गणित कक्षा ३

%= 36fpg'xf;] \ M ! ) ) k};f ?= k};f
— $ * k;} f !))) %)
( % k};f –(@* @%
— @ % k};f ln6/ ldlnln6/
&%) %@% ldlnln6/
^= lx;fa ug'x{ f;] \ M –!@* !)))
±@%) – ^))
ln6/
#))

±@%)

&= Pp6f 3/df %)) ln6/ kfgL c6fpg] Pp6f
efF8f] / @%) ln6/ kfgL c6fpg] csf{] efF8f]
/x5] . olb b'j} ef8F fdf kfgL e/L /x]5 eg]
hDdf slt ln6/ kfgL /x5] <

*= z/0fsf] 3/df !))) ln6/ Ifdtfsf]
6\ofª\sLdf kfgL e/L /flvPsf] lyof] . pSt
6\ofªs\ Laf6 ^%) ln6/ kfgL lemlsP5 eg]
ca 6\ofª\sLdf slt kfgL afsF L xf]nf <

(= vfnL 7fpF egx{' f];\ M

-s_ ! ;]lG6ld6/df ldlnld6/ xG' 5 .

-v_ # ;]lG6ld6/df ldlnld6/ x'G5 .

!)= ldlnld6/df ¿kfGt/ ug'{xf;] \ M

-s_ $ ;]=ld= ≠ ld=ld= -v_ !) ;]=ld= ≠ ld=ld=

 d/] f] ul0ft, sIff # 245

!!= ;l] G6ld6/df ¿kfGt/ ug'x{ f];\ M

-s_ # ld= ≠ ;]=ld=

-v_ % ld= %) ;]=ld= ≠ × % ;]=ld= ± %) ;]=ld=

≠ ;]=ld= ± %) ;]=ld=

≠ ;]=ld=

!@= uf| ddf ¿kfGt/ ug'{xf;] \ M

-s_ % ls=uf| = ≠ u|fd

-v_ @ ls=uf| = !)) uf| d ≠ @ × u|fd ± uf| d
uf| d
≠ uf| d ±
≠ uf| d

!#= tn lbOPsf] tflnsfsf] cfwf/df lrqu|fkm agfpg'xf];\ M

?lrsf] ljifo g[To ;ª\uLt ufog lrqsnf gf6s
ljBfyL{ ;ª\Vof @$ !^ !@ @) $

≠ $ hgf ljBfyL{ dg k/fpg] ljBfyL{ ;ª\Vof
?lrsf] ljifo

cleefjssf] b:tvt
lzIfssf] b:tvt

246 d/] f] ul0ft, sIff #

gfk *

kf7 @@ If]qkmn

tnsf] u|fkm cWoog ugx'{ f;] \ M

lrqdf Pp6f ufpFsf] hUufsf] 6j' |mfx¿nfO{ n]vflrqdf k:| t't ul/Psf] 5 .
lbndfof / /xdfgn] pSt n]vflrqsf af/]df lh1f;f /fv]5g\ / pSt lh1f;fsf
cfwf/df lzIfsn] k:| tl' t u/]5g\ M

D C ZY L K
A B WX

SR
IJ

PQ
PO

MN

dflysf] u|fkmdf ju{ / cfotx¿ lvlrPsf 5g\ . WXYZ Ps PsfO nDafO
ePsf] ju{ xf] . o;sf] If]qkmn Ps ju{ PsfO x'G5 . o;nfO{ PsfO ju{ klg
elgG5 .
ABCD Pp6f ju{ xf] . o;df ;fgf $ cf]6f PsfO ju{x¿ 5g\ . cyf{t\ ju{
ABCD leq $ cf]6f PsfO ju{ jf ! ju{ PsfOsf $ cf]6f juf{sf/ sf]7fx¿
5g\ .
To;}n] ju{ ABCD sf] If]qkmn $ ju{ PsfO xG' 5 . PQRS Pp6f cfot xf] .
o;df % cf]6f PsfO ju{x¿ c6fPsf 5g\ . To;}n] cfot PQRS sf] If]qkmn
% ju{ PsfO xG' 5 .
cfot IJKL df !@ cf]6f ;fgf PsfO ju{x¿ c6fPsf 5g\ . To;}n] cfot
IJKL sf] If]qkmn !@ ju{ PsfO x'G5 .
MNOP klg Pp6f cfot xf] . o;leq !$ cf]6f ;fgf PsfO ju{x¿ c6fPsf
5g\ . To;}n] cfot MNOP sf] If]qkmn !$ ju{ PsfO x'G5 .

d/] f] ul0ft, sIff # 247

tnsf] uf| km cWoog u/L vfnL 7fpFdf eg'x{ f];\ M

DC P O

A B
H G

M N

EF LK

WX

IJ PsfO
ZY ju{ PsfO

ABCD PsfO ju{ xf] . PsfO
ABCD sf] If]qkmn ju{ PsfO xG' 5 .
EFGH leq cf]6f PsfO ju{x¿ c6fPsf 5g\ .
To;}n] EFGH sf] If]qkmn ju{ PsfO xG' 5 .

