गणित कक्षा ४

;dfwfg
11 hgfn] km6' an lsGg p7fPsf] dN" o = 100 × 11 = ?= 1100
Pp6f ansf] dN" o = ?= 350

tLgcf]6f ansf] d"No
slt xfn] f <

tLgcf]6f ansf] d"No = ?= 350 × 3

= ?= 1050

ca pgLx¿;uF ePsf] /sd = ?= 1100

= 1100 > 1050

afsF L /sd = ?= 1100 -1050

= ?= 50

cEof; pgLx¿n] p7fPsf] k;} fn] k'Uof] .

1. lx;fa ug{'xf;] \ M (ii) 8 k;} f × 50
(i) 4 ?lkofF 25 k};f × 15 (iv) 2 ?lkofF 5 k;} f × 88
(iii) 4 ?lkofF 75 k};f × 9

2. ljBfnosf] k/' :sf/ ljt/0f sfoj{ m| ddf 10 cf6] f sfkL NofPsf] lyof] . Pp6f sfkLsf]
dN" o ?= 50 kb5{ eg] hDdf sfkLsf] dN" o slt kb5{ xfn] f <

3. 1 s]hL :ofpsf] d"No ?= 280 kb{5 eg] 15 s]hL :ofpsf] dN" o slt knf{ <

4. ladnn] 85 ?lkofF 50 k;} f kg{] Pp6f vn] fg} f sf/ / lgdn{ n] 120 ?lkofF kg{] Pp6f
aa] n6] lsGof] eg] pgLx¿n] hDdf slt ?lkofF vr{ u/,] kQf nufpgx' f;] \ .

5. sg' } Pp6f :6;] g/L k;nsf ;fduL| / ltgsf] dN" o lbOPsf] 5 . pSt dN" o ;r" L
x]/L tnsf] k|Zgsf] pQ/ lbg'xf];\ .

94 ul0ft M sIff $

?= 75 980 ?lkofF 50 k;} f 75 ?lkofF 25 k};f ?= 230

(a) kfFrcf6] f sndsf] dN" o slt knf{ <
(b) Pp6f 8fo/L / 2 cf6] f Hofldlt afs;sf] dN" o slt knf{ <
(c) Pp6f 8fo/L lsGg ?= 100 lbof] eg] slt ?lkofF lkmtf{ kfOG5 xfn] f <
(d) tLgcf]6f SofNs'n6] /sf] d"No slt k5{ xf]nf <

kl/ofh] gf sfo{ (Project work)

tkfO‘s{ f] 3/df tkfO‘{ k9g\ ] sf7] fdf ePsf ;fduL| x¿sf] d"No cleefjs;uF ;f]w]/
n]Vgx' f;] \ . ;a} ;fdu|Lsf] d"No hf]8/] x]g'{xf;] \ .

ul0ft M sIff $ 95

3.2.3 db' f| ;DaGwL efu

ljm| ofsnfk 1

tkfO‘{x¿ ldn]/ sIffsf7] fdf ;dosf] hfgsf/Lsf nflu ?= 680 kg]{ leQ] 38L /fVg
;an} ] a/fa/ /sd p7fpg] ;Nnfx ug'e{ of] . ca pSt 38L lsGg slt /sd ;ªs\ ng
ugk{' nf{, 5nkmn ugx'{ f];\ .
h:t}, 38Lsf] d"No Ö ?= 680, sIffdf ljBfyL{ ;ªV\ of 34 hgf 5g\ . Ps hgfn] ltgk'{ g{]
/sd slt xf]nf <
Ps hgfn] ltg'k{ g{] /sd = 680 ÷ 34 = ?= 20
Ps hgf ljBfyL{sf] efudf ?= 20 kbf{]/x5] .

lj|mofsnfk 2

tnsf] tflnsf k/" f ugx{' f;] \ M

j:t'sf] ;ª\Vof hDdf d"No Pp6fsf] dN" o

1. ?= 100 –

2. ?= 400

3. ?= 80

4. ?= 52

Pp6f j:t'sf] dN" o lgsfNg hDdf d"NonfO{ j:t'sf] ;ªV\ ofn] efu ug'{kb{5 .
pbfx/0f 1
rf/ Kofs]6 la:s6' sf] dN" o ?= 324 k5{ eg] Ps Kofs]6 la:s6' sf] d"No slt knf{ <
;dfwfg
rf/ Kofs]6sf] dN" o ?= 324
1 Kofs]6sf] dN" o = ?= 324 ÷ 4
96 ul0ft M sIff $

81

4 324
-32
4
-4
0

Ps Kofs]6 la:s6' sf] d"No ?= 81 ?lkofF kb{5 .

cEof;

1. lglstfn] cfˆgf] hGdlbgdf 6 hgf ;fyLx¿nfO{ n88\ ' vj' fpg ?= 354 vr{ ul/g\
eg] Ps hgf ;fyLsf nflu pgn] slt /sd vr{ u/s] L /lx5g\, kQf nufpgx' f];\ .

2. s'g} sf/vfgfdf sfd ug]{ 8 hgf dhb/' sf] tna ?= 12,000 5 eg] 1 hgf

dhb/' sf] tna slt xf]nf, kQf nufpg'xf;] \ .

3. 3 cf]6f sndsf] d"No ?= 185 kb{5 eg] Pp6f sndsf] dN" o slt knf{ <

4. 5 ls=u|f= rfdnsf] d"No ?= 854 ?lkofF kb{5 eg] 1 ls=u|f= rfdnsf] dN" o slt

knf{, kQf nufpg'xf];\ .

