ul0ft
sIff $
gk] fn ;/sf/
lzIff, lj1fg tyf kl| jlw dGqfno
kf7o\ jm| d ljsf; sG] b|
;fgf]l7dL, eStk'/
ks| fzs
gk] fn ;/sf/
lzIff, lj1fg tyf k|ljlw dGqfno
kf7\oj|md ljsf; s]Gb|
;fgfl] 7dL, eStk/'
© ;jfl{ wsf/ kf7\oj|md ljsf; s]Gb|
o; kf7\ok':ts;DaGwL ;Dk0" f{ clwsf/ kf7o\ j|md ljsf; s]Gb| ;fgfl] 7dL, eStk/' df
lglxt /xs] f] 5 . kf7\oj|md ljsf; s]Gbs| f] lnlvt :jLs[ltlagf Jofkfl/s ko| f]hgsf
nflu o;sf] k'/} jf cfl+ zs efu xa' x' ks| fzg ug{, kl/jt{g u//] k|sfzg ug,{ s'g}
ljBt' Lo ;fwg jf cGo kl| jlwaf6 /s] 8{ ug{ / k|ltlnlk lgsfNg kfOg] 5}g .
k/LIf0f ;+:s/0f M lj=;= @)&*
ky| d ;:+ s/0f M lj=;= @)&(
d'b0| f M
dN" o ?=
kf7o\ k':ts;DaGwL kf7sx¿sf s'g} klg ks| f/sf ;'´fjx¿ ePdf kf7o\ j|md
ljsf; sG] b,| ;dGjo tyf ks| fzg zfvfdf k7fOlbgx' 'g cg'/fw] 5 . kf7sx¿af6
cfpg] ;'´fjx¿nfO{ sG] b| xflb{s :jfut u5{ .
xfd|f] egfO
kf7\ojm| d lzIf0f l;sfOsf] d"n cfwf/ xf] . kf7\ok:' ts ljBfyLd{ f ckl] Ift bIftf ljsf; ug{] Ps dV' o
;fwg xf] . o; kIfnfO{ bl[ i6ut ub} kf7o\ jm| d ljsf; s]Gb|n] ljBfno lzIffnfO{ Jofjxfl/s, ;do;fkI] f
/ u0' f:t/Lo agfpg] p2]Zon] kf7o\ j|md tyf kf7o\ k':tssf] ljsf; tyf kl/dfhg{ sfo{nfO{ lg/Gt/tf
lbbF } cfPsf] 5 . cfwf/et" lzIffn] afnaflnsfdf cfwf/et" ;fIf/tf, ul0ftLo cjwf/0ff / l;k Pjd\
hLjgf]kofu] L l;ksf] ljsf;sf ;fy} JolStut :jf:Yo tyf ;/;kmfO;DaGwL afgLsf] ljsf; ug]{ cj;/
k|bfg ugk{' 5{ . cfwf/et" lzIffsf dfWodaf6 afnaflnsfx¿n] k|fs[lts tyf ;fdflhs jftfj/0fkl| t
;r]t eO{ cgz' f;g, ;bfrf/ / :jfjnDag h:tf ;fdflhs Pjd\ rfl/lqs u0' fsf] ljsf; ug{'k5{ . o;n]
lj1fg, jftfj/0f / ;r" gf k|ljlw;DaGwL cfwf/et" 1fgsf] ljsf; u/fO{ snf tyf ;fG} bo{kl| t cle?lr
hufpgk' 5{ . zf/Ll/s tGb'?:tL, :jf:Yos/ afgL Pjd\ l;h{gfTdstfsf] ljsf; tyf hfthflt, wd{, efiff,
;+:s[lt, If]qkl| t ;Ddfg / ;defjsf] ljsf; klg cfwf/e"t lzIffsf ckl] Ift kIf x'g\ . b]zk|d] , /fli6«o
Pstf, nfs] tflGqs d"NodfGotf tyf ;:+ sf/ l;sL Jofjxfl/s hLjgdf k|of]u ug{,' ;fdflhs u0' fsf]
ljsf; tyf gful/s stJ{ okl| t ;hutf ckgfpg,' / b}lgs hLjgdf cfOkg{] Jofjxfl/s ;d:ofx¿sf]
klxrfg u/L ;dfwfgsf pkfosf] vf]hL ug'{ klg cfwf/e"t txsf] lzIffsf cfjZos kIf x'g\ . o;
kIfnfO{ bl[ i6ut u/L ljBfno lzIffsf] /fli6«o kf7\ojm| d k|f¿k, @)&^ sf] dd{cg'¿k b]zsf ljleGg
ljBfnodf k/LIf0f u/L kf| Kt ki[ 7kfi] f0fsf cfwf/df kl/dfh{g u//] cfwf/e"t lzIff -sIff $_ sf] ul0ft
ljifosf] kf7\oj|mdcg'¿k of] k:' ts ljsf; ul/Psf] xf] .
;?' df >L xl/gf/fo0f pkfWofo, >L ;h' g sfˆn,] >L ;/nf bj] sf]6f, >L /Lt' >]i7, >L huGgfy clwsf/L / >L
/fdrGb| 9sfn /xs] f] sfob{ naf6 n]lvPsf] o; kf7o\ k':tsnfO{ >L ;Togf/fo0f dxh{g, >L ;fd] sd' f/ >]i7,
>L e[s'6Ltf/f 9sfn;d]t ;b:o /xs] f] sfob{ naf6 ;'wf/ ul/Psf] xf] . o; ¿kdf Nofpg] sfo{df o; s]Gb|sf
dxflgb]{zs >L c0fk;| fb Gof}kfg,] 8f= /fdhLk|;fb kl08t, >L nIdLgf/fo0f ofbj, >L js} '07k|;fb vgfn,
>L kl| dnf avtL, >L si[ 0fk;| fb kf]v/n] , >L ufd] f >]i7, >L clg?b|k;| fb Gof}kfg,] >L /fhs'df/ dfy]df,
k|f=8f= xl/k;| fb pkfWofo, >L sz] j/fh kmn' f/f, >L /fd xf8f / >L lgd{nf uft} dsf] ofu] bfg /xs] f] 5 .
o;sf] efiff ;Dkfbg 8f= u0fz] k;| fb e66\ /fO{ / >L lrgfsd' f/L lg/fn} faf6 ePsf] xf] . o; k':tssf]
nc] fp6 l8hfOg >L v8f]; ;'g'jf/af6 ePsf] xf] . o;sf] ljsf;df ;+nUg ;Dk"0fk{ l| t sG] b| xflb{s
s[t1tf k|s6 u5{ .
o; kf7\ok:' tsn] ljBfyLd{ f lgwfl{ /t ;Ifdtf ljsf;sf nflu ljBfyL{nfO{ ;xofu] ug]{ 5 . o;n]
ljBfyLs{ f] l;sfOdf ;xof]u k'¥ofpg] Pp6f dxŒjk0" f{ / cfwf/e"t ;fdu|Lsf ¿kdf sIff lj|mofsnfkaf6
x'g] l;sfOnfO{ dha't agfpg ;xof]u ug]{ 5 . To;}n] of] lzIfssf] l;sfO ljm| ofsnfksf] of]hgf
geO{ ljBfyL{sf l;sfOnfO{ ;xofu] k¥' ofpg] ;fdu|L xf] . kf7\ok':tsnfO{ ljBfyL{sf] l;sfOdf ;xofu]
k¥' ofpg] dxŒjk"0f{ cfwf/sf ¿kdf afnsl] Gb|t, l;sfOsl] Gbt| , cg'ejs]lGbt| , p2Z] odn" s, ko| fu] dv' L /
ljm| ofsnfkdf cfwfl/t agfpg] k|of; ul/Psf] 5 . l;sfO / ljBfyLs{ f] hLjGt cg'ejlar tfbfTDo
sfod ub{} o;sf] ;xh ko| fu] ug{ lzIfsn] ;xhstf{, pTk/]| s, k|jw{s / vfh] stfs{ f ¿kdf e"ldsfsf]
ck]Iff ul/Psf] 5 . o; k':tsnfO{ c´ kl/ist[ kfgs{ f nflu lzIfs, ljBfyL,{ cleefjs, a'l4hLjL Pjd\
;Dk"0f{ kf7sx¿sf] ;d]t ljzi] f e"ldsf /xg] xbF' f ;Da4 ;a}sf] /rgfTds ;'´fjsf nflu kf7\oj|md
ljsf; sG] b| xflb{s cg'/fw] u5{ .
lj=;+= @)&( kf7\ojm| d ljsf; s]Gb|
;fgf]l7dL, eStk'/
ljifo;"rL
kf7 lzif{s k[i7;ªV\ of
! /v] fx¿ / sf]0fx¿ (Lines and angles) !
@ ;dtnLo cfs[ltx¿ (Plane figures) *
# 7f]; j:t'x¿ (Solid objects) !%
$ ;ªV\ ofsf] 1fg (Number sense) @^
% ul0ftsf cfwf/e"t ljm| ofx¿ (Basic operations of mathematic) $!
^ leGg, bzdnj / k|ltzt (Fraction, decimal and percentage) &#
& ;do (Time) (&
* d'b|f (Currency) !!#
( b/' L (Distance) !@)
!) Ifdtf (Capacity) !#@
!! tfn} (Weight) !$)
!@ kl/ldlt / If]qkmn (Perimeter and area) !%@
!# lan / ah]6 (Bill and budget) !^#
!$ :tDe lrq (Bar diagram) !*(
!% aLhul0ft (Algebra) @)$
kf7 1 M /v] fx¿ / sf]0fx¿ (Lines and Angles)
1.1.1 k'g/jnf]sg (Review)
tnsf cfs[ltx¿ x]//] 5nkmn ug'{xf];\ / o;sf] lgisif{ sIffsf]7fdf k:| tt' ug{'xf];\ M
i. dflysf cfsl[ tx¿df sxfF sxfF sf0] f ags] f 5g\ <
ii. s'g cfs[ltdf ;aeGbf 7n' f] / ;aeGbf ;fgf] sf]0f ag]sf] 5, x]//] eGg'xf;] \ .
iii. o:t} cGo ;fdu|Lx¿ ;ª\sng u/L lrq sf/] ]/ o;sf zLifl{ aGb,' eh' f / sf0] fx¿
b]vfpgx' f];\ .
