) #% !%) @%

!= sltcf]6f l;;fsnd laj|mL ePsf /x]5g\ <

@= sltcf]6f sfkL laj|mL ePsf /x]5g\ <

#= sg' ;fduL| ;a}eGbf a9L lajm| L ePsf] /x]5 <

$= O/]h/ / l;;fsnddWo] sg' a9L lajm| L ePsf] /x]5 <

1fg' aS' ; PG8 :6];g/L, ;fgfl] 7dLaf6 jz} fv Ps ut]sf
lbg laj|mL ePsf kf7o\ k':tssf] ljj/0f tnsf] tflnsfdf
lbOPsf] 5 M

laj|mL ePsf kf7\ok':tssf] ljj/0f sIff $
sIff sIff ! sIff @ sIff # %)
kf7\ok:' ts ;]6 #) @% $)

dflysf] tflnsf cjnf]sg u/L tnsf kZ| gx¿sf] pQ/ lbg'xf];\ M

!= sIff ! df slt ;]6 kf7\ok:' ts lajm| L ePsf /x]5g\ <
@= sg' sIffsf kf7\ok':ts ;a}eGbf a9L laj|mL ePsf /x]5g\ <
#= sg' sIffsf kf7\ok':ts ;a}eGbf sd laj|mL ePsf /x]5g\ <
$= sIff # sf] kf7\ok:' ts sIff $ sf] kf7\ok:' tseGbf

slt sd jf a9L laj|mL ePsf /x]5g\ <

d/] f] ul0ft, sIff @ 195

tflnsfaf6 hfgsf/L

kmn" dfofn] tLg lbgdf lajm| L u/s] f kmnkm"nx¿sf] kl/df0f
tnsf] tflnsfdf lbOPsf] 5 M

kmn" dfofn] tLg lbgdf lajm| L u/]sf kmnkmn" sf] kl/df0f lsnf]uf| ddf

lbg kmnkm"n :ofp ;G' tnf df};d cgf/

klxnf] % !) % ^

bf];f| ] & * $ (

t];f| ] * !@ # !)

hDdf @) #) !@ @%

dflysf] tflnsf cjnf]sg u/L tnsf kZ| gx¿sf] pQ/ lbgx' f];\ M

!= km"ndfofn] klxnf] lbg slt lsnf]u|fd ;G' tnf laj|mL ul/5g\ <

@= km"ndfofn] tLg lbgdf hDdf slt lsnf]u|fd df};d laj|mL ul/5g\ <

%= bf];|f] lbgdf ;a}eGbf a9L laj|mL ePsf] kmnkm"n sg' xf] <

xl/n] sIff !, @ / # sf ljBfyL{x¿nfO{ ;ae} Gbf dg kg{]
v]nsf] ljj/0f tof/ kf/L sfkLdf nV] g'eof] . cfkm\gf] 8:] sdf
/fvs] f] pSt sfkLdf kfgL kfl] vP/ tn lbOPcg';f/ efu
d]l6P5 .

v]ns'b sIff ! sIff @ sIff # hDdf
& !!
Aof8ldG6g $ # !$
!*
lj|ms]6 @ %

km6' an ^

hDdf !%

d]l6Psf] efudf /x]sf] ;ª\Vof eg'{xf];\ .

196 d]/f] ul0ft, sIff @

hgfj/x¿sf] ;ª\Vof lrqu|fkmaf6 kf| Kt hfgsf/L tflnsfdf k|:t't ugx{' f];\ M
;l' :dtfsf 3/df ePsf hgfj/x¿sf] ljj/0fnfO{ tnsf] lrquf| kmdf
lbOPsf] 5 M
;'l:dtfsf 3/df ePsf hgfj/x¿

*
&
^
%
$
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ss' '/ s'v'/f xfF; e]8f ufO{

dflysf] lrqu|fkm cjnf]sg u/L kf| Kt hfgsf/LnfO{ tnsf] tflnsfdf
k:| t't ug'{xf];\ M

;'l:dtfsf 3/df ePsf hgfj/x¿
hgfj/ ss' /' sv' '/f xfF; e]8f ufO{
;ª\Vof

d]/f] ul0ft, sIff @ 197

ljBfyL{ ;ª\Vof sIff @ sf ljBfyLx{ ¿nfO{ kfgL, h';, skmL, bw' / lrofdWo]

sg' ko] kbfy{ dg k5{ egL kZ| g ;fl] wPsf] lyof] . pSt k|Zgdf
kf| Kt hjfkmnfO{ ;ª\st] sf] k|of]u u/L tnsf] lrqu|fkmdf k|:tt'
ul/Psf] 5 M

kfgL h'; skmL b'w lrof
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#
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dflysf] lrquf| kmaf6 kfgL, h';, skmL, b'w / lrof dg k/fpg] ljBfyL{
;ª\VofnfO{ tflnsf agfO{ k:| t't ug'{xf];\ M