5. tn lbOPsf j:tx' ¿sf] Pp6f dN" o kQf nufpg'xf];\ M

ljj/0f hDdf d"No b/
?= 2250 –
1.

2. ?= 3300 –

3. ?= 3850 –

kl/of]hgf sfo{ (Project work)

tkfO{s‘ f] 3/df xfn;fn g} ;fdfgx¿ vl/b u/]sf lan cWoog ugx{' f];\ . pSt landf
ePsf] hDdf d"No / Pp6fsf] d"Nosf] ljj/0f l6kf]6 ug{'xf;] \ / sIffsf7] fdf k|:t't
ug{x' f];\ .

ul0ft M sIff $ 97

3.3 b'/L (Distance)
3.3.1 kg' /jnfs] g

tn lbOPsf j:ts' f] nDafO / b'O{ :yfglarsf] b/' Lsf] pko'St PsfO -ldlnld6/,
;]lG6ld6/, ld6/ / lsnfl] d6/_ cg'dfg / gfk n]Vg'xf;] \ .

ljj/0f pkoS' t PsfO cgd' fg gfk
-s_ tkfO{s‘ f] ul0ft lstfa

-v_ tkfO{n‘ ] ko| f]u ug]{ O/]h/
-u_ sIffsf]7fdf ko| f]u ePsf] z}Ifl0fs

kf6L
-3_ tkfO‘{sf] 3/bl] v ljBfno;Ddsf] b/' L
-ª_ sf7df8fb}F ]lv x6] f8}F f;Ddsf] b/' L

b/'[ L gfKgsf nflu ldlnld6/ -ld=ld=_, ;l] G6ld6/ -;=] ld=_, ld6/ -ld=_, lsnfl] d6/ -ls=ld=_
cflb PsfOsf] ko| fu] ul/G5 .
3.3.2 b/' Lsf PsfOx¿nfO{ Pscsf{df ¿kfGt/0f (Conversion of unit of distance

each other)

(A) ldlnld6/ / ;]lG6ld6/
ljm| ofsnfk

?n/sf] k|ofu] u/L cfk"mn] ko| fu] u/s] f l;;fsnd gfKg'xf;] \ M

(i) l;;fsndsf] nDafO gfKg sg' PsfOsf] ko| fu] pko'St x'G5 < ul0ft M sIff $
(ii) l;;fsndsf] nDafO slt xf]nf <
(iii) l;;fsnd gfKgsf nflu ?n/sf] k|ofu] lsg ul/Psf] xfn] f <

98

?n/df 10 ;]=ld= / 11 ;=] ld= sf] lardf dl;gf wsfx{ ¿n] 10 cf]6f PsfOx¿df
ljefhg u/]sf 5g\ . b'O{ wsfl{ arsf] b/' L 1 ldlnld6/ xG' 5 . l;;fsndsf] nDafO 10

;l] G6ld6/ 4 ldlnld6/ 5 . 10 ;]lG6ld6/ a/fa/ slt ldlnld6/ xfn] f < ;]lG6ld6/nfO{

ldlnld6/df abNg s] ug{'knf,{ 5nkmn ug{x' f;] \ .

1 ;=] ld= = 10 ld=ld=

;]=ld= nfO{ ldlnld6/df abNg 10 n] u0' fg ug'{kb{5 eg] ldlnld6/nfO{ ;l] G6ld6/df

abNg 10 n] efu ugk'{ b{5 . ÷ 10

ld=ld= ;=] ld=

10 ×

(B) ;]lG6ld6/ / ld6/
lj|mofsnfk 2

d]hl/ª 6k] sf] k|of]u u//] tkfO{s‘ f] sIffsf]7fsf] nDafO gfKg'xf];\ M

1 ld6/df slt 1 ld6/df 100
;]lG6ld6/ xG' 5 < ;]lG6ld6/ x'G5 .

2 ld6/df slt 2 ld6/df = 100 × 2 =
;l] G6ld6/ xG' 5 < 200 ;l] G6ld6/ xG' 5 . ld6/nfO{
;l] G6ld6/df n}hfg 100 n] u0' fg

ul/G5 eg] ;l] G6ld6/nfO{ ld6/df
nh} fg 100 n] efu ug'{kb5{ .

(a) sf]7fsf] nDafO slt eof] < 99
(b) sf]7fsf] nDafOsf] gfknfO{ ;l] G6ld6/df kl/jt{g ug{ s] ugk{' nf{ <

ul0ft M sIff $

(C) ld6/ / lsnf]ld6/
ljm| ofsnfk 3

tn lbOPsf cj:yfdf nDafO / b/' L gfksf nflu
s'g s'g PsfOsf] ko| f]u ul/G5 < pSt gfknfO{ csf]{
PsfOdf ¿kfGt/0f ug{ s] ug'{knf{ < ;d"xut 5nkmn
ugx{' f;] \ .
(a) ljBfnosf] vn] db} fgsf] nDafO
(b) tkfO{‘sf] sIffsf7] fb]lv k:' tsfno;Ddsf] b/' L
(c) 3/af6 glhs}sf] a;:6;] g;Ddsf] b'/L
(d) k[YjL /fhdfu{sf] nDafO
(i), (ii) / (iii) df lbOPsf gfk cj:yfcg;' f/ ld6/ jf lsnfl] d6/df xg' ;S5g\ . kY[ jL
/fhdfus{ f] nDafOnfO{ lsnf]ld6/ PsfOdf n]Vbf pko'St x'G5 .

ld6/ jf lsnfl] d6/sf] ¿kdf /x]sf PsfOx¿nfO{ Pscsfd{ f ¿kfGt/0f ug{ s] ug]{
xf]nf, 5nkmn ug'x{ f;] \ .