1.1.2 rfFb (Protractor)
ljm| ofsnfk 1
rf/ rf/ hgf ljBfyL{x¿sf] ;d"x agfO{ Hofldlt afs;df tn lbOPsf h:t} ;fdu|L
x]//] o;df sltbl] v slt;Dd ;ªV\ of pNn]v ul/Psf] 5 < cGo efux¿ s] s] 5g\ <
o;sf] ko| f]u s] sfdsf nflu ul/G5, 5nkmn ug{x' f];\ .
o:tf] HofldtLo ;fdu|LnfO{ rfbF (Protractor) elgG5 .
lj|mofsnfk 2
sG] b|laGb' cfwf/ /]vf
Hofldlt afs;df ePsf ;fduL| x¿dWo] dfly lrqdf b]vfOP h:t} ;fdu|L rfFb
ul0ft, sIff $ 1
(Protractor) xf] . o;sf] cw{jQ[ fsf/ 3/] fnO{ 180 a/fa/ efudf ljefhg ul/Psf]
x'G5 . x/s] Ps efu a/fa/ 1 l8u|L xG' 5 . o;nfO{ ;ªs\ ]tdf 1o n]lvG5 . rfFbdf b'O{
tl/sfaf6 0o bl] v 180o ;Ddsf :s]nx¿ pNn]v ul/Psf] x'G5, lsg xfn] f < o;sf]
ko| fu] s] s] sf nflu ul/G5, 5nkmn ug{'xf;] \ .
sf]0fsf] gfk lng tyf sf0] fsf] /rgf ug{ k|ofu] ul/g] cw{j[Qfsf/ ;fdu|LnfO{ k|f]6«ofS6/
elgG5 . rfbF df cw{j[Qfsf/ efusf] tnlt/sf] l;wf /v] fnfO{ cfwf/ /v] f elgG5 . o;
/v] fsf] b'j} 5p] df 0 / 180 n]lvPsf] xG' 5 . 90 nl] vPsf] /v] f l;wf tn cfwf/ /]vf;Fu
hfl] 8Psf] :yfgnfO{ s]Gb|laGb' elgG5 . sf0] fsf] gfk lng / sf0] fsf] /rgf ug{ rfbF sf]
ko| f]u ul/G5 .
1.1.3 rfbF sf] k|of]u u//] sf0] fsf] gfk / /rgf (Measurement and construction
of angle using protractor)
-s_ sf0] fsf] gfk A
Z
X lrq (i) Y BC
lrq (ii)
lj|mofsnfk 1
dflysf sf]0fx¿sf] gfk s;/L kQf nufpg] xfn] f <
(i) rfbF sf] sG] b|laGb' / sf0] fsf] zLifl{ aGb' ldNg] u/L rfbF sf] cfwf/ /]vfnfO{ lrq (i)
/ (ii) sf sf0] fsf] cfwf/ eh' f;Fu vlK6g] u/L ldnfP/ /fVg'xf;] \ .
A
Z
XY BC
(ii) cfwf/ eh' fdf sf0] f agfpg] csf{] /v] fn] rfFbdf bv] fPsf bO' c{ f6] f ;ª\VofdWo] sg'
;ªV\ ofn] sf]0fsf] gfk hgfpF5 .
sf]0fsf] gfk lnbF f cfwf/ /v] fsf] 0 af6 sf]0f agfpg] /]vflt/ uGb} hfgk' 5{ .
2 ul0ft, sIff $
∠XYZ df zLif{laGb' Y / cfwf/ /]vf XY 5 . X ePsf] lt/af6 uGb} hfbF f ZY n]
rfbF sf] 130 df b]vfPsf] 5 . To;n} ] ∠XYZ = 130o eof] . To:t} ∠ABC df zLifl{ aGb'
B / cfwf/ /]vf BC 5 . C ePsf] lt/af6 uGb} hfFbf AB n] rfbF sf] 60 df bv] fPsf]
5 . To;}n] ∠ABC = 60o eof] .
lj|mofsnfk 2
kf| ]6o« fS6/ lgdf0{ f u/f}F M
zI} fl0fs ;fduL| M sf8{kk] /, k|f6] «ofS6/, l;;fsnd / ?n/
sf8k{ k] /df kf| 6] «ofS6/ /fv/] 6;«] u/L tnsf] h:t} kf| 6] «ofS6/ lgdf0{ f ug'{xf];\ .
-v_ sf0] fsf] /rgf BC
lj|mofsnfk 3 •A
rfFbsf] k|ofu] u/]/ sf0] fsf] /rgf s;/L ug]{ xf]nf < BC
rfbF sf] k|of]u u//] sf0] f ∠ABC = 40o sf] /rgf 3
(i) ?n/sf] ;xfotfn] BC /]vfv08 lvRgx' f];\ .
(ii) laGb' B nfO{ rfFbsf] s]Gb|df kg{] u/L l7s
ldnfP/ /fVg'xf];\ .
(iii) C af6 uGb} uP/ 40 df ;ªs\ t] u/L A gfd
lbg'xf;] \ .
ul0ft, sIff $
(iv) rfbF nfO{ x6fP/ ?n/sf] ;xfotfn] AB /]vfv08nfO{ hf8] \gx' f];\ . sf]0f ABC
tof/ eof] . ∠ABC = 40o eof] .
A A
BC 40o C
pbfx/0f 1 B
rfbF sf] k|ofu] u/]/ ∠PQR sf] gfk kQf nufpg'xf];\ M
P
P
QR QR
;dfwfg
∠PQR df cfwf/ /v] f QR / zLif{laGb' Q 5 . R af6 uGb} hfbF f PQ n] rfbF sf] 50 df
b]vfPsf] 5 . To;n} ] ∠PQR = 50o eof] .
ljm| ofsnfk 4
tn rfbF n] sf0] fx¿ gfks] f] b]vfOPsf] 5 . ;fyL;uF 5nkmn u/L gfk nV] gx' f;] \ M
(a) 60o (b) 70o
L P
∠LMN = 60o ∠PQR = 70o
M N QR
4 ul0ft, sIff $
(c) 110o (d) 150o
X A
∠XYZ = 110o ∠ABC = 150o
Y Z BC
pbfx/0f 2
rfFbsf] k|of]u u/]/ tnsf gfksf sf]0fx¿ b'O{ tl/sfaf6 JoSt ul/Psf] :s]n ko| f]u
u/L /rgf ug'x{ f;] \ M
(a) 30o (b) 120o
;dfwfg
(a) 300 sf] sf0] fnfO{ k|f6] «ofS6/df b'O{ tl/sfaf6 JoSt ul/Psf] :sn] k|ofu] u/L
/rgf ubf{
AD
BC FE
(b) 1200 sf] sf0] fnfO{ k|f]6«ofS6/df bO' { tl/sfaf6 JoSt ul/Psf] :s]n ko| f]u u/L
/rgf ubf{
PS
Q RM O
cEof;
1. vfnL 7fpF eg{x' f];\ M
(i) HofldtLo ;fdu|L rfbF sf] cfsf/ ============== x'G5 .
(ii) rfbF df 0 b]lv ============== ;Dd nl] vPsf] xG' 5 .
(iii) rfbF df tnsf] l;wf /v] fnfO{ ============== elgG5 .
(iv) sf]0f gfKg sf] k|of]u ul/G5 .
ul0ft, sIff $ 5
2. tnsf dWo] sg' ;aeGbf ;fgf] sf0] f xf] < gfk/] eGgx' f];\ M
(a) (b) (c) (d)
3. HofldtLo ;fdu|L rfbF sf] k|ofu] ss] f nflu ul/G5 < nV] g'xf;] \ M
4. rfbF sf] ko| fu] u/L tnsf k|Tos] sf]0fx¿nfO{ gfk/] ltgLx¿sf] gfk l8u|Ldf
n]Vg'xf];\ M
(i) (ii) (iii)
AD G
B C E I H
F
(iv) (v) (vi)
JM R
Q
P
K LO N
(vii) (viii)
B M
S
PT N
5. tn lbOPsf gfksf sf]0fx¿ rfFbsf] ;xfotfn] lvRgx' f;] \ M
(i) 60o (ii) 20o (iii) 50o (iv) 100o (v) 120o
6 ul0ft, sIff $
6. tn lbOPsf cfsl[ tx¿sf] leqL sf0] fsf] gfk rfbF sf] ;xfotfn] gfKgx' f];\ M
P S SO
A X
B C Q R Y ZM
7. tnsf] lrqdf slt 7fpFdf sf]0fx¿ ags] f 5g\, kQf nufpgx' f];\ . k|Tos] sf0] fnfO{
gfk/] sfkLdf n]Vg'xf];\ M
PQ
R U
S T
VW
kl/of]hgf sfo{ (Project work)
1. tkfO‘s{ f] 3/, ljBfno jl/kl/ /xs] f] ljleGg efudf sf0] f ags] f j:t'x¿ ;ª\sng
u//] lrq sfg] {'xf;] \ / pSt j:td' f ags] f sf]0f rfFbsf ;xfotfn] gfk]/ sIffsf]7fdf
k:| tt' ug{\xf];\ .