MNOP Pp6f cfot xf] . o;sf] nDafO PsfO / rf}8fO
5g\ .
MNOP leq cf]6f PsfO ju{x¿ 5g\ . o;sf] If]qkmn
x'G5 .

WXYZ Pp6f cfot xf] . o;sf] nDafO PsfO / rf}8fO
5g\ .
WXYZ leq cf]6f PsfO ju{x¿ c6fPsf 5g\ .
WXYZ sf] If]qkmn ju{ PsfO x'G5 .

IJKL Pp6f cfot xf] . o;leq cf]6f PsfO ju{x¿ 5g\ .
o;sf] If]qkmn ju{ PsfO xG' 5 .

248 d]/f] ul0ft, sIff #

If]qkmn kQf nufcf}‘ M ! ju{ ;]=ld=

of] Pp6f ju{ xf] . ! ;]=ld=
o;sf] eh' fsf] nDafO ! ;]=ld= 5 . ! ;]=ld=
rf}8fO klg ! ;]=ld= 5 .
o;n] Ps ju{ ;]=ld= 7fpF lnG5 .

of] Pp6f cfot xf] . cfot

o;sf] nDafO @ ;]=ld= 5 .

rf}8fO ! ;]=ld= 5 . ! ju{ ;]=ld= ! ju{ ;]=ld=

o;df @ cf]6f ! ju{ ;]=ld=sf ju{x¿ c6fPsf 5g\ .

To;}n] of] cfotsf] If]qkmn @ ju{ ;]=ld= xG' 5 .

of] cfot # ;]=ld=nfdf] 5 o;sf] rf}8fO ! ;]=ld= 5 . ! ;]=ld=

o;df sltcf]6f ! ju{ ;]=ld=sf ju{x¿ c6fPsf 5g\ < ! ju{ ! ju{ ! ju{

of] cfotdf # cf]6f ! ju{ ;]=ld=sf ju{x¿ c6fPsfn] ;]=ld= ;]=ld= ;]=ld=
o;sf] If]qkmn # ju{ ;]=ld= xG' 5 .

o;sf] nDafO # ;]=ld= 5 . @ ;]=ld=
rf}8fO @ ;]=ld= 5 .
o;df sltcf]6f ! ju{ ;]=ld=sf ju{x¿ 5g\ < u0fgf u/f¹ . # ;]=ld=
oxfF hDdf ^ cf]6f ! ju{ ;]=ld=sf ju{x¿ 5g\ .
To;}n] of] cfoftsf] If]qkmn ^ ju{ ;]=ld= x'G5 .

d/] f] ul0ft, sIff # 249

tnsf lrqx¿df ju{ sf7] fx¿sf] ;ªV\ of uGtL u/L Ifq] kmn nV] gx' f;] \ M

ju{ PsfO ju{ PsfO

ju{ PsfO ju{ PsfO

ju{ sf]7fx¿ u0fgf u/L Ifq] kmn kQf nufpgx' f;] \ M

!= @=

$ ;]=ld=

# ;]=ld=

@ ;]=ld= ju{ ;]=ld= $ ;]=ld=

250 d/] f] ul0ft, sIff # ju{ ;]=ld=

ju{ sf]7fx¿ u0fgf u/L If]qkmn kQf nufpgx' f;] \ M

!= @=

$ ;]=ld= % ;]=ld=

% ;]=ld= ^ ;]=ld= $ ;]=ld=

ju{ ;]=ld= ju{ ;]=ld=

#= $= & ;]=ld=

# ;]=ld= ju{ ;]=ld=
% ;]=ld=

ju{ ;]=ld=

d]/f] ul0ft, sIff # 251

If]qkmn kQf nufcf‘} M # ;]=ld=

kLtfDa/ / ljm| l:6gfn] If]qkmn;DaGwL Pp6f kl/of]hgf sfo{ u/]5g\ . pgLx¿n]
kl/of]hgf sfo{af6 k|fKt u/]sf s/' fx¿ sIffsf]7fdf k:| t't ubf{ lgDgcg;' f/
u/]5g\ M

Pp6f cfotsf/ ;txdf sltcf]6f PsfO ju{
c6fpF5g\, ;f] ;ª\Vof u0fgf u/L If]qkmn kQf
nufOG5 h:t}M

of] cfotsf] nDafO ^ ;]=ld=/ rf}8fO ^ ;]=ld=
# ;]=ld=5 . o;nfO{ PsfO ju{df ljefhg
ubf{ sltcf]6f PsfO ju{ c6fpg ;S5g\ < ^ × # ju{ ;]=ld=