1 lsnf]ld6/ = 1000 ld6/ xG' 5 . ld6/nfO{ lsnf]ld6/df kl/jt{g ug{ 1000 n] efu
ug'k{ 5{ . lsnfl] d6/nfO{ ld6/df kl/jt{g ug{ 1000 n] u'0fg ug'{kb{5 .

pbfx/0f 1

tkfOs{‘ f] sndsf] nDafO 12 ;]lG6ld6/ 5 eg] slt ldlnld6/ xG' 5, kQf nufpgx' f];\ M

;dfwfg 1 ;]lG6ld6/ = 10 ldlnld6/

sndsf] nDafO = 12 ;=] ld=
12 ;=] ld= = (12 x 10) ld=ld= = 120 ld=ld=

pbfx/0f 2
3/df sk8f ;'sfpgsf nflu ko| f]u ul/Psf] gfOngsf] 8f]/Lsf] nDafO 5 ld6/ 20
;]lG6ld6/ 5 eg] pSt 8f/] Lsf] nDafO slt ;]lG6ld6/ xG' 5, kQf nufpg'xf];\ .

100 ul0ft M sIff $

;dfwfg

8f]/Lsf] nDafO = 5 ld= 20 ;]=ld=
xfdLnfO{ yfxf 5,
1 ld= = 100 ;=] ld=
o;}n], 5 ld= = 5 x 100 = 500 ;]=ld=
ca, 5 ld= 20 ;=] ld= = 500 ;]=ld= + 20 ;=] ld=
= 520 ;]=ld=

pbfx/0f 3

Pp6f sf7] fsf] nDafO 750 ;l] G6ld6/ 5 eg] pSt sf]7fsf] nDafO ld6/ / ;]lG6ld6/df
slt x'G5, kQf nufpgx' f];\ .

;dfwfg

oxfF, sf]7fsf] nDafO = 750 ;=] ld=

= 7500 ld= 1 ld6/ = 100 ;]lG6ld6/
100

= 100)750(7

- 700

50

= 7 ld6/ 50 ;l] G6ld6/

pbfx/0f 4

w'Gr]b]lv nfd6fª;Ddsf] b/' L 33 lsnf]ld6/ 600 ld6/ 5 eg] ld6/df hDdf slt /x5] ,
lgsfNg'xf;] \ .

;dfwfg

wG' r]bl] v nfd6fª;Ddsf] b/' L = 33 lsnf]ld6/ 600 ld6/
33 lsnf]ld6/ 600 ld6/ = 1000 × 33 + 600

= 33000 + 600

= 33600 ld6/
wG' r]bl] v nfd6fª;Ddsf] b/' L 33600 ld6/ /x5] .

ul0ft M sIff $ 101

pbfx/0f 5

cGgk"0f{ lxdfnsf] prfO ;db' | ;txb]lv 8091 ld6/ 5 eg] lsnfl] d6/ / ld6/df o;sf]
prfO slt xG' 5, kQf nufpgx' f;] \ .
;dfwfg

oxf F cGgk"0f{sf] prfO = 8091 ld=

= 8000 ld= + 91 ld= 1000 ld6/ = 1 lsnf]ld6/
= 8 ls=ld= 91 ld=

8091 ld= = 8091 ls=ld=
1000

8
= 1000 8091

- 8000

91

cGgk"0f{sf] prfO 8 lsnf]ld6/ 91 ld6/ x'G5 .

cEof;

1. tn lbOPsf] vfnL 7fpFdf plrt jfSo eg{x' f;] \ M

(i) 10 ;l] G6ld6/ = ldlnld6/ x'G5 .

(ii) 1000 ld6/ = 1 x'G5 .

(iii) 7 ld6/ nDafO af6f] = ;l] G6ld6/ x'G5 .

(iv) ;]lG6ld6/ = 3 ld6/ xG' 5 .

(v) 4 lsnfl] d6/ af6fsf] nDafO = ld6/ x'G5 .

2. sfi] 7df lbOPsf] PsfOsf cfwf/df ?kfGt/0f ug'{xf];\ M
(i) 3 ld6/ 20 ;=] ld= -;=] ld=_ (ii) 15 ls=ld= -ld6/_

(iii) 5 ;=] ld= 3 ld=ld= -ld=ld=_ (iv) 2 ls=ld= 200 ld= -ld6/_

102 ul0ft M sIff $

(v) 250 ;]=ld= -ld6/_ (vi) 12000 ld6/ -ls=ld=_

(vii) 22 ld=ld= -;]=ld=_

3. Pp6f 6a] nsf] nDafO 2 ld6/ eP o;sf] nDafO ;]lG6ld6/df slt
xfn] f, kQf nufpg'xf;] \ .

4. uf]/vfbl] v sf7df8fF};Ddsf] l;wf b/' L 74800ld6/ 5 eg] pSt b'/L lsnf]ld6/df slt
xfn] f, kQf nufpgx' f;] \ .