2. cªu\ h|] L j0f{dfnfsf cIf/x¿dWo] sg' s'g cIf/df sf]0f ags] f] xG' 5 / sg' sg'
cIf/df sf]0f ag]sf] x'bF g} , cjnfs] g ugx{' f];\ . sf0] f ags] f sg' } tLgcf]6f cªu\ h]| L
j0f{dfnfsf cIf/x¿ rf6k{ ]k/df n]vL ltgsf] sf]0fsf] gfk lngx' f];\ .
ul0ft, sIff $ 7
kf7 2 M ;dtnLo cfs[lt (Plane Surface)
2.1 kg' /jnf]sg (Review)
ljBfyLx{ ¿ pko'St ;ª\Vofdf ;d"xdf a:gx' f];\ . h;' sf kfOk÷l;Gsfx¿ ;ªs\ ng
ug'x{ f];\ . pSt l;Gsfx¿sf] k|ofu] u/L ljleGg HofldtLo cfs[ltx¿ agfP/ sIffsf7] fdf
k:| tt' u/L 5nkmn ug'x{ f];\ .
2.2 ;dtnLo cfs[ltx¿ (Plane figures)
lj|mofsnfk 1
tn lbOPsf cfs[ltx¿ cjnf]sg ug'x{ f;] \ . o;sf dflyNnf] ;txdf sltcf]6f
lsgf/f 5g\ < sg' fx¿ slt 5g\ < Pscfk;df 5nkmn u//] vfH] g'xf];\ M
(i) (ii)
(iii) (iv)
lj|mofsnfk 2
rf/ rf/ hgfsf] ;d"x agfpgx' f];\ . x/]s ;d"xn] tn lbOPsf] h:t} sx] L l;;fsnd
lngx' f;] \ . l;;fsnd hf8] ]/ km/s km/s vfnsf lqe'h / rt{e' h' lgdf{0f u/L ljleGg
efux¿ -eh' f / sf0] f_ sf af/d] f ;d"xut 5nkmn ug'x{ f;] \ M
eh' f sg' f
e'hf zLif{laGb'
8 ul0ft, sIff $
lj|mofsnfk 3
tLg tLg hgfsf] ;d"xdf a:gx' f;] \ . lbOPsf ;dtnLo cfsl[ tx¿ cjnfs] g u/L tnsf
kZ| gdf cfwfl/t eP/ 5nkmn ugx{' f];\ M
(i) (ii) (iii)
(iv) (v) (vi)
(i) kT| os] cfsl[ tdf sltcf]6f eh' f 5g\ <
(ii) dflysf kT| o]s cfs[ltdf sltcf6] f zLif{laGb' /x]sf 5g\ <
(iii) pSt cfs[ltx¿sf] gfd s] s] xf]nf <
;dtnLo cfs[ltdf /xs] f l;wf /]vfv08nfO{ eh' f / bO' { eh' f hf]l8Psf] ljGb'nfO{
zLif{laGb' elgG5 / bO' { eh' flarsf] km66\ fOnfO{ sf0] f elgG5 .
pbfx/0f 1
tn lbOPsf] ;dtnLo cfs[ltsf] gfd nv] L eh' fx¿ / zLifl{ aGb'x¿sf] gfd nV] gx' f];\ M
(i) A (ii) P S
BC QR
(iii) M P Q T
O S
N (iv)
R
;dfwfg
(i) lqe'h ABC (ii) ju{ PQRS
eh' fx¿ AB, BC, CA e'hfx¿ PQ, QR, RS, SP
zLif{laGb'x¿ A, B, C xg' \ . zLif{laGb'x¿ P, Q, R, S xg' \ .
ul0ft, sIff $ 9
(iii) cfot MNOP (iv) rte' h'{ QRST
e'hfx¿ MN, NO, OP, PM e'hfx¿ QR, RS, ST, TQ
zLif{laGb'x¿ M, N, O, P x'g\ . zLifl{ aGbx' ¿ Q, R, S, T xg' \ .
pbfx/0f 2
lbOPsf] lrq cjnf]sg ugx'{ f;] \ . ;dtnLo cfsl[ tx¿sf] eh' fx¿ / lzif{laGb'x¿sf]
gfd n]Vgx' f];\ M
AD P
B CQ R
L O
TS
M NU Z E
V Y F I
W X G H
;dfwfg (iv) k~re'h EFGHI df
(i) ju{ ABCD df e'hfx¿ EF, FG, GH, HI, IE
eh' fx¿ AB, BC, CD, DA zLifl{ aGb'x¿ E, F, G, H, I x'g\ .
zLif{laGb'x¿ A, B, C, D x'g\ . (v) ci6e'h STUVWXYZ df
(ii) lqeh' PQR df e'hfx¿ ST, TU, UV, VW, WX, XY,
eh' fx¿ PQ, QR, RP
zLifl{ aGbx' ¿ P, Q, R xg' \ . YZ, ZS
(iii) cfot LMNO df
e'hfx¿ LM, MN, NO, OL zLifl{ aGbx' ¿ S, T, U, V, W, X, Y, Z xg' \ .
zLif{laGbx' ¿ L, M, N, O xg' \ .
ul0ft, sIff $
10
1.2.3 ;dtnLo cfsl[ tx¿sf] eh' fsf] gfk (Measurement of sides of plane figures)
ljm| ofsnfk 1
?n/ / rfFbsf] ko| f]u u/L tn lbOPsf ;dtnLo cfs[ltx¿sf] e'hfsf] gfk lnO{
sIffsf]7fdf k:| t't ug'x{ f];\ M
(i) (ii)
A DX
Z
B C Y T
H
(iii) (iv)
G
C P
D Q
EF RS
lj|mofsnfk 2
kfFr kfFr hgfsf] ;dx" df a:gx' f;] \ . tn lbOPsf 7f;] j:tx' ¿nfO{ sfkLdf /fvL Pp6f
;txsf] 6];« ug{x' f];\ . pSt cfsl[ tx¿sf e'hfsf] gfk s;/L kQf nufpgx' 'G5, 5nkmn
u/L k|:t't ug'{xf;] \ M
(i) (ii)
(iii) (iv)
ul0ft, sIff $ 11
pbfx/0f 1
O/h] / / cfotsf/ ;fa'gnfO{ sfkLdf 6«;] u/]/ lsgf/fx¿sf] nDafO kQf nufpg'xf];\ M
;dfwfg lzIfsnfO{ bv] fpgx' f];\ .
cEof;
1. vfnL 7fpF eg'x{ f;] \ M cf]6f zLifl{ aGb' xG' 5g\ .
(i) lqeh' df x'G5g\ .
(ii) ju{sf ;a} eh' fx¿
(iii) cfotsf ;Ddv' eh' fx¿ x'G5g\ .
2. ?n/sf] k|ofu] u/L tnsf] h:t} juf{ª\lst sfuhdf lgDg nDafO ePsf] jus{ f]
lrq agfpg'xf];\ .
(a) 5 PsfO (b) 6 PsfO (c) 7 PsfO
ul0ft, sIff $
12
3. ?n/sf] ko| fu] u/]/ rf/ cf]6f ;dtnLo cfs[lt agfpg'xf];\ . C
4. tnsf cfsl[ t x/] ]/ o;sf eh' f / zLifl{ aGb'x¿sf] gfd n]Vgx' f;] \ M
(i) (ii)
A CA
BB
(iii) R (iv) M P
P S N O
Q
5. tn lbOPsf cfsl[ tsf] e'hfsf] gfk ?n/sf] ;xfotfn] gfk]/ nV] g'xf;] \ M
(i) (ii) (iii) K
A E HI
D
B C F G J
S
(iv) (v)
R
L P
13
P
M O
N Q
ul0ft, sIff $
6. tLgcf6] f eh' f ePsf km/s km/s tLgcf]6f ;dtnLo cfs[ltx¿ agfpg'xf];\ /
?n/sf] ;xfotfn] eh' fx¿ gfk/] n]Vgx' f;] \ .
7. tnsf ;dtnLo cfs[ltsf e'hfx¿sf] gfd / gfk n]Vg'xf;] \ M
(i) (ii) O
C P
M N
B
A P
(iii) Q
T
SR
kl/of]hgf sfo{ (Project work)
tkfOs{‘ f] 3/df ko| fu] ePsf s'g} kfrF cf]6f ;dtnLo ;tx ePsf j:t'x¿sf] ;ªs\ ng
u/L sfkLdf 6;]« u/L o;nfO{ sIffsf7] fdf k:| t't ug'{xf;] \ . 3/ j/k/ jf ;fj{hlgs
:yndf o:tf cfsl[ tx¿ sxL‘ ko| f]u ePsf] b]Vge' Psf] 5 < 5 eg] tL ;fdu|Lsf] gfd
l6kf6] ug'x{ f];\ .
14 ul0ft, sIff $
kf7 3 M 7f;] j:tx' ¿ (Solid objects)
3.1 kg' /jnf]sg (Review)
tnsf j:t'x¿sf] cjnf]sg u/L sg' s'gdf s:tf s:tf ;dtnLo ;tx 5g\, sIffsf]7fdf
5nkmn ug'{xf;] \ M
(i) (ii) (iii) (iv)
3.2 7f]; j:t'sf cfsf/x¿ (Shapes of solid objects)
lj|mofsnfk 1
tn lbOPsf 7f]; j:tx' ¿nfO{ p:t} p:t} cfs[ltsf] ;d"xdf 5'6o\ fP/ /fVg'xf;] \ . ;dx" df
bO' { bO' c{ f]6f cfs[lt yKg'xf;] \ M
(i) (ii) (iii)
(iv) (v) (vi)
ul0ft, sIff $ 15
tnsf 7f;] cfsl[ t / o;sf ef}lts gd'gf xg] x'{ f];\ M
cfsl[ tsf] gfd ef}lts gd'gf -pbfx/0f_
3g
nª\u/' ah' fs{ f] uf6] L ?la|S; 3gfsf/ afs;
cfotsf/ if8\dv' f
k:' ts ;'6s;] h';sf] a66\ f
3gsf] ;a} ;tx ;dtnLo / jufs{ f/ x'G5g\ .
ljm| ofsnfk 2
pkoS' t ;ª\Vofdf ;d"xsf] lgdf{0f ug'{xf];\ x/]s ;d"xn] Pp6f Pp6f 7f;] j:t' lng'xf;] \ .
pSt 7f]; j:t'sf] cjnf]sg u/L hDdf sltcf6] f ;tx 5g\ / s:tf 5g\ .