198 d]/f] ul0ft, sIff @

sIff @ sf ljBfyLx{ ¿nfO{ sg' ljifo dg k5{ egL ;f]lwPsf]

k|Zgdf kf| Kt hjfkmcg;' f/ ;ªs\ ]tsf] k|ofu] u/L tnsf]
lrqu|fkmdf k:| tt' ul/Psf] 5 M

ljBfyL{ ;ª\Vof ^
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$ cª\u|]hL ul0ft xfdf| ] ;]/f]km]/f]
#
@
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dflysf] lrqu|fkmaf6 g]kfnL, cª\u]|hL, ul0ft / xfd|f] ;]/f]km]/f]
dg k/fpg] ljBfyL{ ;ª\VofnfO{ tflnsf agfO{ k|:tt' \ ug{'xf];\ .

d]/f] ul0ft, sIff @ 199

kf7 !% db' f|

gf6] x¿ cjnf]sg u/L nV] gx' f;] \ M
gf]6x¿ k|Zgx¿
-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ o; gf]6df s'g hgfj/sf] lrq 5 <
-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ o; gf]6df s'g hgfj/sf] lrq 5 <
-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ o; gf]6df s'g hgfj/sf] lrq 5 <
-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ of] gf]6df s'g hgfj/sf] lrq 5 <
-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ o; gf]6df sg' hgfj/sf] lrq 5 <

200 d]/f] ul0ft, sIff @

gf]6x¿ kZ| gx¿
-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ o; gf]6df sg' hgfj/sf] lrq 5 <

-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ o; gf]6df s'g hgfj/sf] lrq 5 <

-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ o; gf]6df s'g hgfj/sf] lrq 5 <

-s_ of] slt ?lkofFsf] gf]6 xf] <
-v_ o; gf]6df sg' hgfj/sf] lrq 5 <

tn lbOPsf l;Ssfx¿ xg] x'{ f];\ / slt ?lkofF xf] lrg/] n]Vgx' f];\ M

?= !

d/] f] ul0ft, sIff @ 201

tn lbOPsf gf]6x¿sf lrqx¿ x]g{'xf;] \ / slt ?lkofFsf] xf]
lrg]/ nV] g'xf];\ M

?= %



tn lbOPsf l;Ssfsf lrqx¿ xg] x{' f;] \ / slt k;} fsf] xf]
lrg]/ n]Vg'xf;] \ .

k}= !

?= !))) ;Ddsf gf]6x¿ cjnf]sg u/L vfnL 7fpF egx{' f;] \ M

;a}eGbf yf]/} ?lkofF hgfpg] gf]6 ?= sf] xf] .

;a}eGbf w]/} ?lkofF hgfpg] gf]6 ?= sf] xf] .

af3sf] lrq ePsf] gf]6 ?= sf] xf] .

xfQLsf] lrq ePsf] gf]6n] ?= hgfpF5 .

202 d/] f] ul0ft, sIff @

hf8] ug{x' f;] \ M

?= % ?= % ?= @) ?= !)

?= !) ?= #)

?= % ± ?= % ≠ ?= !) ?= @) ± ?= !) ≠ ?= #)

/fdn] ?= !) sf] Pp6f l;;fsnd / ?= %) sf] Pp6f sfkL
lsg5] g\ eg] k;nn] fO{ hDdf slt ?lkofF ltgk{' nf{ <

?= !) ?= %) ?= !) ± ?= %)
?= ^) ≠ ?= ^)

k;n]nfO{ lt/]sf] hDdf
?lkofF ≠ ?= ^)

d/] f] ul0ft, sIff @ 203

db' |f;DaGwL hf8]

k]Dafn] ?= #) sf] sfkL, ?= @) sf] l;;fsnd / ?= !) sf]

O/]h/ lsg5] g\ . ca, pgn] k;nn] fO{ slt ?lkofF ltgk'{ 5{ .

?= #) ± ?= @) ± ?= !) ≠ ?= ^)

?= #) ?= #) ?= @) ?= !)
?= @) ?= ^)
± ?= !)
?= ^)

vfnL 7fpF eg{'xf;] \ M

?= % ± ?= !) ≠ ?= !% ?= @) ± ?= #) ≠ ?=
?= #) ± ?= ≠ ?= %) ?= ± ?= @) ≠ ?= #)
hf8] ug{'xf;] \ M

?= # ?= @% @) k};f $) k};f
± ?= !) ?= !% ± !) k};f ± @% k};f
± ?= !)

/Ltfn] pgsf ;fyLsf] hGdlbgdf pkxf/
lbgsf nflu ?= $) sf] snd / ?= %)
sf] sfkL lslgg\ eg] pgn] hDdf slt
?lkofsF f] pkxf/ lslg5g\ .

204 d/] f] ul0ft, sIff @

db' f| ;DaGwL 36fp

zflGt;Fu ?= @) lyof] . zflGtn] ?= !) sf] Pp6f
rsn6] lslgg\ . pgn] k;n]nfO{ ?= @) sf] gf6]
lbOg\ eg] slt ?lkofF lkmtf{ kfplng\ <

?= @) — ?= !) ≠ ?= !) ?= @)

zflGt;Fu hDdf ?= !) ?= !)
?= !) afFsL /xG5 .

vfnL 7fpF eg{x' f];\ M
?= !@) – ?= !@ ≠ ?= $% – ?= #% ≠
?= () – ?= ≠ ?= !) ?= &% – ≠ ?= &)
@% k};f – !) k};f ≠ k;} f %) k;} f – @% k};f ≠ k};f
?= – ?= #)) ≠ ?= $)) ?= – ?= @%) ≠ ?= #))

tkfO‘{;uF ?= !) sf $ cf]6f gf6] x¿, ?= % sf % cf6] f gf]6x¿
/ ?= ! sf ^ cf6] f gf]6x¿ 5g\ . olb tkfO{n‘ ] hDdf ?= $% sf