5. Pp6f 3/sf] df6] fO 15 ld6/ eP ;]lG6ld6/df slt xf]nf, kQf nufpgx' f;] \ .

6. Pp6f lstfasf] rf8} fO 4 ;]=ld= 5 eg] o;sf] df6] fO slt ldlnld6/ /x5] <

7. 40 ;]=ld= nDafO ePsf 5 cf6] f l/agx¿ hf8] /] Pp6} agfpbF f slt ld6/ nfdf] xG' 5,
kQf nufpgx' f;] \ .

kl/ofh] gf sfo{ (Project work)

tkfO‘{sf] 3/df ePsf ;fdu|Lx¿ -b/fh, ;T' g] knª, ;T' g] sf]7f_ sf] gfk lngx' f;] \ .
ld6/ jf ;]lG6ld6/ sd] f 5 < ld6/df ePsf] gfknfO{ ;]lG6ld6/df abn]/ xg] x{' f];\ /
sIffsf7] fdf k:| tt' ug{x' f];\ .

ul0ft M sIff $ 103

3.3.3 ;l] G6ld6/, ld6/ / lsnf]ld6/;DaGwL hf8] (Addition related to centimeter,

meter and kilometer)

lj|mofsnfk 1

bO' {cf6] f km/s km/s gfk ePsf n6\7L lngx' f;] \ . logLx¿sf] cnu cnu gfk lng'xf;] \ .
km]l/ n67\ LnfO{ hf]8/] o;sf] gfk lngx' f;] \, slt cfof] < ca n67\ Lx¿sf] cnu cnu
gfk / bj' } n67\ L hf]8]kl5sf] nDafOlarsf] ;DaGw lgsfNgx' f;] \ .
h:t}

klxnf] n67\ Lsf] nDafO = 1 ld6/ 25 ;l] G6ld6/
bf];f| ] n67\ Lsf] nDafO = 1 ld6/ 15 ;]lG6ld6/
b'j} n67\ L hf]8]kl5 n6\7Lsf] nDafO = 2 ld6/ 40 ;l] G6ld6/

1 ld6/ 25 ;l] G6ld6/

1 ld6/ 15 ;l] G6ld6/

1 ld6/ 25 ;l] G6ld6/ 1 ld6/ 15 ;]lG6ld6/

2 ld6/ 40 ;]lG6ld6/

ld6/ ;l] G6ld6/
1 25

+ 1 15

2 ld6/ 40 ;l] G6ld6/

gfk;DaGwL hf]8 ubf{ ;dfg PsfOlar hf]8 ugk{' b{5 .
n6\7Lsf] cnu cnu gfksf] hf8] / n6\7L hf]8/] lnPsf] gfk ;dfg 5 .

pbfx/0f 1

dfgf}, tkfOs‘{ f] sIffsf7] fb]lv kw| fgfWofkssf] sf7] f;Ddsf] b'/L 10 ld6/ 50 ;]=ld=
5 . o:t} kw| fgfWofkssf] sf7] fb]lv k:' tsfno;Ddsf] b'/L 9 ld6/ 85 ;]=ld= 5 .
104 ul0ft M sIff $

sIffsf7] fbl] v k|wfgfWofkssf] sf]7f xF'b} k':tsfno;Ddsf] b/' L slt xfn] f <

;dfwfg

sIffsf]7fbl] v kw| fgfWofkssf] sf]7f;Ddsf] b'/L = 10 ld6/ 50 ;]lG6ld6/
k|wfgfWofkssf] sf7] fb]lv k':tsfno;Ddsf] b'/L = 9 ld6/ 85 ;]lG6ld6/

ld6/ ;l] G6ld6/
10 50

+ 9 85 100 ;=] ld= = 1 ld=
135 ;]=ld= = 1 ld= 35 ;=] ld=
19 ld6/ 135 ;l] G6ld6/

1 ld6/

20 ld6/ 35 ;l] G6ld6/

pbfx/0f 2

Pp6f ls;fgsf] 3/af6 t/sf/L v]tL u/]sf] af/L;Ddsf] b/' L 1 lsnfl] d6/ 200 ld6/
5 . o:t} t/sf/L af/Lbl] v t/sf/L ahf/;Ddsf] b'/L 950 ld6/ 5 eg] p;nfO{ 3/af6
t/sf/L ahf/;Dd k'Ubf slt b'/L kf/ ug'{knf{ <

;dfwfg

oxfF,

3/af6 t/sf/L af/L;Ddsf] b'/L Ö 1 ls=ld= 200 ld=

t/sf/L af/Lb]lv t/sf/L ahf/;Ddsf] b'/L Ö 950 ld=

lsnf]ld6/ ld6/

1 200
+ 950
1 1150

1

2 ld6/ 150 ;]lG6ld6/

ul0ft M sIff $ 105

cEof;

1. hf]8 ugx'{ f];\ M

(i) ld= ;]=ld= (ii) ld= ;=] ld= (iii) ls=ld= ld=

50 35 17 22 250 500

+ 15 51 + 19 85 + 300 200

(iv) ls=ld= ld= ;]=ld= (v) ls=ld= ld= ;]=ld=

15 150 12 95 880 50

+ 20 120 16 + 15 200 40

2. sg' } ljBfnodf dflyNnf] sIffsf ljBfyLs{ f nflu 200 ld6/ 50 ;]=ld= nDafOsf]
v]nd}bfg 5 . o:t} ;fgf afnaflnsfsf nflu kfs;{ lxtsf] 100 ld6/ 85
;l] G6ld6/ nDafOsf] csf]{ vn] d}bfg 5 eg] bj' } vn] d}bfgsf] hDdf nDafO slt
xfn] f <

3. sf7df8fFa} f6 ufb] fjf/L;Dd ;8ssf] nDafO 15 lsnfl] d6/ 700 ld6/
5 . o:t} uf]bfjf/Laf6 gu/sf]6;Dd ;8ssf] nDafO 29 lsnfl] d6/ 800 ld6/
5 . sf7df8fa}F f6 ufb] fjf/L xFb' } gu/sf]6f;Dd ;8ssf] nDafO slt xG' 5, kQf
nufpg'xf];\ .