(i) (ii) (iii) (iv)
n8' f]sf] uf]6L lrofsf] a66\ f ld7fO{sf] afs; rssf] a66\ f
dflysf ;a} 7f;] j:t'x¿df 6/6 cf]6f ;dtnLo ;tx 5g\ . n8' fs] f] uf]6L / rssf]
a66\ fsf ;a} ;tx juf{sf/ 5g\ . To;}n] oL j:tx' ¿ 3gfsf/ j:t' x'g\ . lrofsf] a6\6f
/ ld7fO{sf] afs;sf ;a} ;tx cfotsf/ 5g\ / ljk/Lt ;tx a/fa/ 5g\ . To;n} ] oL
j:t'x¿ cfotsf/ if8\dv' f x'g\ .
16 ul0ft, sIff $
pbfx/0f 1
tnsf 7f;] j:t'sf] cfsf/ s:tf] 5, x/] /] eGgx' f;] \ M
(i) (ii) (iii) (iv)
;dfwfgM (i) cfotfsf/ if8\d'vf (ii) cfotfsf/ if8d\ 'vf
(iii) 3gfsf/ (iv) cfotfsf/ if8d\ 'vf
cEof; 3
1. tnsf k|Tos] 7f]; j:t'sf] gfd / cfsf/ s:tf] 5, n]Vgx' f;] \ M
(i) (ii) (iii)
(iv) (v)
2. 3gfsf/sf b'Oc{ f]6f / if8\d'vfsf/sf b'O{cf6] f :yfgLo 7f;] j:t'x¿sf] gfd
nV] g'xf;] \ .
ul0ft, sIff $ 17
3.3 7f;] j:ts' f] ;tx, lsgf/f / zLifl{ aGb' (Faces, edges and vertices of solid objects)
ljm| ofsnfk 1
tn nu' f w'g] ;fa'gsf] lrq lbOPsf] 5 . lrqsf] cjnfs] g ug'{xf];\ . o;df sltcf]6f
;dtnLo ;tx 5g\ < lsgf/f / s'gfx¿ slt sltcf6] f 5g,\ n]Vgx' f];\ / sIffsf7] fdf
k|:t't ug{'xf];\ .
lj|mofsnfk 2
lzIfssf] ;xfotfdf h;' kfOk jf ux'Fsf] 5\jfnL jf l;Gsfaf6 3g / if8d\ v' fsf vf]jm| f]
gdg' f lgdf{0f ug{'xf];\ . pSt 3g / if8\dv' fsf] ;txdf km/s km/s /ªsf] sfuh
6fF;L ;tx 56' o\ fpg'xf];\ . 3g / if8d\ 'vfdf sltcf]6f ;tx lsgf/f / zLifl{ aGb' 5g,\
sIffsf]7fdf k:| t't ug{'xf];\ .
h'; kfOkx¿ hfl] 8Psf] s'gfnfO{ zLifl{ jGb' elgG5 . h;' kfOkx¿ hf]l8P/ ag]sf] aGb
;dtnLo cfs[lt ;tx xf] eg] bO' {cf]6f ;txx¿ hf]l8Psf] :yfgnfO{ lsgf/f elgG5 .
18 ul0ft, sIff $
pbfx/0f 1
(i) tnsf 7f;] j:t'sf] ;tx, zLif{ljGb' / lsgf/fx¿ b]vfpgx' f];\ M
;dfwfg
lsgf/f ;tx
zLifl{ jGb'
;tx
zLif{ljGb' lsgf/f
(ii) tnsf] 7f]; j:t'sf] ;tx, zLifl{ jGb' / lsgf/fx¿sf] gfd nV] g'xf;] \ .
A D ;dfwfg
B C ;txx¿ M ABCD, AEFB, BFGH, CGHD,
AEHD, EFGH
E H lsgf/fx¿ M AB, BC, CD, DA, AE, EF, FB,
F G FH, GH, EH, GC
zLifl{ jGbx' ¿ M A, B, C, D, E, F, G, H
cEof;
1. tn lbOPsf] cfsl[ t h:t} 7f;] j:t'sf] lgdf{0f u/L o;sf zLif{ljGb', lsgf/f /
;tx bv] fpgx' f];\ M
19
ul0ft, sIff $
2. tnsf 7f;] j:t' jf o:t} ;fdu|Lsf ;tx, zLif{ljGb' / lsgf/f b]vfpg'xf;] \ M
(i) (ii) (iii)
(iv) (v) (vi)
3. tnsf 7f;] j:t'sf ;tx, zLifl{ jGb' / lsgf/f s] s] x'g,\ nV] g'xf];\ .
AD
;txx¿ M
B C zLif{ljGb'x¿ M
E F lsgf/fx¿ M
HG
4. tnsf] 7f;] j:ts' f] zLifl{ jGb'sf gfds/0f u/L ;tx / lsgf/fx¿ n]Vg'xf;] \ .
;txx¿ M
zLif{ljGb'x¿ M
lsgf/fx¿ M
kl/of]hgf sfo{ (Project work)
1. tkfOsF{ f] 3/df ko| fu] ug]{ kfFr kfFrcf6] f 3gfsf/, if8\d'vfsf/ j:tx' ¿ ;ªs\ ng
u/L ltgLx¿sf] gfd;lxt sIffsf]7fdf k:| tt' ug'x{ f];\ . cfotfsf/ if8\dv' f /
3gsf] df]8n tof/ ugx{' f];\ .
20 ul0ft, sIff $
ldl>t cEof;
1. ldNg] pQ/df ufn] f] -_ 3]/f nufpgx' f;] \ M
(i) rfbF df tnsf] l;wf /]vfnfO{ s] elgG5 <
(a) ;/n /]vf (b) cw{jQ[ fsf/ (c) cfwf/ /v] f (d) k0" f{ /]vf
(ii) if8d\ 'vfdf sltcf]6f lsgf/f x'G5g\ <
(a) 6 (b) 8 (c) 12 (d) 16
(iii) tnsf dWo] s'g 3gfsf/ j:t' xf] <
(a) an (b) ;nfOs{ f] a6\6f (c) lstfa (d) 8fO;
(iv) d rf/cf6] f e'hf ePsf] / ;a} sf]0f a/fa/ ePsf] aGb cfsl[ t x'F eg] d s] x'F <
(a) lqe'h (b) cfot (c) ju { (d) j[Q
(v) d rf/cf]6f a/fa/ eh' f ePsf] / ;a} sf0] f a/fa/ ePsf] aGb cfs[lt xF' eg] d
s] xF' <
(a) lqeh' (b) cfot (c) ju{ (d) j[Q
2. vfnL 7fpFdf ldNg] zAb egx{' f];\ M
(i) Pp6f lqeh' df cf6] f e'hfx¿ x'G5g\ .
(ii) rt'e'{hdf cf6] f zLif{ljGbx' ¿ x'G5g\ .
(iii) k~reh' df cf]6f e'hfx¿ xG' 5g\ .
(iv) lbOPsf] sf0] fnfO{ nl] vG5 .
A
BC
3. ?n/sf] k|of]u u/L tn lbOPsf /v] fv08x¿ gfKg'xf;] \ M
(i) A B (ii) C
ul0ft, sIff $ D
21
(iii) (iv)
FG
EH
4. lbOPsf ljGb'x¿ hf]8g\ 'xf;] \ / o;/L aGg] /v] fv08sf] gfk kQf nufpg'xf];\ M
(i) P (ii)
Y
Q X
(iii) (iv) P
M O
N
5. tn lbOPsf] gfkcg';f/sf /]vfv08 cfˆgf] sfkLdf lvRgx' f];\ M
(i) 5 cm (ii) 7 cm (iii) 4.5 cm
(iv) 10 cm (v) 9.5 cm
6. lbOPsf 7f];j:t' s:tf] cfsf/sf 5g,\ n]Vgx' f;] \ M
7. tkfO{n‘ ] ko| f]u ug]{ bO' c{ f6] f ;dtnLo ;tx ePsf] j:ts' f] gfd n]Vg'xf;] \ .
8. rfbF sf] ko| f]u u//] tnsf sf]0fx¿sf] gfKgx' f];\ / n]Vgx' f;] \ M
(i) (ii) (iii)
A
X
PY
B C Q R Z
22
ul0ft, sIff $
(iv) (v) (vi)
I LN Y
J K M WX
9. rfbF sf] ko| f]u u/]/ tnsf sf]0fsf] /rgf ugx'{ f;] \ M
(i) 30o (ii) 60o (iii) 70o (iv) 90o
(v) 110o (vi) 150o
10. tn lbOPsf cfs[ltx¿sf] zLifl{ jGb' / eh' fsf] gfd nV] g'xf;] \ M
(i) (ii) (iii)
AD P G
D
B Q R E F
C
11. ?n/sf] ;xfotfn] tnsf cfs[ltsf] eh' fx¿ gfk/] n]Vg'xf;] \ M
(i) (ii)
AP
S
B C QR
(iv)
(iii)
X
MP
N O Y
ul0ft, sIff $ Z
23
12. lbOPsf 7f];j:ts' f] zLifl{ jGb', lsgf/f / ;tx 5'6o\ fpgx' f];\ M
(i) (ii) (iii)
13. tnsf lrqsf] cjnfs] g ug'{xf;] \ / ;f]lwPsf kZ| gx¿sf] pQ/ lbg'xf];\ M
(a) (b)
D D
A BC AB
C
(i) dflysf] lrqdf ∠ABD / ∠CBD gfkL nV] g'xf;] \ .