:6;] g/L ;fdfg lsGg'eof] eg] slt sltsf] gf6] ldnfP/ s'g sg'
tl/sfn] :6];g/Lsf] lan ltg{ ;Sgx' G' 5 <

d]/f] ul0ft, sIff @ 205

d'b|f;DaGwL 36fp

Ozfg;uF ?= () lyof] . pgn] o;af6 ?= @) df bO' {cf6] f

l;;fsnd lsg] . ca Ozfg;Fu slt ?lkofF afsF L /xG5 <

?= () ?=@)

— ?= @) Ozfg;Fu ? &)
?= &) afFsL 5 .

k|efn] ?= #% lnP/ ahf/ uOg\ . Pp6f dg' f
klqsf lsGbf ?= @) vr{ ul/g\ . ca ke| f;uF

slt ?lkofF afsF L /xG5 <

?= #% ke| f;Fu ?= ?= #%
— ?= @) afFsL 5 . ?= @) <

lx;fa ugx{' f;] \ M ?= $% ?= &%
?= #) — ? =@@ — ?= #%

— ?= !)

206 d]/f] ul0ft, sIff @

36fpgx' f;] \ M

?= !) ?= !% ?= @) ?= (%
— ?= # — ?= % — ?= ^%
— ?= &
?= #

?= &% ?= #) %) k};f &% k};f
— ?= @% — ?= @)
— !% k};f — @% k};f

!$) k};f %) k};f &% k};f () k};f
— %) k};f — !) k};f — $) k};f — #% k};f

lji0f'n] ?= $) sf] Pp6f sfkL lsg] . pgn] ?= !)) sf] gf]6
k;n]nfO{ lbP eg] k;nn] ] slt ?lkofF lkmtf{ lbgk' nf{ <

d]/f] ul0ft, sIff @ 207

d'bf| sf] hf]8 tyf 36fp;DaGwL s'g} b'O{ bO' {cf6] f ul0ftLo
;d:of nv] L ;dfwfg ug{x' f;] \ .

208 d]/f] ul0ft, sIff @

;~rf/ kl| jlw / ahf/

x/] f,‘} d}n] slt l;sF] <

!= tn lbOPsf gf6] x¿sf] lrq x]g'x{ f;] \ / slt ?lkofFsf] xf] lrg/]
n]Vgx' f];\ M

?= ?= ?=
@= hf8] g\ x' f;] \ M

?= % ± ?= @) ≠ ?= ?= %) ± ?= !) ≠ ?=

?= ± ?= ?= ± ?=
≠ ?= ≠ ?=

#= 36fpg'xf;] \ M

?= !)) ?= %%) %) k;} f () k};f
— ?= %) — ?= #@) — !) k};f — ^% k};f

d/] f] ul0ft, sIff @ 220099



$= sIff @ sf ljBfyLx{ ¿nfO{ km6' an, lj|ms6] , Sof/daf8] {, r];,

n'8F fd] Wo] s'g s'g vn] dgk5{ egL kZ| g ;f]lwPsf] lyof] . pSt
k|Zgsf] hjfkmnfO{ tnsf] lrquf| kmdf k:| tt' ul/Psf] 5 M

%

ljBfyL{ ;ª\Vof $

#

@

!
)
km6' an ljm| s]6 Sof/daf]8{ r]; n'F8f]

dflysf lrqu|fkm x]g{'xf];\ / kT| o]s v]n v]Ng dg k/fpg] ljBfyL{ ;ª\Vof
slt slt /x]5, n]Vgx' f];\ M

km'6an M Sof/daf]8{ M n'F8f] M

ljm| s]6 M r]; M

cleefjssf] b:tvt
lzIfssf] b:tvt

22110 d/] f] ul0ft, sIff @

ul0ftsf cfwf/e"t ljm| of @ (
kf7 !^ u0' fg @

v/fofs] f sfg uGgx' f;] \ M

@ Ps k6s ≠ @ @±@ ≠
@×! ≠ @ b'O{ k6s ≠

@×@ ≠

@±@±@ ≠ @±@±@±@ ≠

@ tLg k6s ≠ @ rf/ k6s ≠

@×# ≠ @×$ ≠

@±@±@±@±@ ≠

@ kfFr k6s ≠

@×% ≠

@±@±@±@±@±@ ≠
@ 5 k6s ≠
@×^ ≠

d/] f] ul0ft, sIff @ 211

v/fofs] f sfg uGgx' f;] \ M @×! ≠ @
@×@ ≠ $
@ ± @ ± @ ± @ ± @ ± @ ± @ ≠ @×# ≠
@×$ ≠
@ ;ft k6s ≠ @×% ≠
@×^ ≠
@×& ≠ @×& ≠
@×* ≠
@±@±@±@±@±@±@±@≠ @×( ≠
@ × !) ≠