3. Pp6f af6fsf] nDafO 12 ls=ld=, 750 ld= / 50 ;=] ld= 5 . csf]{ af6fsf] nDafO 9
ls=ld= 300 ld= / 15 ;=] ld= 5 eg] tL b'O{ af6fsf] hDdf nDafO kQf nufpg'xf];\ .

kl/of]hgf sfo{ (Project work)

tkfOs{‘ f] ljBfnosf] sIff $ sf] sf]7f / clkm; sf]7fsf] nDafOsf] gfk lnO{ hf8] g\ x' f];\
/ sIffsf]7fdf k|:tt' ug'x{ f;] \ .

106 ul0ft M sIff $

3.3.4 ;]lG6ld6/, ld6/ / lsnfl] d6/;DaGwL 36fp (Subtraction related to5 meter 50 centimeter

centimer, meter and kilometer)

ljm| ofsnfk 1
tnsf] ;j+ fb xg] 'x{ f;] \ / 5nkmn ug'{xf];\ M

Pp6f ?v 5 ld6/ 50 ;=] ld= cUnf] 5 .
o;sf] dflyNnf] 2 ld6/ 20 ;]=ld= efu
xfjfn] efFlrof] eg] ca slt afFsL 5 <

o;sf nflu hDdf ?vsf] prfOaf6
xfjfn] eflF rPsf] efu 36fpgk' 5{ .

s;/L 36fpg] xf]nf < ;dfg PsfOx¿nfO{ nx/df ldnfP/
/fVg] clg 36fpg] .
pbfx/0f 1
ld6/ ;]lG6ld6/

5 50

- 2 20

3 ld6/ 30 ;]lG6ld6/

Pp6f ;ef xnsf] nDafO 10 ld6/ 50 ;l] G6ld6/ 5 . rf}8fO 8 ld6/ 75 ;l] G6ld6/ 5
eg] nDafO rf}8fOeGbf sltn] a9L 5 <

;dfwfg

oxf F ;ef xnsf] nDafO = 10 ld6/ 50 ;]lG6ld6/
;ef xnsf] rf8} fO = 8 ld6/ 75 ;]lG6ld6/

ld6/ ;l] G6ld6/
10 9 100 + 50 = 150

- 8 75

1 ld6/ 75 ;]lG6ld6/

sf]7fsf] nDafO rf8} fOeGbf 1 ld6/ 75 ;]lG6ld6/ a9L /x]5 .

ul0ft M sIff $ 107

cEof; (ii)

1. 36fp ug'{xf];\ M ld= ;]=ld=

(i) 270 15
ld= ;=] ld= - 11
25 12 10
- 11 10

(iii) (iv)

ld= ;=] ld= ld= ;]=ld=
3 250 52 80
- 1 650 - 45
92

2. 25 ld6/ 52 ;]=ld= nfdf] kvfn{ jiffo{ fddf 10 ld6/ 35 ;=] ld= elTsof] eg] ca
slt ;]=ld= afsF L 5 xfn] f <

3. ;ljgf;uF 4 ld6/ 35 ;=] ld= nfdf] l/ag lyof] . pgn] s]xL efu srF} Ln] sf6/]
v;' LnfO{ lbOg\ . ca pgL;Fu 1 ld6/ 85 ;]=ld= dfq afsF L 5 eg] slt l/ag
lbPsL /lx5g\, kQf nufpg'xf];\ .

4. Pp6f a; 250 ls=ld= ofqf ugk{' g{] 5 . 95 ls=ld= 750 ld= ofqf ul/;s]kl5
tn] e¥of] eg] ca slt ofqf ug{ afFsL 5, lgsfNgx' f];\ .

kl/ofh] gf sfo{ (Project work)

tkfO{‘n] k9\g] ljBfnosf] sIff $ sf] sf]7fsf] nDafO / rf}8fOsf] gfk lng'xf;] \ . nDafO
rf8} fOeGbf slt nfdf] /x]5, kQf nufO{ sIffsf]7fdf k|:tt' ugx{' f;] \ .

108 ul0ft M sIff $

3.4 Ifdtf (Capacity)

3.4.1 k'g/jnfs] g
tnsf j:tx' ¿sf cfwf/df 5nkmn ug'{xf];\ M

1 ltr. 250 ml. 2 ltr. 20 ltr. 1000 ltr.
lrqdf x/]s j:t'n] t/n j:t'sf] c6\g] Ifdtf hgfPsf] 5 . lbOPsf t/n j:tx' ¿ ln6/
/ ldlnln6/sf] OsfOdf 5g\ . o:t} t/n kbfy{ /fVg] efF8fx¿ c¿ s] s] xg' ;S5g,\
5nkmn ug'{xf;] \ .
Ifdtf gfKg] PsfOx¿ ln6/ -ln=_ / ldlnln6/ -ld=ln=_ xg' \ . sg' } ef8F fdf slt t/n
kbfy{ c6g\ ;S5 Tof] g} pSt ef8F fsf] Ifdtf xf] .
3.4.2 ln6/ / ldlnln6/nfO{ Pscfk;df ¿kfGt/0f (Conversion of liter and

mililiter eachother)

lj|mofsnfk 1
tn lbOPsf Ifdtf gfKg] j:t'sf cfwf/df kZ| gsf] hjfkm lbg'xf];\ .