(ii) 7n' f] sf0] f / ;fgf] sf]0f 5'6o\ fpgx' f;] \ .
(iii) ;fgf] sf]0fnfO{ 7'nf;] Fu a/fa/ agfpg slt hf]8\gk' 5{ <
14. Pp6f 5 cm nfdf] eh' f AB lvRg'xf;] \ . A / B b'jd} f 800 sf] sf]0f lvRg'xf];\ . tL
e'hfx¿ sfl6Psf] ljGb'nfO{ C gfds/0f ug{'xf];\ M
(i) ca s] sf] lrq aGof] < gfd nV] g'xf;] \ .
(ii) eh' fx¿ BC / AC sf] gfk nV] g'xf;] \ .
(iii) AC / BC sf] ;DaGw s] 5, nV] g'xf;] \ .
15. Pp6f 6 cm nfdf] e'hf PQ lvRgx' f];\ . P / Q b'jd} f 600 sf] sf0] f lvRgx' f];\ . P
/ Q af6 /v] f sfl6Psf] ljGb'nfO{ R gfds/0f ug'{xf;] \ M
(i) e'hfx¿ PR / QR sf] gfk n]Vgx' f];\ .
(ii) ∠PQR sf] gfk gfk]/ n]Vg'xf;] \ .
(iii) lqeh' PQR sf e'hfx¿lar s:tf] ;DaGw 5, nV] g'xf];\ .
(iv) lqe'h PQR sf sf0] fx¿lar s:tf] ;DaGw 5, nV] gx' f];\ .
24 ul0ft, sIff $
16. tn lbOPsf nDafO / rf8} fOx¿nfO{ juf{ª\lst sfuhdf PsfO uGtL ub{} /v] f
tfg/] cfot agfpg'xf;] \ M
(i) nDafO = 6 PsfO, rf}8fO = 3 PsfO
(ii) nDafO = 3 PsfO, rf8} fO = 2 PsfO
(iii) nDafO = 5 PsfO, rf}8fO = 4 PsfO
17. tnsf lrqsf] cjnfs] g ugx{' f];\ / ;f]lwPsf k|Zgx¿sf] pQ/ lbg'xf];\ M
(a) (b)
A P
B CQ R
(i) dflysf] lrqdf ;a} sf]0fx¿ gfk]/ sfkLdf n]Vgx' f;] \ .
(ii) ;a} eh' fx¿ gfk/] n]Vg'xf;] \ .
(iii) ;aeGbf 7'nf] sf0] f / nfdf] e'hflar s:tf] ;DaGw 5, nV] gx' f];\ .
(iv) ;aeGbf ;fgf] sf0] f / 5f6] f] e'hflar s:tf] ;DaGw 5, n]Vgx' f];\ .
ul0ft, sIff $ 25
kf7 4 M ;ª\Vofsf] 1fg (Number sense)
4.1 kg' /jnf]sg (Review)
tkfO‘{sf] kl/jf/sf] ;b:o ;ªV\ of slt 5 < tkfO{s‘ f] 6f]ndf ePsf] hg;ª\Vof slt
xf]nf < tkfO{s‘ f] lhNnfsf] hg;ªV\ of slt xf]nf <
g]kfnsf] hDdf hg;ªV\ of slt xf]nf < s] tL ;an} fO{ uGtL ug{ ;Dej 5 < cj:o
5 . To;/L ;a} kmnkm" nsf] ;ªV\ of / ;a} hg;ªV\ of uGtL ugs{ f] nflu xfdLn] uGtLsf
;ª\Vofx¿ ko| f]u u5f{}‘ . h:t} M 1, 2, 3 ... . xfd|f k'vf{x¿n] uGtLsf ;ª\Vofx¿sf] ljsf;
x'ge' Gbf cufl8 j:t'x¿sf] u0fgf s;/L uy]{ < ;f] ;DaGwdf lzIfs;uF 5nkmn ug{'xf];\ .
xfd|f kv" fx{ ¿n] ;ªV\ ofsf] k|ofu] ;'? xg' 'eGbf klxnf klg j:tx' ¿sf] u0fgf uy]{ .
;?' df cfˆgf kl/jf/sf ;b:ox¿ / cfˆgf 3/kfnj' f hgfj/x¿sf] ;ª\Vof yfxf kfpg
e'O{‘df wsf{ tfGg], leQfdf wsf{ tfGg] uy{] . lbgel/ vfg]s/' f vf]Hg 3/af6 lg:sbF f
kl/jf/sf ;b:o / wsf{ Ps Ps ;ªu\ lt xg' ] u/L e'O{d‘ f tfGy] . a]n'sL kms]k{ l5 kg' M
kl/jf/sf ;b:o / eO' ‘d{ f tfgs] f wsf{ Ps Ps ;ªu\ lt xg' ] u/L d]6y\ ] . olb eO' d‘{ f
wsf{ afsF L /xd] f kl/jf/sf] ;b:o x/fPsf] yfxf kfP/ vfh] L uy{] . e'O‘{df wsf{ sfb] f{
d]l6g] ePsfn] leQfdf wsf{ tfGg yfn] . kl5 kl5 9'ªu\ f jf 5]:sfnfO{ Ps Ps
;ªu\ lt ug]{, n67\ Ldf lrx\g nufpg], 8f]/Ldf uf7F f] kf//] j:t'x¿sf] u0fgf ug{] h:tf
ljm| ofsnfk u/]sf] kfOG5 .
ljsf;j|md;Fu} dflg;x¿n] j:tx' ¿sf] u0fgf ug{ ;ªV\ ofx¿sf] k|of]u ug{ yfn] .
;ªV\ ofx¿sf] ljsf;jm| ddf a]lanfl] gog, OlhlK;og, /f]dg, hfkflgh, rfOlgh, lus| ,
lxGb' c/]lasx¿sf] dxìjk0" f{ e"ldsf /xs] f] 5 . xfdLn] ko| f]u ug]{ ;ª\Vof k|0ffnL lxGb'
c/l] as ;ªV\ of k|0ffnL xf] . o; k0| ffnLdf 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 u/L 10 cf6] f
cª\sx¿sf] k|ofu] x'G5 . of] ;ª\Vof k|0ffnL bzdnj ;ªV\ of k0| ffnL xf] .
26 ul0ft, sIff $
4.2 ;ft cªs\ ;Ddn] ags] f ;ªV\ ofx¿ (Numbers formed upto seven digits)
(A) :yfgdfg (Place Value)
ljm| ofsnfk 1
xfdLn] tLg sIffdf g} kfFr cªs\ n] ags] f ;ª\Vofx¿ nV] g / k9\g l;ls;ss] f 5fF} t;y{
oxfF xfdLn] ;ft cª\sn] ags] f ;ª\Vofx¿ nV] g / k9\g l;Sg] 5f}F . To;sf nflu tnsf]
tflnsf cWoog ugx'{ f];\ M
slt cª\sn] ag]sf] ;ªV\ of ;fªl\ Vos gfd
Ps cªs\ n] ags] f] ;a}eGbf ;fgf] ;ªV\ of 1 Ps (one)
b'O{ cªs\ n] ags] f] ;ae} Gbf ;fgf] ;ªV\ of 10 bz (Ten)
tLg cª\sn] ags] f] ;a}eGbf ;fgf] ;ªV\ of 100 ;o (Hundred)
rf/ cªs\ n] ags] f] ;ae} Gbf ;fgf] ;ªV\ of 1000 xhf/ (Thousand)
kfrF cª\sn] ags] f] ;ae} Gbf ;fgf] ;ªV\ of 10000 bz xhf/ (Ten Thousand)
5 cªs\ n] ags] f] ;ae} Gbf ;fgf] ;ªV\ of 100000 nfv (Lakh)
;ft cª\sn] ag]sf] ;a}eGbf ;fgf] ;ªV\ of 1000000 bz nfv (Ten Lakh)
1000000 nfO{ :yfgdfg tflnsfdf /fVbf,
bz nfv nfv bz xhf/ xhf/ ;o bz Ps
1000000
lj|mofsnfk 2
;Fu} lbOPsf] Ans cjnfs] g u/L tnsf] :yfgdfg tflnsfdf cª\s eg{x' f;] \ M
xhf/ ;o bz Ps
xhf/ ;o bz Ps
ul0ft, sIff $ 27
lrqdf 4 cf6] f Ps, 3 cf6] f bz, 2 cf]6f ;o / 3 cf6] f xhf/ 5g\ t;y{ :yfgdfg
tflnsfdf cª\sx¿ ebf{ lgDgfg';f/ x'G5 M
xhf/ ;o bz Ps
3 2 34
cªs\ df M 3,234
cIf/df M tLg xhf/ b'O{ ;o rf}lt;
ljm| ofsnfk 3
;Fu} lbOPsf] cafs; x]/L :yfgdfg tflnsfdf cª\sx¿ eg{'xf];\ M
bz nfv nfv bz xhf/ xhf/ ;o bz Ps
bz nfv nfv bz xhf/ xhf/ ;o bz Ps
lrqdf lbOPsf] cafs;df 7 cf]6f Ps, 3 cf6] f bz, 5 cf]6f ;o, 7 cf6] f xhf/, 4
cf6] f bz xhf/, 1 cf6] f nfv / 4 cf6] f bz nfv 5g\, ;a}nfO{ lgDgfg;' f/ :yfgdfg
tflnsfdf k:| t't ug{ ;lsG5 M
bz nfv nfv bz xhf/ xhf/ ;o bz Ps
41 4 7537
28 ul0ft, sIff $
lj|mofsnfk 4
;ft ;dx" df a:g'xf];\ . k|Tos] ;dx" sf] kl| tlglwTj bz nfv 5
ug{] u/L Ps÷Ps hgf kfnk} fnf] cufl8 cfpg'xf];\ 2 ;o
/ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 nl] vPsf] ;ªV\ ofklQ
lnP/ km/s km/s ef8F fdf Ps÷Ps cf]6f 8 9
;ª\VofklQ /fVgx' f];\ . ;a} ;d"xn] kT| os] ef8F fdf nfv bz
/fv]sf cª\sklQx¿ x/] L pSt cªs\ x¿af6 aGg]
;ªV\ ofnfO{ :yfgdfg tflnsfdf k|:tt' u/L sIffdf bz xhf/
5nkmn ug{'xf;] \ . 3
h:t} M ljBfyL{x¿n] jm| d;} Fu Ps, bz, ===== bz nfv 6
n]lvPsf] efF8fdf 1, 9, 5, 6, 3, 8 / 2 v;fn5] g\ . xhf/
1
Ps
ca :yfgdfg tflnsfdf k|:t't ul/;sk] l5 tnsf kZ| gx¿sf] pQ/ lbgx' f];\ .