@ cf7 k6s ≠

@×* ≠

@ ± @ ± @ ± @ ± @ ± @ ± @ ± @ ± @ ≠

@ gf} k6s ≠

@×( ≠

@ ± @ ± @ ± @ ± @ ± @ ± @ ± @ ± @ ± @ ≠
@ bz k6s ≠
@ × !) ≠

212 d/] f] ul0ft, sIff @

km" nsf y'uF f uGg'xf];\ M # ± # ≠ ^
# Ps k6s ≠ #
# × ! ≠ # # b'O{ k6s ≠ ^
# × @ ≠ ^

# ± # ± # ≠ ( # ± # ± # ± # ≠ !@
# tLg k6s ≠ ( # rf/ k6s ≠
# × # ≠ ( # × $ ≠

# ± # ± # ± # ± # ≠ !%
# kfFr k6s ≠
# × % ≠

# ± # ± # ± # ± # ± # ≠ !*
# 5 k6s ≠
#×^ ≠

d]/f] ul0ft, sIff @ 213

k"mnsf y'uF f uGg'xf];\ M #×! ≠ #
#×@ ≠ ^
# ± # ± # ± # ± # ± # ± # ≠ @! #×# ≠ (
# ;ft k6s ≠ #×$ ≠
# × & ≠ #×% ≠
#×^ ≠
# ± # ± # ± # ± # ± # ± # ± # ≠ @$ #×& ≠
# cf7 k6s ≠ #×* ≠
# × * ≠ #×( ≠
# × !) ≠

# ± # ± # ± # ± # ± # ± # ± # ± # ≠ @&
# gf} k6s ≠
# × ( ≠

# ± # ± # ± # ± # ± # ± # ± # ± # ± # ≠ #)
# bz k6s ≠
# × !) ≠

214 d]/f] ul0ft, sIff @

s';Ls{ f v6' \6f uGg'xf];\ M $±$ ≠
$ Ps k6s ≠ $
$×!≠ $ b'O{ k6s ≠

$ × @ ≠

$ ± $ ± $ ≠ !@ $ ± $ ± $ ± $ ≠
$ tLg k6s ≠ !@
$ × # ≠ !@ $ rf/ k6s ≠

$ × $ ≠

$±$±$±$±$≠ $ kfFr k6s ≠
$×%≠

$±$±$±$±$±$≠ $ 5 k6s ≠
$×^≠

d]/f] ul0ft, sIff @ 215

s';Ls{ f v6' \6f uGg'xf;] \ M $×! ≠
$×@ ≠
$±$±$±$±$±$±$≠ $×# ≠
$×$ ≠
$ ;ft k6s ≠ $×&≠ $×% ≠
$×^ ≠
$ ± $ ± $ ± $ ± $ ± $ ± $ ± $ ≠ $×& ≠
$ cf7 k6s ≠ $ × * ≠ $×* ≠
$×( ≠
$ × !) ≠

$ ± $ ± $ ± $ ± $ ± $ ± $ ± $ ± $ ≠

$ gf} k6s ≠ $×(≠

$±$±$±$±$±$±$±$±$±$≠

$ bz k6s ≠ $ × !) ≠

216 d/] f] ul0ft, sIff @

xftsf cf}‘nf uGgx' f];\ M % ± % ≠ !)
% b'O{ k6s ≠
% Ps k6s ≠ %×@ ≠
%×! ≠ %

%±%±% ≠ % ± % ± % ± % ≠

% tLg k6s ≠ % rf/ k6s ≠
%×# ≠
%×$ ≠

%±%±%±%±%≠ % kfFr k6s ≠
%×%≠

%±%±%±%±%±%≠ % 5 k6s ≠
%×^≠
d]/f] ul0ft, sIff @ 217

xftsf cf}n‘ f uGgx' f];\ M %×! ≠ %

% ± % ± % ± % ± % ± % ± % ≠ % × @ ≠ !)
% ;ft k6s ≠
%×& ≠ %×# ≠
%×$ ≠
%±%±%±%±%±%±%±%≠
% cf7 k6s ≠ %×% ≠
%×* ≠
%×^ ≠

%×& ≠

%×* ≠

%×( ≠

% × !) ≠

%±%±%±%±%±%±%±%±%≠
% gf} k6s ≠
%×( ≠

%±%±%±%±%±%±%±%±%±%≠
% bz k6s ≠
% × !) ≠

218 d/] f] ul0ft, sIff @

cfs[ltsf s'gf uGgx' f;] \ M

^ Ps k6s ≠ ^ ± ^ ≠
^ × ! ≠
^ bO' { k6s ≠
^×@ ≠

^ ± ^ ± ^ ≠ ^ tLg k6s ≠
^ × # ≠

^±^±^±^≠ ^ rf/ k6s ≠
^×$≠

^±^±^±^±^≠ ^ kfFr k6s ≠
^×%≠

^±^±^±^±^±^≠ ^ 5 k6s ≠
^×^≠
d/] f] ul0ft, sIff @ 219

cfs[ltsf s'gf uGg'xf;] \ M ^×! ≠ ^
^ × @ ≠ !@
^±^±^±^±^±^±^≠ ^×# ≠
^×$ ≠
^ ;ft k6s ≠ ^×% ≠
^×^ ≠
^ × & ≠ ^×& ≠
^×* ≠
^ ± ^ ± ^ ± ^ ± ^ ± ^ ± ^ ± ^ ≠ ^×( ≠
^ × !) ≠
^ cf7 k6s ≠

^ × * ≠

^ ± ^ ± ^ ± ^ ± ^ ± ^ ± ^ ± ^ ± ^ ≠
^ gf} k6s ≠
^×( ≠

^±^±^±^±^±^±^±^±^±^≠
^ bz k6s ≠
^ × !) ≠

220 d/] f] ul0ft, sIff @

tf;sf kQLdf ePsf cfsl[ t uGgx' f;] \ M

& Ps k6s ≠ & ± & ≠
&×!≠& & bO' { k6s ≠
& × @ ≠

& ± & ± & ≠ @!