200 ml 500 ml 2 liter 20 liter

(i) 200 ldlnln6/sf] efF8fn] slt k6s kfgL /fvk] l5 1 ln6/sf] af]tn el/G5 <
(ii) 500 ldlnln6/sf] efF8fn] slt k6s kfgL /fv]kl5 1 ln6/sf] af]tn el/G5 <

ul0ft M sIff $ 109

(iii) 20 ln6/df slt ldlnln6/ x'G5 xf]nf < of] efF8f] eg{ 500 ldlnln6/n] slt
k6s kfgL /fVgk' nf{ <

oxf,F
(i) 200 ldlnln6/sf] ef8F faf6 5 k6s vGofpbF f 1 ln6/sf] af]tn el/of] .
200 ld=ln= x 5 = 1000 ld=ln= = 1 ln6/
(ii) To:t} 500 ld=ln= sf] ef8F fn] 2 k6s vGofpbF f 1 ln6/sf] af]tn el/of] .
500 ld=ln= × 2 = 1000 ld=ln= = 1 ln6/
hf/n] ln6/df Ifdtf dfkg ub5{ .
o:t},
(iii) 20 ln6/ = 1000 × 20 ldlnln6/ x'G5 .
20 ln6/ hf/ eg{ = 500 × 40 = 40 k6s egk'{ b{5 .

lj|mofsnfk 2
tkfO{n‘ ] ko| f]u ug]{ lkpg] kfgLsf] aft] n lng'xf];\ . o;sf] Ifdtf slt 5, cg'dfg
ugx'{ f;] \ . af]tnsf] Ifdtf ln6/df 5 eg] ldlnln6/df / ldlnln6/df 5 ln6/df kl/jtg{
ug{ s] ug{] xf]nf < 5nkmn u/L lgisif{ lgsfNgx' f];\ .

ln6/nfO{ ldlnln6/df kl/jt{g ubf{ 1000 nfO{ u0' fg ul/G5 eg] ldlnln6/nfO{
ln6/df kl/jt{g ubf{ 1000 n] efu ul/G5 .

pbfx/0f 1
tkfO{‘sf 3/df /xs] f] kfgL 6o\ fª\sLsf] Ifdtf 500 ln6/ 5 eg] slt ldlnln6/ Ifdtf
/x5] .
;dfwfg

1 ln6/ = 1000 ldlnln6/
500 ln6/ = 1000 × 500 = 5,00,000 ldlnln6/

110 ul0ft M sIff $

pbfx/0f 2

b'w /fVg] ;fgf] Sofgsf] Ifdtf 250 ldlnln6/ 5 . o;n] 2 ln6/sf] efF8f] eg{ slt k6s
pSt Sofgn] bw' vGofpg' knf{ <

;dfwfg

;fgf] Sofgsf] Ifdtf = 250 ldlnln6/
7n' f] efF8fsf] Ifdtf = 2 ln6/ = 1000 × 2 = 2000 ln6/

;fgf] Sofgaf6 7n' f] ef8F fdf vGofpbF } hfFbf ;fgf] Sofgsf] Ifdtf hf]8b\ f,

250 + 250 + 250 + 250 + 250 + 250 + 250 + 250 = 2000

250 × 8 = 2000

ctM 8 k6s egk{' 5{ . efu u//] x/] fF}

2000 ÷ 250

250)2000(8

- 2000

0

∴ To;}n] 8 k6s bw' /fVgk' 5{ .

pbfx/0f 3

2500 ldlnln6/df slt ln6/ slt ldlnln6/ xG' 5, n]Vgx' f];\ .

;dfwfg 1000 ld=ln= = 1 ln=

2500 ldlnln6/ = 2000 ldlnln6/ + 500 ldlnln6/
= 2 ln= 500 ld=ln=

efu u//] x]/f}F, 111

2500 ÷ 1000
1000 )2500( 2
- 2000
500

o;}n] 2500 ld=ln= = 2 ln=, 500 ld=ln= x'G5 .

ul0ft M sIff $

cEof;

1. ldlnln6/df ?kfGt/0f ugx'{ f];\ M

(i) 15 ln6/ = ld=ln=

(ii) 9 ln6/ 90 ldlnln6/ = ld=ln=

(iii) 6 ln6/ 400 ldlnln6/ = ld=ln=

(iv) 22 ln6/ 200 ldlnln6/ = ld=ln=

(v) 56 ln6/ 600 ldlnln6/ = ld=ln=

(vi) 23 ln6/ 150 ldlnln6/ = ld=ln=

2. ln6/ / ldlnln6/df ?kfGt/0f ug{'xf;] \ M

(i) 7500 ldlnln6/ (ii) 6350 ldlnln6/

(iii) 3571 ldlnln6/ (iv) 1575 ldlnln6/

(v) 3300 ldlnln6/

3. lrqdf b]vfOPsf] t]nsf] ef8F fsf] Ifdtf s'g PsfOdf 5 < o;nfO{

ldlnln6/df kl/jtg{ ugx{' f;] \ .