(i) nfv n]lvPsf] efF8fdf sg' ;ªV\ of 5 <
(ii) 3 slt n]lvPsf] efF8fdf 5 <
(iii) 8 nfv nl] vPsf] ef8F fdf ePsf] cª\ssf] hDdf dfg slt xfn] f <
(iv) efF8fdf v;flnPsf] ;a} cª\sx¿n] agfpg] ;ª\Vof slt xfn] f <
o;/L ef8F fdf v;flnPsf ;a} cªs\ x¿n] agfpg] ;ªV\ of 2836591 x'G5 . ;ª\Vofdf
/xs] f cªs\ sf b'Oc{ f6] f dfgx¿ x'G5g\ . Pp6f b]lvg] dfg / csf]{ :yfgdfg . 8 sf]
bl] vg] dfg 8 g} xG' 5 . nfv nl] vPsf] efF8fdf 8 5, To;n} ] 8 sf] :yfg nfv x'G5 . To;n} ]
8 sf] :yfgdfg 1,00,000 × 8 = 8,00,000 x'G5 .
;ªV\ ofdf /x]sf cª\sx¿sf 3 cf6] f dfg xG' 5g\ . klxnf] b]lvg] dfg (face value)
/ bf;] |f] :yfg (place) / :yfgdfg (place value) . h:t}M 2832510 df 5 sf] b]lvg]
dfg 5 g} xf] eg] :yfg ;o xf] . To;n} ] 5 sf] :yfgdfg 100 × 5 = 500 x'G5 .
ul0ft, sIff $ 29
pbfx/0f 1
56,33,431 nfO{ :yfgdfg tflnsfdf k|:t't u/L 6 sf] bl] vg] dfg, :yfg / :yfg dfg
nV] g'xf;] \ .
;dfwfg
oxfF ;ª\Vof 56,33,431 nfO{ :yfgdfg tflnsfdf k|:t't ubf{,
bz nfv nfv bz xhf/ xhf/ ;o bz Ps
5633431
6 sf] bl] vg] dfg Ö6
6 sf] :yfg Ö nfv
6 sf] :yfgdfg Ö 6 × 1,00,000 Ö 6,00,000
(B) lj:tfl/t ¿k (Expanded Form)
sg' } klg ;ª\VofnfO{ pSt ;ª\Vofsf] x/]s cª\s / ;DalGwt cªs\ /x]sf :yfg ae' mfpg]
dfgnfO{ u0' fg u/L ofu] kmnsf ¿kdf k|:tt' ugn{' fO{ pSt ;ªV\ ofsf] lj:tfl/t ¿k
elgG5 .
pbfx/0f 2
;ªV\ of 57,34,298 nfO{ lj:tfl/t ¿kdf nV] gx' f];\ M
;jk{ y| d :yfgdfg kQf nufpbF f,
5 7 3 4 2 9 8 :yfg :yfgdfg
Ps (ones) 8 × 1 = 8
bz (Tens) 9 × 10 = 90
;o (Hundreds) 2 × 100 = 200
xhf/ (Thousands) 4 × 1000 = 4,000
bz xhf/ (Ten Thousands) 3 × 10,000 = 30,000
nfv (Lakhs) 7 × 1,00,000 = 7,00,000
bz nfv (Ten Lakhs) 5 × 10,00,000 = 50,00,000
ca, 57,34,298 = 5 × 10, 00, 000 + 7 × 1,00,000 + 3 × 10,000 + 4 × 1,000 +
2 × 100 + 9 × 10 + 8 × 1
30 ul0ft, sIff $
cEof;
1. vfnL 7fpF egx'{ f;] \ M
(i) ;ªV\ of 23,19,891 df 2 sf] b]lvg] dfg ============= xf] .
(ii) ;ªV\ of 18,79,312 df 8 sf] :yfgdfg ============= xf] .
(iii) ;ª\Vof 71,83,294 df 3 sf] :yfgdfg ============= xf] .
(iv) 10,53,216 df bz nfvsf] :yfgdf cª\s ============= 5 .
2. tnsf k|Tos] ;ª\Vofx¿nfO{ :yfgdfg tflnsfdf k:| tt' u/L 5 sf] :yfg dfg
nV] gx' f;] \ M
(i) 93,45,281 (ii) 51,68,719 (iii) 12,67,815
(iv) 34,51,229 (v) 27,35,869 (vi) 83,651
3. tnsf ;ªV\ ofx¿df nfvsf] :yfgdf /xs] f] cªs\ sf] :yfgdfg nV] g'xf;] \ M
(i) 52,34,564 (ii) 10,05,301 (iii) 9,75,608
(iv) 5,63,204
4. tnsf kT| o]s ;ªV\ ofx¿df ufn] f] 3/] f nufOPsf] cª\ssf] :yfgdfg n]Vgx' f];\ M
(i) 1 2 ,45,389 (ii) 2 4,68,135 (iii) 24,5 3 ,289
(iv) 89, 3 4,208
5. tnsf kT| o]s ;ªV\ ofx¿nfO{ lj:tfl/t ¿kdf nV] gx' f];\ M
(i) 34,758 =
(ii) 5,00,230 =
(iii) 8,00,201 =
(iv) 13,25,614 =
(v) 19,82,543 =
(vi) 67,89,123 =
6. tnsf] lj:tfl/t ¿knfO{ 5f6] s/Ldf nV] g'xf;] \ M
(i) 5 × 1,00,000 + 3 × 10,000 + 2 × 1000 + 6 × 100 + 9 × 10 + 4 × 1
ul0ft, sIff $ 31
(ii) 2 × 10,00,000 + 0 × 1,00,000 + 0 × 10,000 + 4 × 1,000 + 3 × 100 +
2 × 10 + 6 × 1
(iii) 4 × 10,000 + 5 × 1,000 + 7 × 100 + 8 × 10 + 9 × 1
(iv) 6 × 10,00,000 + 8 × 1,00,000 + 0 × 10,000 + 4 × 1,000 + 0 × 100 +
2 × 10 + 7 × 1
(v) 8 × 10,00,000 + 5 × 10,000 + 0 × 1,000 + 4 × 100 + 7 × 10 + 3 × 1
kl/of]hgf sfo{ (Project work)
1. cfˆgf cleefjs jf lzIfs;Fu ;fw] ]/ tkfOs‘{ f] :yfgLo txsf] hg;ª\Vof kQf
nufO{ :yfgdfg tflnsfdf k:| tt' ugx'{ f];\ .
2. dfly pNn]v ePsf] ;ª\VofeGbf km/s vfnsf uGtL ug]{ ;ªV\ of k4lt
tkfOxF{ ¿nfO{ yfxf 5 < cfˆgf cleefjsnfO{ ;f]wL tL ;ªV\ ofx¿ s'g sg'
:yfgdf ko| fu] ePsf 5g,\ ;r" L tof/ kfg{x' f;] \ .
32 ul0ft, sIff $
4.3 ;ft cªs\ ;Ddsf ;ªV\ ofx¿ cIf/ (Numbers up to seven digits in words)
lj|mofsnfk 1
tnsf :yfgdfg tflnsfsf] cWoog u/L ;f]lwPsf k|Zgsf] pQ/ lbg'xf;] \ M
bz nfv nfv bz xhf/ xhf/ ;o bz Ps
7 1 2 6 530
(i) hDdf slt nfv 5 <
(ii) hDdf slt xhf/ 5 <
(iii) hDdf slt ;o 5 <
(iv) clGtd bO' { cª\sn] ags] f] ;ª\Vof slt xf] <
(v) dflysf ;ªV\ ofnfO{ s;/L nV] g] / k9g\ ] xfn] f <
dfly lbOPsf ;ªV\ ofnfO{ k9b\ f PsxQ/ nfv 5lAa; xhf/ kfrF ;o tL; (Seventy
one lakh twenty six thousand five hundred and thirty) eg]/ kl9G5 eg] pSt
;ª\Vof nV] bf 71,26,530 nl] vG5 .
;ªV\ ofnfO{ cª\sdf n]Vbf bfofFaf6 afofFlt/ klxnf] tLg cªs\ cufl8 To;kl5 bO' {
b'O{ cª\s cufl8 cw{lj/fd (,) lrxg\ /flvG5 .
pbfx/0f 1
/fli6o« hgu0fgf 2068 sf cg';f/ sf7df8f}F lhNnfsf] hg;ª\Vof 17,44,240 lyof]
h;dWo] 9,13,001 k?' if / 8,31,239 dlxnf lyP . ca oL ;ª\Vofx¿nfO{ cIf/df
nV] g'xf];\ .