& tLg k6s ≠ & × # ≠

& ± & ± & ± & ≠ & rf/ k6s ≠
&×$≠

&±&±&±&±&≠ & kfFr k6s ≠
&×%≠

&±&±&±&±&±&≠ & 5 k6s ≠
&×^≠
d]/f] ul0ft, sIff @ 221

tf;sf kQLdf ePsf cfsl[ t uGg'xf;] \ M &×! ≠
&×@ ≠
&±&±&±&±&±&±&≠ &×# ≠
& ;ft k6s ≠ &×$ ≠
&×& ≠ &×% ≠
&×^ ≠
&±&±&±&±&±&±&±&≠ &×& ≠
& cf7 k6s ≠ &×* ≠
&×* ≠ &×( ≠
& × !) ≠

&±&±&±&±&±&±&±&±&≠

& gf} k6s ≠ &×(≠

&±&±&±&±&±&±&±&±&±&≠
& bz k6s ≠ & × !) ≠

222 d/] f] ul0ft, sIff @

dfnfsf u]8L uGgx' f];\ M

* Ps k6s ≠ *±* ≠
*×! ≠ * bO' { k6s ≠
*×@ ≠

* ± * ± * ≠ @$ *±*±*±*≠
* tLg k6s ≠ * rf/ k6s ≠
* × # ≠ * × $ ≠

*±*±*±*±*≠

* kfFr k6s ≠ * × % ≠

*±*±*±*±*±*≠

* 5 k6s ≠ *×^≠

*±*±*±*±*±*±*≠
*×&≠
* ;ft k6s ≠

d]/f] ul0ft, sIff @ 223

dfnfsf u]8L uGg'xf;] \ M *×! ≠ *

*±*±*±*±*±*±*±*≠ * × @ ≠ !^
* cf7 k6s ≠
*×*≠ * × # ≠ @$

*×$ ≠
*×% ≠

*×^ ≠

*×& ≠

*×* ≠

*×( ≠

* × !) ≠

*±*±*±*±*±*±*±*±*≠
* gf} k6s ≠
*×(≠

*±*±*±*±*±*±*±*±*±*≠
* bz k6s ≠
* × !) ≠

224 d/] f] ul0ft, sIff @

dfnfdf ePsf ?b|fIfsf bfgf uGg'xf;] \ M

( Ps k6s ≠ ( ( ± ( ≠ !*
( × ! ≠ ( ( bO' { k6s ≠ !*
( × @ ≠ !*

( ± ( ± ( ≠ ( ± ( ± ( ± ( ≠
( tLg k6s ≠
(×# ≠ ( rf/ k6s ≠

(×$ ≠

(±(±(±(±(≠ ( kfFr k6s ≠
(×%≠

( ± ( ± ( ± ( ± ( ± ( ≠

( 5 k6s ≠ ( × ^ ≠

(±(±(±(±(±(±(≠

( ;ft k6s ≠ ( × & ≠

d]/f] ul0ft, sIff @ 225

dfnfdf ePsf ?b|fIfsf bfgf uGg'xf;] \ M (×! ≠ (
( × @ ≠ !*
(±(±(±(±(±(±(±(≠ (×# ≠
( cf7 k6s ≠ (×$ ≠
(×*≠ (×% ≠
(×^ ≠
(×& ≠
(×* ≠
(×( ≠
( × !) ≠

(±(±(±(±(±(±(±(±(≠
( gf} k6s ≠
(×(≠

(±(±(±(±(±(±(±(±(±(≠
( bz k6s ≠
( × !) ≠

226 d/] f] ul0ft, sIff @

6]lg; anx¿ uGgx' f;] \ M

!) Ps k6s ≠ !) ± !) ≠ @)
!) × ! ≠ !) !) bO' { k6s ≠
!) × @ ≠ @)

!) ± !) ± !) ≠ #)

!) tLg k6s ≠ !) × # ≠ #)

!) ± !) ± !) ± !) ≠

!) rf/ k6s ≠ !) × $ ≠

!) ± !) ± !) ± !) ± !) ≠

!) kfFr k6s ≠ !) × % ≠

!) ± !) ± !) ± !) ± !) ± !) ≠

!) 5 k6s ≠ !) × ^ ≠

d/] f] ul0ft, sIff @ 227

6l] g; anx¿ uGgx' f];\ M !) × ! ≠ !)
!) × @ ≠ @)
!) ± !) ± !) ± !) ± !) ± !) ± !) ≠ !) × # ≠
!) × $ ≠
!) ;ft k6s ≠ !) × & ≠ !) × % ≠
!) × ^ ≠
!) ± !) ± !) ± !) ± !) ± !) ± !) × & ≠
!) ± !) ≠ !) × * ≠
!) × ( ≠
!) × !) ≠