! ;]=ld=sf] b'/Ldf t];f]{ / 7f8f l;wf /]vfx¿ lvrL ! ;]=ld= nDafO / ! ;]=ld=
rf}8fO ePsf juf{sf/ sf]7fx¿df ljefhg u/L sf]7fx¿ u0fgf u/f¹ . o;/L
oxfF !* cf]6f sf]7fx¿ kfOPsfn] o; cfotsf] If]qkmn !* ju{ ;]=ld=xf] .

dfly h:t} u/L ! ;]=ld=sf] b/' Ldf $ ;]=ld=
t];f]{ / 7f8f] l;wf /]vfx¿ lvrL
juf{sf/ sf]7fx¿df ljefhg ubf{ * ;]=ld=
bfofFk6\l6sf] cfotsf] klg If]qkmn
lgsfNg ;lsG5 . * × $ ju{ ;]=ld=

o;sf] If]qkmn #@ ju{ ;]=ld= xG' 5 .

252 d]/f] ul0ft, sIff #

lrxg\ nufOPsf 7fpaF f6 t];f{] / 7f8f] l;wf/v] f lvrL ju{ sf7] fx¿
agfpg'xf];\ / If]qkmn kQf nufpg'xf];\ M

# ;]=ld= # ;]=ld=

$ ;=] ld= & ;]=ld=

$ ;]=ld= # ;]=ld=

$ ;]=ld= * ;=] ld=

PsfO jux{ ¿ agfO{ If]qkmn kQf nufpgx' f];\ M

@ ;]=ld= # ;]=ld=

% ;]=ld= ^ ;]=ld=

d/] f] ul0ft, sIff # 253

If]qkmn kQf nufpgx' f];\ M
bfofFk6\l6 lbOPsf] lrq cfotsf] xf] . o;sf]
If]qkmn slt xf]nf, cgd' fg ug'{xf];\ .
bfofFk6\l6 lbOPsf] cfotsf] If]qkmn
ju{ ;]=ld= xf]nf .
ca o;sf] nDafO gfKgx' f];\ .
rf}8fO klg gfKg'xf];\ .

t];f]{ / 7f8f] l;wf wsf{ lvlr ! ju{ ;]=ld=sf
PsfO ju{x¿df ljefhg u/L u0fgf ug'{xf];\ .
cg'dfgaf6 cfpg] If]qkmn jf:tljs If]qkmn;Fu
t'ngf ug{'xf];\ .

dfly h:t} bfofFk6\l6sf] cfotsf] If]qkmn klg
cg'dfg ug{'xf];\ .
bfofFk6\l6 lbOPsf] cfotsf] If]qkmn
ju{ ;]=ld= xf]nf .
ca 7f8f] / t];f]{ l;wf /]vfx¿ lvrL jf:tljs
If]qnkmn klg kQf nufpgx' f];\ .
jf:tljs If]qkmn / cg'dflgt If]qkmndf slt
km/s cfof] <

254 d/] f] ul0ft, sIff #

gfk

x/] f‘,} dn} ] slt l;sF] <
!= tn lbOPsf ;txx¿df PsfO ju{ u0fgf u/L If]qkmn kQf

nufpg'xf;] \ M

ju{ PsfO ju{ PsfO

@= lrxg\ nufO{Psf] 7fpFaf6 t];f| ]{ / 7f8f] l;wf /]vf lvrL ju{
sf]7fx¿ agfpgx' f];\ / Ifq] kmn kQf nufpg'xf];\ M

$ ;]=ld=

& ;]=ld=

% ];=ld= * ;]=ld=

 d/] f] ul0ft, sIff # 255

#= tn lbOPsf cfotx¿sf] Ifq] kmn cgd' fg ugx{' f];\ . 7f8f] / t];f{] l;wf
/v] fx¿ lvrL ! ;=] ld= nDafOsf PsfO ju{x¿ agfP/ jf:tljs
If]qkmn klg kQf nufpg'xf;] \ / tnsf] tflnsfdf eg'x{ f;] \ M

!= @= #=

$= %=

^= &=

k|Zg g= cfotsf] cgd' flgt cfotsf] jf:tljs km/s
If]qkmn Ifq] kmn
!=
@=
#=
$=
%=
^=
&=

cleefjssf] b:tvt
lzIfssf] b:tvt

256 d/] f] ul0ft, sIff #

l;sfO zª[ v\ nf

tkfO{“n] lj|mofsnfk k"/f u/]sf] lbg afs;df l7s lrx\g -√_ nufpgx' f];\ .

;'? kf7 ! kf7 @

kf7 #

kf7 ^ kf7 % kf7 $
kf7 !@ kf7 & kf7 !#

kf7 *

kf7 (

kf7 !)

kf7 !!

kf7 !$

d/] f] ul0ft, sIff # 257

kf7 !%

kf7 @) kf7 !( kf7 !^
kf7 !&
kf7 @! kf7 !*

;dfKt kf7 @@

SEE YOU IN
GRADE FOUR!

258 d/] f] ul0ft, sIff #