;dfwfg
dflysf ;ªV\ ofx¿nfO{ tflnsfdf k:| t't ubf,{
bz nfv nfv bz xhf/ xhf/ ;o bz Ps hg;ªV\ of
1 7 4 4 2 4 0 hDdf hg;ªV\ of
9 1 3 0 0 1 k'?ifsf] hg;ª\Vof
8 3 1 2 3 9 dlxnfsf] hg;ªV\ of
ul0ft, sIff $ 33
oxfF,
hDdf hg;ª\Vof = 17,44,240
hDdf k'?ifsf] hg;ª\Vof = 9,13,001
hDdf dlxnfsf] hg;ª\Vof = 8,31,239
cIf/df n]Vbf,
hDdf hg;ª\Vof Ö ;q nfv rjfln; xhf/ bO' { ;o rfln; (Seventeen lakh forty
four thousand two hundred and forty)
hDdf k'?ifsf] hg;ª\Vof Ö gf} nfv t]/ xhf/ Ps (Nine lakh thirteen thousand
and one)
hDdf dlxnfsf] hg;ª\Vof Ö cf7 nfv Pslt; xhf/ b'O{ ;o pgfGrfln; (Eight
lakh thirty one thousand two hundred and thirty nine)
pbfx/0f 2
>Lsi[ 0fn] ufOk{ fng / s'v/' fkfngsf nflu g]kfn ;/sf/n] lbg] sl[ if cg'bfgcGtut{
sl[ if ljsf; a}ª\saf6 k;} 6\7L nfv lqkGg xhf/ kfrF ;o tLg ?lkofF C0f
lnP5g\ . >Lsi[ 0fn] lnPsf] /sdnfO{ cw{lj/fd (,) lrx\gsf] ko| f]u u/L cªs\ df
nV] gx' f];\ / :yfgdfg tflnsfdf bv] fpgx' f;] \ .
;dfwfg
oxfF >Lsi[ 0fn] lnPsf] C0f,
?= 65,00,000 + ?= 53,000 + ?= 500 + ?= 3
= ?= 65,53,503
:yfgdfg tflnsfaf6 b]vfpFbf,
bz nfv nfv bz xhf/ xhf/ ;o bz Ps
6 5 5 3 503
cEof; ul0ft, sIff $
1. vfnL 7fpF eg{x' f];\ M
(i) 1215230 df hDdf ============= nfv 5 .
(ii) 2505110 df hDdf ============= nfv 5 .
34
(iii) 2000010 df hDdf ============= nfv 5 .
(iv) 7000005 df hDdf ============= nfv 5 .
2. tnsf ;ªV\ ofx¿nfO{ cwl{ j/fd (,) lbO{ cIf/df klg nV] g'xf;] \ M
(i) 2520344 (ii) 1000230 (iii) 6524000
(iv) 5820525 (v) 732008
3. cªs\ df n]Vg'xf];\ M
(i) Ps nfv Ps;6\7L xhf/ kfrF ;o 5
(ii) kfFr nfv ;QfO; xhf/ cf7 ;o
(iii) aofln; nfv t]O; xhf/ kfrF ;o aof;L
(iv) rfx} Q/ nfv gf} xhf/ ;ft ;o ;QfO;
(v) c7f;L nfv krkGg xhf/ rf/ ;o aofln;
(vi) la; nfv kfFr xhf/ kfFr
(vii) Eighty three lakh thirty thousand four hundred and one
(viii) Five lakh eight thousand four hundred and seventy three
(ix) Thirty five lakh two thousand seven hundred and ninty one
(x) Fifty one lakh twelve thousand nine hundred and twenty three
(xi) Twenty one lakh fifteen thousand three hundred and seventy five
(xii) Seven lakh six thousand and fifty seven
4. cª\u]h| L / gk] fnL b'j} dfWodaf6 cIf/df nV] gx' f];\ M
(i) 6,24,005 (ii) 25,27,003 (iii) 26,18,598
(iv) 48,02,212 (v) 24,00,005 (vi) 92,51,000
kl/of]hgf sfo{ (Project work)
1. cfˆgf] 3/sf s'g} kfFrcf]6f ;fdfgsf] d"No cleefjs;Fu ;fw] ]/ pSt dN" onfO{
:yfgdfg tflnsfdf k:| tt' ugx'{ f];\ .
ul0ft, sIff $ 35
4.4 ;ª\Vofx¿sf] z"GofGt (Rounding off of numbers)
ljm| ofsnfk 1
dfgfF}, tkfO{‘sf] ljBfnoaf6 3/ 100 m 6f9f 5 . tkfO{‘ ljBfnoaf6 3/ hfbF f olb kfgL
k¥of] eg] ljBfno / 3/sf lardf cft] nfUg] 7fpF 5}g / tkfO‘{;Fu 5ftf klg 5g} eg]
tnsf] cj:yfdf s] ug{'xG' 5, lsg < 5nkmn ugx{' f;] \ .
(i) ljBfnoaf6 20 m lx8F k] l5 kfgL k/d] f
(ii) ljBfnoaf6 50 m lxF8k] l5 kfgL k/]df
(iii) ljBfnoaf6 60 m lx8F k] l5 kfgL k/d] f
(iv) ljBfnoaf6 85 m lx8F k] l5 kfgL k/]df
ljm| ofsnfk 2
;a} ljBfyL{x¿sf] hDdf 2 cf6] f ;dx" agfP/ ljBfnosf] rp/df hfgx' f];\ . rp/df
tnsf] h:t} ;ªV\ of/]vf agfpgx' f;] \ .
;'? clGtd
0 1 2 3 4 5 6 7 8 9 10
;?' clGtd
Ps ;d"xsf ljBfyL{x¿ ;ªV\ of/]vfsf] Psflt/ / csf{] ;dx" sf ljBfyLx{ ¿ csf{]lt/
a:gk' g]{ 5 . ca k|To]s ;dx" af6 1/1 hgf v]n v]Ng cufl8 cfpg] 5g\ / lhTgn] ]
1 cªs\ kfpg] 5 . cGtdf ;ae} Gbf a9L cª\s Nofpg] ;dx" nfO{ ljht] f 3fl] ift u/L
ul/g] 5 . v]nsf] lgod o;k|sf/ 5 M
(i) ;ª\Vof /]vfsf] dfly / tn b'O{ ;d"xaf6 1/1 hgf ;'?sf] laGbd' f pleg] 5g\ .
(ii) Ps hgf dfbn ahfpg] JolSt xg' ] 5 / p;n] dfbn ahfO/xbF f cfˆgf Ifq] k6l\ 6
/xs] f] sf]7fdf km8s\ f] df/L lxF8\gk' g]{ 5 .
(iii) dfbn aHg aGb ePkl5 hf] hxfF 5 pm ToxL‘ plegk' g{] 5 . olb 5 jf 5 eGbf
dflysf cªs\ x¿;uF } /xs] f] sf7] fdf plePsf] JolSt clGtd sf7] fdf uP/ plegk' g{]
5 / 5 eGbf ;fgf] cªs\ sf] sf7] fdf plePsf] JolSt ;?' sf] sf7] fdf uP/ plegk' g{]
5.
36 ul0ft, sIff $
(iv) h;n] lgodsf] ;xL kfngf u/L a9L cªs\ Nofp5F p;nfO{ ljht] f 3fl] ift ul/g] 5 .
lj|mofsnfk 3
lbbL, tkfO;‘{ Fu d;Fu ?= 50 hlt
slt ?lkofF 5 < 5.
;Gtf]ifn] ug]/ x]/] t/ uGbf hDdf ?= 48 /x5] .
lbbL, tkfO‘{ t s:tf] dnfO{ 10, 20, 30, 40, 50 cflb cGTodf zG" o
96F j' f x'g' xF'bf] /x]5 Û ePsf ;ªV\ of uGg ;lhnf] 5 / glhssf]
;ª\Vof 50 ePsfn] ?= 50 egs] f] x'F .
6f9f glhs
4 0 41 42 43 44 45 46 47 4•8 49 50
;ªV\ of/v] fdf 50 sf] glhs 48 5 t/ 40 af6 6f9f 5 . o;/L lbOPsf ;ª\VofnfO{ 10,
20, 30, ..., 100, 200, 300, ... cflb clGtddf z"Go ePsf] glhssf] ;ªV\ ofdf n]Vg]
tl/sfnfO{ ;ªV\ ofx¿sf] z"GofGt elgG5 .
glhssf] bzdf zG" ofGt ul/Psf ;ªV\ ofx¿ M 10, 20, 30, ..., 120, 150, ..., 2350
cflb .
glhssf] ;odf zG" ofGt ul/Psf ;ªV\ ofx¿ M 100, 200, ..., 2300 cflb .
ul0ft, sIff $ 37
pbfx/0f 1
37 nfO{ glhssf] bzdf z"GofGt ugx'{ f;] \ .
;dfwfg
6f9f glhs
30 31 32 33 34 35 36 3•7 38 39 40
40 sf] glhs 37 kg]{ ePsfn] 37 nfO{ glhssf] bzdf z"GofGt ubf{ 40 xG' 5 .
pbfx/0f 2
563 nfO{ glhssf] bzdf zG" ofGt ugx'{ f;] \ .
;dfwfg
glhs 6f9f
560 561 562 56•3 564 565 566 567 568 569 570
560 sf] glhs 563 kg{] ePsfn] 563 nfO{ glhssf] bzdf z"GofGt ubf{ 560 xG' 5 .
pbfx/0f 3
45 nfO{ glhssf] bzdf z"GofGt ug'{xf;] \ .
;dfwfg
a/fa/ a/fa/
40 41 42 43 44 4•5 46 47 48 49 50
40 / 50 af6 a/fa/ b/' Ldf 45 kg]{ ePsfn] 45 nfO{ glhssf] bzdf z"GofGt ubf{ 50
nV] g] ul/G5 .
pbfx/0f 4
3573 nfO{ glhssf] bzdf z"GofGt ug'{xf;] \ .