!) cf7 k6s ≠ !) × * ≠

!) ± !) ± !) ± !) ± !) ± !) ± !) ± !) ± !) ≠

!) gf} k6s ≠ !) × ( ≠

!) ± !) ± !) ± !) ± !) ± !) ± !) ± !) ±
!) ± !) ≠

!) bz k6s ≠ !) × !) ≠

228 d/] f] ul0ft, sIff @

u0' fg tflnsf k/" f ug'{xf;] \ / k9\g'xf];\ M
× ! @ # $ % ^ & * ( !)
! ! @ #$
@@$^
##^
$$
%
^
&
*
(
!)

d/] f] ul0ft, sIff @ 229

u0' fg ug'{xf];\ M

@×#≠ $ × % ≠ #×^≠
%×&≠ %×#≠ ^×@≠
&×#≠ *×(≠ !) × %≠
$×&≠ #×*≠ (×^≠

;ªV\ of /]vfdf km8\s] u0fgf ugx{' f;] \ M
@ ×&

) @ $ ^ * !) !@ !$ !^ !* @) !$

# ×^
) # ^ ( !@ !% !* @! @$ @& #) ## #^
^ ×(
) ^ !@ !* @$ #) #^ $@ $* %$ ^) ^^ &@
* ×%
) * !^ @$ #@ $) $* %^ ^$ &@ *) ** (^
& ×^

) & !$ @! @* #% $@ $( %^ ^# &) && *$
( ×*
) ( !* @& #^ $% %$ ^# &@ *! () (( !)*

230 d]/f] ul0ft, sIff @

tn lbOPsf] ul0ftLo jfSonfO{ ;ªV\ of/]vfdf bv] fpgx' f];\ M
# ×%

$ ×*

^ ×^

& ×%
( ×$

d]/f] ul0ft, sIff @ 231

u0fgf u/L n]Vgx' f;] \ M

! # rf/ k6s $ tLg k6s ! @ #
@ # × $ ≠ !@ $ × # ≠ !@
#
$ # × $ ≠ $ × # ≠ !@

, k6s , k6s

××
≠≠

× ≠ ×≠

, k6s ≠ , k6s

×≠ ×≠
× ×≠

232 d]/f] ul0ft, sIff @

u0fgf u/L n]Vgx' f;] \ M

, k6s ≠ , k6s

×≠ ×≠
×≠
×

, k6s ≠ , k6s

×≠ ×≠
×≠
×
d/] f] ul0ft, sIff @ 233

u0' fg tflnsf ko| fu] u/L lx;fa ug{'xf];\ M cf]6f eh' fx¿

!= Pp6f rte' {'hdf rf/cf]6f e'hfx¿
xG' 5g\ eg] kfFrcf]6f rte' {'hdf
sltcf]6f eh' fx¿ x'G5g\ <

×≠

@= k|To]s ljBfyL{;Fu % cf]6f l;;fsnd eP ^ hgf;Fu sltcf]6f
l;;fsnd xf]nfg\ <

×≠ cf]6f l;;fsnd

#= Pp6f 6f]s/Ldf kfFrcf]6f ;'Gtnf c6fpF5g\ eg] p:t} ;ftcf]6f
6f]s/Ldf sltcf]6f ;G' tnf c6fpnfg\ <

×≠ cf]6f ;G' tnf

$= Pp6f a]Grdf $ hgf ljBfyL{ c6fpF5g\ eg] o:t} & cf]6f a]Grdf
slt hgf ljBfyL{ c6fpF5g\ <

×≠ hgf ljBfyL{

%= Ps hgf ljBfyL{;Fu % cf]6f lstfa 5g\ eg] ToxL b/n] * hgf
ljBfyL{;Fu sltcf]6f lstfa xf]nfg\ <

×≠ cf]6f lstfa

234 d/] f] ul0ft, sIff @

kf7 !& efu

ufd] fn] cfkm";uF ePsf hDdf !@ cf6] f :ofp rf/ hgf ljBfyLn{ fO{

a/fa/ xg' ] u/L aflF 8g\ . ca, k|Tos] ljBfyL{n] sltcf6] f :ofp
kf| Kt u/] xf]nfg\ <

!@ cf]6f :ofp rf/ hgf ljBfyL{x¿nfO{ a/fa/ xg' ] u/L afF8\bf kT| o]s
ljBfyL{n] tLgcf]6fsf b/n] :ofp kf| Kt ub{5g\ . o;nfO{ ul0ftLo efiffdf
o;/L n]Vg ;lsG5 M

!@ ÷ $ ≠ #

hDdf :ofpsf] ljBfyL{ k|To]s ljBfyL{n] k|fKt j:tx' ¿nfO{ a/fa/
;ª\Vof ;ª\Vof ug]{ :ofpsf] ;ª\Vof ;ª\Vofsf ;d"xdf
afF8\g'nfO{ ‘efu’
kT| o]sn] # cf]6f :ofp kfP . # × $ ≠ !@ ug{' elgG5 . efu
ul0ftLo jfSonfO{ hgfpg '÷' ;ª\s]t
k|of]u ul/G5 .
#
$ !@ tl/sfn] klg n]Vg ;lsG5 .