4. 5200 ldlnln6/ b'w /fVg slt ln6/ Ifdtf ePsf] ef8F f] cfjZos k5{ <
5. Pp6f 6o\ fªs\ Lsf] 750 ln6/ kfgL c6\g] Ifdtf 5 eg] Tof] slt ldlnln6/ xf] <

kl/ofh] gf sfo{ (Project work)
tkfOs‘{ f 3/df ePsf t/n j:t' /fVg] sg' } 10 cf]6f ef8F fsf] ;ªs\ ng ug'x{ f;] \ . tL
j:t'x¿sf] Ifdtf cgd' fg ugx{' f;] \ . ltgLx¿sf] l6kf6] u//] ldlnln6/ eP ln6/df /
ln6/df eP ldlnln6/df kl/jtg{ u/]/ k|:tt' ug{x' f;] \ .

112 ul0ft M sIff $

3.4.3 ln6/ / ldlnln6/sf] hf]8 / 36fp (Addition and subtraction of litre

and mililitre)

lj|mofsnfk 1
lrqdf bl} gs hLjgdf pkof]udf cfpg] ;fdu|Lx¿ bv] fOPsf] 5 . tL ;fduL| x¿sf]
Ifdtfsf cfwf/df tnsf kZ| gx¿sf] hjfkm lbg'xf;] \ M

500 ml 1 liter 5 liter 20 liter

(i) slt lunf; kfgL vGofPdf s6] n\ L el/G5 <

(ii) hf/ el/g slt s6] \nL kfgL vGofpgk' nf{ <

(iii) lunf;, hu, s]6\nL / hf/df ePsf] hDdf kfgLsf] kl/df0f slt xfn] f <

(iv) hf/df ePsf] kfgLaf6 1 s]6\nL / 1 hu kfgL lgsfnd] f hf/df slt kfgL afFsL
/xg5, kQf nufpg'xf];\ .

pbfx/0f 1

Pp6f bw' 8/] Ln] Pp6f ls;fgsf] kmfda{ f6 20 ln= 750 ld=ln= / csf{] ls;fgsf]
kmfda{ f6 30 ln6/ 450 ldlnln6/ bw' lnG5 eg] hDdf slt bw' n}hfg] /x5] <

;dfwfg

oxf,F klxnf] kmfda{ f6 20 ln6/ 750 ld=ln=
bf];|f] kmfd{af6 30 ln6/ 450 ld=ln= b'w nh} fG5 .

ln6/ ldlnln6/ 1200 ld=ln= = (1000 + 200) ld=ln=
= 1 ln= 200 ld=ln=
20 750

+ 30 450

50 1200
1

51 ln6/ 200 ldlnln6/ 113
o;n} ] hDdf 51 ln= 20 0 ld=ln= b'w n}hfg] /x]5 .

ul0ft M sIff $

pbfx/0f 2

Pp6f df6] /;fOsn rfnsn] 4 ln6/ 250 ldlnln6/ k]6f« n] df6] /;fOsndf /fvs] f
lyP . ofqfsf jm| ddf 1 ln6/ 750 ldlnln6/ l;l4of] . ca slt k6] f« n] afsF L /xG5,
kQf nufpgx' f];\ .

;dfwfg df]6/;fOsndf afFsL k]6«fn]
kQf nufpg 36fpgk' b5{ .
ln6/ ldlnln6/

4 250

- 1 750

o;nfO{ ldnfP/ ;dfwfg ubf{

ln6/ ldlnln6/

4 3 1000 + 250 = 1250 1 ln= = 1000 ld=ln=

- 1 750

2 ln6/ 500 ld=ln=

df6] /;fOsndf 2 ln= 500 ld=ln= k]6f« ]n 5 .

pbfx/0f 3

2 liter 1 liter 3 liter 250 liter

lrqdf lbOPsf cfwf/df hDdf h';sf] kl/df0f slt xfn] f, kQf nufpg'xf];\ .

;dfwfg

hDdf kl/df0f Ö ln= ld=ln=

2 0
1 0
+ 3 250

6 ln= 250 ldlnln6/

o;n} ] 3 cf]6f efF8fdf /xs] f] hDdf t/n kbfy{ 6 ln6/ 250 ldlnln6/ /x5] .

114 ul0ft M sIff $

cEof;
1. Pp6f t/n kbfy{ gfKg] ef8F fsf cfwf/df csf{sf] Ifdtf kQf nufpg'xf];\ M

(a) 60 ld=ln= ± 5 ld=ln= = 60 ml 5 ml

(b) 1 ln= – = 900 ld=ln=

1 liter 100 ml

(c) 1000 ln= ± 500 ld=ln= =

(d) 20 ln= ± = 23 ln6/ 1000 ltr 5000 ltr
20 ltr 3 ltr

(e) 3 ln= ± 1 ln= =

5 ltr 1 ltr
1 ltr
(f) 4 ln= × =
115
2. hf8] ug{'xf];\ M 4 ltr
-s_ 750 ld=ln= + 670 ld=ln= =
-v_ 2 ln= + 650 ld=ln= + 1 ln= 300 ld=ln= =

3. 36fp ug'{xf];\ M

-s_ ln= ld=ln= -v_ ln= ld=ln=

6 400 49 380

- 2 500 - 44 290

ul0ft M sIff $

4. Pp6f efF8fdf 4 ln6/ 660 ldlnln6/ kfgL 5 . o;nfO{ el/ agfpg tkfO‘{n]

1 ln6/ 550 ldlnln6/ kfgL yKge' of] eg] pSt ef8F fsf] Ifdtf slt /x]5, kQf

nufpg'xf];\ .