;dfwfg
glhs 6f9f
3570 3571 3572 35•73 3574 3575 3576 3577 3578 3579 3580
3570 sf] glhs 3573 kg{] ePsfn] 3573 nfO{ glhssf] bzdf z"GofGt ubf{ 3570
x'G5 .
38 ul0ft, sIff $
pbfx/0f 5
4655 nfO{ glhssf] bzdf z"GofGt ugx'{ f];\ .
;dfwfg
a/fa/ a/fa/
4650 4651 4652 4653 4654 46•55 4656 4657 4658 4659 4660
4650 / 4660 sf] l7s lardf 4655 kg{] ePsfn] 4655 nfO{ glhssf] bzdf zG" ofGt
ubf{ 4660 x'G5 .
pbfx/0f 6
550 nfO{ glhssf] ;odf z"GofGt ug'x{ f];\ .
;dfwfg
a/fa/ a/fa/
500 510 520 530 540 55•0 560 570 580 590 600
500 / 600 sf] l7s lardf 550 kg{] ePsfn] 550 nfO{ glhssf] ;odf z"GofGt ubf{
600 x'G5 .
pbfx/0f 7
4833 nfO{ glhssf] ;odf zG" ofGt ug'{xf;] \ .
;dfwfg
glhs 6f9f
4800 4810 4820 4830• 4840 4850 4860 4870 4880 4890 4900
4800 sf] glhs 4833 kg{] ePsfn] 4833 nfO{ glhssf] ;odf z"GofGt ubf{ 4800
x'G5 .
pbfx/0f 8
9285 nfO{ glhssf] ;odf zG" ofGt ug{'xf;] \ .
;dfwfg
6f9f glhs
9200 9210 9220 9230 9240 9250 9260 9270 9280• 9290 9300
ul0ft, sIff $ 39
9300 sf] glhs 9285 kg{] ePsfn] 9285 nfO{ glhssf] ;odf z"GofGt ubf{ 9300
xG' 5 .
sg' } klg ;ª\VofnfO{ glhssf] :yfgdf zG" ofGt ubf{ zG" ofGt uge{] Gbf Ps :yfg 36L
-;o eP bzsf] :yfg bz eP Pssf] :yfgdf_ x]/L pSt :yfgdf /x]sf] cªs\ 5 jf
5 eGbf a9L ePdf zG" ofGt ug{] :yfgsf] cª\sdf 1 ykL k5fl8sf] cª\snfO{ zG" o
kfgk{' 5{ . o:t} 5 eGbf sd ePdf zG" ofGt ug{] eGbf k5fl8sf cªs\ nfO{ zG" o kf/L
nV] gk' 5{ .
cEof;
!= vfnL 7fpF egx{' f];\ M
(i) 15 sf] tnsf] bz ============= / dflysf] bz ============= x'G5 .
(ii) 426 sf] tnsf] bz ============= / dflysf] bz ============= xG' 5 .
(iii) 4824 sf] tnsf] bz ============= / dflysf] bz ============= xG' 5 .
(iv) 832 sf] tnsf] ;o ============= / dflysf] ;o ============= xG' 5 .
(v) 7542 sf] tnsf] ;o ============= / dflysf] ;o ============= xG' 5 .
2. tnsf ;ªV\ ofx¿nfO{ glhssf] bzdf zG" ofGt ug{x' f];\ M
(i) 16 (ii) 78 (iii) 245 (iv) 561
(v) 1680 (vi) 7825 (vii) 2456
3. tnsf ;ªV\ ofx¿nfO{ glhssf] ;odf zG" ofGt ug{'xf;] \ M
(i) 390 (ii) 505 (iii) 450 (iv) 5820
(v) 4850 (vi) 8270 (vii) 9234
kl/ofh] gf sfo{ (Project work)
sf7df8fFa} f6 kf]v/f, sf7df8f}Faf6 d'lUnª / sf7df8faF} f6 8d' ;]| Ddsf] b'/L slt slt
lsnf]ld6/ 5, kQf nufpg'xf];\ / glhssf] bzdf zG" ofGt u/L n]Vgx' f];\ .
40 ul0ft, sIff $
kf7 5 M ul0ftsf cfwf/et" ljm| ofx¿ (Basic operations of mathematics)
5.1 kg' /jnfs] g (Review)
A. tnsf k|Zgx¿sf] cWoog u/L 5nkmn ug{'xf;] \ M
(i) tkfO‘{;Fu ?= 115 lyof] / cfdfn] tkfO‘{nfO{ ?= 225 ylklbge' of] eg] ca
tkfO{‘;Fu hDdf slt ?lkofF x'G5 xf]nf <
(ii) tkfO{‘ sg' } k;ndf Pp6f ;fdfg lsGg hfge' of] / pSt ;fdfgsf] dN" o ?= 295
/x5] . tkfO{‘n] k;nn] fO{ ?= 500 lbg'eof] eg] ca k;n]n] tkfO‘{nfO{ slt /sd
lkmtf{ lbg'knf{ <
(iii) tkfO{‘nfO{ a'afn] ?= 50 sf 12 cf]6f gf]6 lbg'eof] eg] tkfO;‘{ uF hDdf slt /sd
x'G5 xfn] f <
(iv) tkfO;‘{ Fu 20 cf6] f rsn]6 5g\ ca 5 hgf ldNg] ;fyLx¿nfO{ a/fa/ efu
nufpg'kbf{ Ps hgfsf] efudf hDdf sltcf6] f rsn6] k5{g\ xf]nf <
ul0ftsf cfwf/et" ljm| ofx¿cGtu{t hf8] , 36fp, u0' fg / efu k5{g\ .
B. tnsf vfnL sf7] fdf pkoS' t cª\s egx'{ f];\ M
(i) (ii)
4 43 8
+ 57 4
+ 23
63
9 8 7 5
(iii) 9 (iv)
6
504
- 21 5 - 238
7 5 3 1
(v) (vi)
24 × 57 = 42 × 56 =
ul0ft, sIff $ 41
2. tn lbP h:t} u/L Pssf] hf8] nfO{ k'gM bz / Pssf] ;dx" sf] ¿kdf JoSt
ug{'xf;] \ M
h:t} M 6 Ps ± 7 Ps Ö 13 Ps = 1 bz + 3 Ps
(i) 5 Ps ± 9 Ps Ö
(ii) 8 Ps ± 9 Ps Ö
(iv) 5 Ps ± 5 Ps Ö
(v) 2 Ps ± 8 Ps Ö
5.2 hf]8 (Addition)
lj|mofsnfk 1
lbOPsf] Ans cjnfs] g u/L :yfgdfg tflnsfdf cª\s e/L hf]8 ug'{xf;] \ M
xhf/ ;o bz Ps
±
dfly lbOPsf lrqdf klxnf] ;dx" df Pssf Ans 3 cf6] f, bzsf Ans 2 cf]6f, ;osf]
Ans 3 cf]6f / xhf/sf Ans 1 cf]6f 5 . To;} u/L bf;] |f] ;d"xdf Pssf Ans 6
cf]6f, bzsf] Ans 3 cf]6f, ;osf Ans 2 cf]6f / xhf/sf Ans 2 cf6] f 5g\ . ltgnfO{
:yfgdf tflnsfdf k:| t't ubf{ lgDgfg;' f/ xG' 5 M
42 ul0ft, sIff $
xhf/ ;o bz Ps
1 323
±2 2 3 6
dflysf Ansx¿ Ps 7fpFdf ld;fpFbf,
o;/L ld;fpFbf Pssf Ansx¿ 9 cf6] f, bzsf Ansx¿ 5 cf6] f, ;osf Ansx¿ 5
cf6] f / xhf/sf Ansx¿ klg 3 cf]6f 5g\ . ca oL s'/fx¿nfO{ tflnsfdf ebf,{
xhf/ ;o bz Ps
1 323
±2 2 3 6
3 559
o;/L Pp6f ;d"xdf ePsf j:tx' ¿nfO{ csf{] ;dx" ;uF ld;fpg], hDdf ug]{ h:tf
zAbx¿n] hf]8nfO{ hgfp5F .
ljm| ofsnfk 2 43
d"No cg'dfg ug]{ / hf8] g\ ]
h:t} M
lzIfs M l6lesf] dN" o slt knf{ <
ljBfyL{ M ?= 54,450
ul0ft, sIff $
lzIfs M df]6/;fOsnsf] dN" o slt knf{ <
ljBfyL{ M ?= 2,15,000
lzIfs M b'j}sf] d"No hDdf slt xG' 5 <
ljBfyL{ M 54,450
+ 2,15,000
2,69,450
?= 2,69,450 x'G5 .
pbfx/0f 1
hf]8 ugx{' f;] \ M
8 3 5 7 6
+ 2 3 4 1 2
10 6 9 8 8
pbfx/0f 2
;h' gnfO{ k|f]hS] 6/ / Nofk6k cfjZos eP/ OnS] 6«fl] gS; k;ndf lsGg uP5g\ .
k;ndf k|fh] ]S6/ / Nofk6ksf] dN" o j|mdzM ?= 28,345 / ?= 39,676 cª\lst ul/Psf]
5 . ca ;h' gnfO{ b'j} ;fdfg lsGbf hDdf slt ?lkofF ltgk{' 5,{ kQf nufpg'xf;] \ .
;dfwfg
k|f]h]S6/sf] dN" o Nofk6ksf] dN" o
?= 28,345 ?= 39,676
?= 39,676
hDdf d"No
?= 28,345 + ?= 39,676 = ?
:yfgdfg tflnsfdf /fv]/ hf8] f,F}
?= 28,345
44 ul0ft, sIff $