– !@
)

d]/f] ul0ft, sIff @ 235

!% cf]6f l;;fsnd tLg hgf ljBfyLn{ fO{ a/fa/ x'g] u/L
af8F b\ f k|Tos] ljBfyLn{ ] sltcf]6f l;;fsnd kf| Kt ub{5g\ <

ul0ftLo jfSodfM !% ÷ #
lrq jf 7f]; j:ts' f] k|of]u u/L tn lbOPcg';f/ afF8\g ;lsG5 .

Ps hgf ljBfyL{n] Pscf]6f dfq !×#≠#
l;;fsnd kf| Kt ug]{ ePdf, @ × # ≠ ^
olb Ps hgf ljBfyL{n] bO' {cf]6f dfq
l;;fsnd k|fKt ug]{ ePdf,

Ps hgf ljBfyL{n] tLgcf]6f dfq # × # ≠ (
l;;fsnd kf| Kt ug]{ ePdf,

Ps hgf ljBfyL{;Fu rf/cf]6f dfq $ × # ≠ !@
l;;fsnd ePdf,

Ps hgf ljBfyL{n] kfFrcf]6f dfq % × # ≠ !%
l;;fsnd kf| Kt ug]{ ePdf,

o;nfO{ ul0ftLo jfSodfM k|To]s ljBfyL{;Fu ljBfyL{ hDdf
!% ÷ # ≠ % n]lvG5 . ePsf l;;fsndsf] ;ª\Vof ;ª\Vof
;ª\Vof

kT| o]s ljBfyL{n] % cf]6f l;;fsnd kf| Kt ub{5g\ .

236 d/] f] ul0ft, sIff @

!% ÷ # kQf nufpg × # ≠ !% sf] lx;fa ug{
;lsG5 . o;sf nflu # n] sltnfO{ u0' fg ubf{ !%
x'G5 egL u0' fg tflnsf x]g{ ;lsG5 .

k|To]s ljBfyL{;Fu ePsf ljBfyL{ ;ª\Vof ≠ hDdf ;ª\Vof

l;;fsndsf] ;ª\Vof ×

k|To]s ljBfyL{;Fu ePsf ≠ hDdf ;ª\Vof ÷ ljBfyL{ ;ª\Vof
l;;fsndsf] ;ª\Vof

@$ cf6] f rsn]6 cf7 hgf ljBfyL{x¿nfO{ a/fa/ x'g] u/L
af8F \bf kT| o]s ljBfyL{n] sltcf6] f rsn]6 kfpnfg\ <

d]/f] ul0ft, sIff @ 237

u'0fg tflnsfsf] k|ofu] u/L efu ug{'xf;] \ M

!* ÷ ^ ≠ × ^ ≠ !*

!$ ÷ @ ≠ × @ ≠ !$
@$ ÷ $ ≠ × $ ≠ @$

$* ÷ ^ ≠ × ^ ≠ $*

@* ÷ & ≠ × & ≠ @*

u0' fg tflnsfsf] ko| f]u u/L efu ug'{xf;] \ M

@! ÷ & ≠ #@ ÷ * ≠

#^ ÷ $ ≠ @% ÷ % ≠

@$ ÷ $ ≠ @& ÷ # ≠

& $@ ( %$

* %^ !) &)

238 d/] f] ul0ft, sIff @

tn lbOPsf] lrqdf Pp6f aG] rdfly hDdf !@ cf6] f :ofp

5g\ . olb Pp6f ljBfyL{nfO{ rf/cf]6fsf b/n] :ofp pknAw
u/fpg] xf] eg] hDdf slt hgf ljBfyLx{ ¿nfO{ af8F g\ kU' 5 <

ljBfyL{ ;ª\Vof ≠ # hgf

!@ cf]6f :ofp hDdf tLg hgf ljBfyL{nfO{ kl| t ljBfyL{ rf/cf]6fsf b/n]
afF8\g ;lsG5 . o;nfO{ ul0ftLo efiffdf tn b]vfOPcg';f/ n]Vg
;lsG5 M

!@ ÷ $≠ #

hDdf :ofpsf] kT| o]s ljBfyL{n] k|fKt ljBfyL{sf]
;ª\Vof ug]{ :ofpsf] ;ª\Vof ;ª\Vof

d/] f] ul0ft, sIff @ 239

!% cf]6f l;;fsnd 5g\ . k|lt ljBfyL{ tLg tLgcf6] fsf b/n]
af8F \bf slt hgf ljBfyLn{ fO{ af8F \g ;lsG5 <
ul0ftLo jfSodfM ÷

Ps hgf ljBfyL{nfO{ # × ! ≠ #
bO' { hgf ljBfyL{nfO{ # × @ ≠ ^
tLg hgf ljBfyL{nfO{ # × # ≠ (
rf/ hgf ljBfyL{nfO{ # × $ ≠ !@
kfFr hgf ljBfyL{nfO{ # × % ≠ !%

k|To]s ljBfyL{n] kfPsf ljBfyL{ hDdf l;;fsndsf]
l;;fsnd ;ª\Vof ;ª\Vof ;ª\Vof

!% cf]6f l;;fsnd # cf]6fsf b/n] afF8\bf % cf]6f ;d"x aGb5 .

!%÷# a/fa/ slt xG' 5 egL # × ≠ !% sf] lx;fa
ug{ ;lsG5 . o;sf nflu # nfO{ sltn] u0' fg ubf{ !%
xG' 5 egL u'0fg tflnsf x]g'{kb{5 .

ul0ftLo jfSodf n]Vbf M !% ÷ # ≠ %

kT| o]s ljBfyL{n] kfPsf × ljBfyL{ ;ª\Vof ≠ hDdf ;ª\Vof
l;;fsndsf] ;ª\Vof

ljBfyL{ ;ª\Vof ≠ hDdf ;ª\Vof ÷ kT| o]s ljBfyL{n] kfPsf
l;;fsndsf] ;ª\Vof

240 d/] f] ul0ft, sIff @

hDdf !* cf]6f rsn]6 5g\ . k|lt ljBfyL{ b'O{ bO' {cf]6fsf b/n]

afF8\bf slt hgf ljBfyL{nfO{ af8F \g ;lsG5 <
Pp6f kª\lStdf ^ hgfsf b/n] $* hgf ljBfyLn{ fO{ /fVbf

sltcf]6f kª\lStdf /fVg' k5{ <

8fS6/n] xl/sf a'afnfO{ #@ 6\ofan6] cf}ifwL lbge' of] . olb
xl/sf aa' fn] kl| tlbg $ cf]6f 6o\ fan6] vfg'k5{ eg] pSt

cfi} fwLn] hDdf slt lbg kU' 5 <

ul0ftLo jfSo, ×≠
÷≠

cf}ifwL vfgk' g]{ lbg ;ª\Vof ≠

d]/f] ul0ft, sIff @ 241

lrqdf cf7cf6] f s]/f lbOPsf 5g\ . o;af6 *÷$ nfO{ ;dfwfg
ugx'{ f];\ M

*÷$ *÷$

cf7cf]6f s]/f hgf cf7cf]6f s]/f lbOPsf 5g . olb
Ps hgf ljBfyL{n] cf]6f
ljBfyL{x¿nfO{ a/fa/ x'g] u/L s]/f kfpg] u/L a/fa/L ;ª\Vofdf

afF8\bf k|To]s ljBfyL{n] afF8\bf hDdf hgf

cf]6f s]/f kf| Kt u5{g\ . ljBfyL{nfO{ s]/f afF8\g ;lsG5 .

pQ/ kQf nufpg tnsf] ul0ftLo pQ/ kQf nufpg tnsf] ul0ftLo
jfSo ko| f]u ug{ ;lsG5 . jfSo k|of]u ug{ ;lsG5 .

×@≠* @× ≠*
hDdf s]/f
hDdf s]/f

dflysf b'j} pQ/x¿ $ sf] u0' fg tflnsfaf6 x]g{ ;lsG5 .

$ Ps k6s ≠ $ x'G5 eg] $ bO' { k6s ≠ * xG' 5 .

efu ugx{' f;] \ M
tnsf] efu ug{ sg' s'g cª\ssf] u0' fg tflnsf k|of]u ul/G5, 5nkmn
ug{'xf];\ M
!^ ÷ * ≠ @& ÷ ( ≠ #% ÷ % ≠

242 d]/f] ul0ft, sIff @

tn bv] fP h:t} u/L afs;df ;ªV\ of eg'x{ f];\ M

) ! @ # $ % ^ & * ( !) !! !@ !# !$ !% !^ !& !* !( @) @! @@ @# @$

k'Ug' kg]{ ;ª\Vof ≠ @$, plk|mPsf] k6s ≠ #, Psk6s pkm| g' kg]{ ;ª\Vof ≠ *

@$ ÷ # ≠ *

) ! @ # $ % ^ & * ( !) !! !@ !# !$ !% !^ !& !* !( @) @! @@ @# @$ @% @^ @& @* @( #)

÷# ≠

) ! @ # $ % ^ & * ( !) !! !@ !# !$ !% !^ !& !* !( @) @! @@ @# @$ @% @^ @& @* @( #)

÷≠

) ! @ # $ % ^ & * ( !) !! !@ !# !$ !% !^ !& !* !( @) @! @@ @# @$ @% @^ @& @* @( #)

÷≠

) ! @ # $ % ^ & * ( !) !! !@ !# !$ !% !^ !& !* !( @) @! @@ @# @$ @% @^ @& @* @( #)

÷≠

d]/f] ul0ft, sIff @ 243

tn b]vfPcg;' f/ vfnL 7fpF eg'{xf];\ M

$÷$ cf]6fsf] ;d"x agfpFbf, ^÷^ cf]6fsf] ;d"x agfpFbf,
@$ ÷ $ ≠ ^ ÷≠
Pp6f ;d"xdf ^ cf]6f :ofp k/] .
Pp6f ;d"xdf cf]6f an k/] .

#÷# cf]6fsf] ;d"x agfpFbf, &÷& cf]6fsf] ;d"x agfpFbf,

÷≠ ÷≠

Pp6f ;d"xdf cf]6f ;G' tnf k/] . Pp6f ;d"xdf cf]6f sfutL k/] .

$÷$ cf]6fsf] ;d"x agfpFbf, *÷* cf]6fsf] ;d"x agfpFbf,

÷≠ ÷≠

Pp6f ;d"xdf cf]6f sfpnL k/] . Pp6f ;d"xdf cf]6f 6df6/ k/] .

244 d/] f] ul0ft, sIff @