5. 1 1 ln6/sf] ef8F f] eg{ 500 ldlnln6/sf] hf/n] sltk6s eg'k{ b{5 <
2

6. Ps hgf la/fdLn] 8fS6/sf] k/fdzc{ g;' f/ 500 ldlnln6/sf] emfn] cfi} fwL lsg]/

Nofof] . p;n] laxfg 10 ldlnln6/ / a]ns' f 10 ldlnln6/ b/n] cf}ifwL ;j] g

u¥of] eg],

-s_ 3 lbgdf p;n] slt cfi} fwL vfof] xfn] f <

-v_ 8 lbgkl5 p;n] cfi} fwL vfg 5f8\of] eg] ca slt ldlnln6/ cf}ifwL afsF L
xfn] f <

7. /dfn] yd{;df /fvs] f] 2 ln6/ 770 ldlnln6/ lrofdWo] 1 ln6/ 15 ldlnln6/
lajm| L ul/g\ eg] ca slt lrof afsF L xfn] f <

kl/of]hgf sfo{ (Project work)

tkfOs‘{ f] 3/df ePsf] t/nj:t'sf] Ifdtf gfKg] j:tx' ¿sf] ;ª\sng ugx'{ f];\ . pSt
efF8fdf Ifdtf cgd' fg ugx{' f;] \ . Ifdtf yfxf gePsf] ef8F fs] f] Ifdtf yfxf ePsf]
j:t'dfkm{t\ kQf nufpgx' f;] \ .

116 ul0ft M sIff $

3.5 tf}n (Weight)

3.5.1 k'g/jnf]sg
xfdL b}lgs hLjgdf ljleGg ;fduL| x¿sf] vl/b ug{] ub{5f}F . ahf/af6 lsg]/ NofOg] o:tf
;fduL| x¿sf] tf}n lngsf lgldQ s] s:tf pks/0fsf] k|ofu] ub5{ fF} < oL ;fduL| x¿sf]
ko| f]u s;/L ul/G5, 5nkmn ug{x' f];\ .

3.5.2 lsnfu] f| d / uf| dnfO{ Pscfk;df ¿kfGt/0f (Conversion of kilogram and

gram each other)

lj|mofsnfk 1 M
tnsf lrqx¿ / kZ| gx¿df cfwfl/t /xL 5nkmn ug'{xf;] \ M

k|Zgx¿
(i) tkfOs‘{ f ufp3F / tyf k;ndf j:ts' f] tfn} lngsf nflu sg' sg' ;fduL| sf] ko| fu]

ul/G5 <

(ii) k/Dk/fut ¿kdf ko| fu] ub}{ cfPsf] t/fh' / l8lh6n t/fh'df s] km/s 5 <

(iii) tfhs' f] Psflt/ 1 lsnf]uf| d csf]l{ t/ 100 u|fdsf] sltcf6] f 9s /fVbf t/fh'df
a/fa/ x'G5 <

ul0ft M sIff $ 117

(iv) 200 uf| dsf sltcf6] f 9s /fVbf 1 lsnfu] |fd;uF a/fa/ xG' 5 <
(v) 500 uf| dsf sltcf]6f 9sn] 1 lsnf]uf| d agfpF5 <
1 lsnf]u|fd -ls=uf| =_ df 200 u|fd -u|f=_ sf 5 cf6] f 9sx¿ x'G5g\ . o;u} /L 500 sf 2
cf]6f 9sx¿ x'G5g\ . o:t} 100 u|fdsf 10 cf]6f 9sx¿ x'G5g\ . t;y{ 1 lsnf]u|fd
= 1000 uf| d x'G5 .

ljm| ofsnfk 2
tn lbOPsf ;fdu|Lx¿sf] cjnf]sg ug'{xf;] \ . oL ;fduL| x¿sf] tfn} sf] gfk lsnf]uf| d
jf u|fd s]df gfKg pkoS' t xfn] f, cg'dfg ug{x' f];\ . u|fddf ePsf] j:tn' fO{ lsnfu] f| d
cyjf lsnfu] |fdnfO{ u|fddf ¿kfGt/0f ug{ s] ugk{' nf{, 5nkmn ug'{xf;] \ . tkfO‘{sf] 3/df
klg s'g} ;fdu|L tfn} /] NofPsf] xg' ;S5 . tL ;fdu|Lx¿ tf}nsf] u|fd jf lsnf]u|fd s]df
gfKg pko'St xG' 5, sIffsf]7fdf k|:tt' ug'{xf];\ .

lsnfu] |fdnfO{ uf| ddf n}hfbF f 1000 nfO{ u'0fg ul/G5 eg] uf| dnfO{ lsnf]u|fddf n}hfbF f
1000 n] efu ul/G5 .

pbfx/0f 1
l/hgn] 3 ls=u|f= 500 u|fd :ofp ahf/af6 NofP eg] slt uf| d xf]nf <
;dfwfg
3 ls=u|f= 500 uf| d = (1000 × 3) u|fd + 500 u|fd

= 3000 uf| d + 500 uf| d
= 3500 u|fd

118 ul0ft M sIff $

pbfx/0f 2
sg' } af6f] vGg] j|mddf 8f]h/n] 22000 uf| dsf] 9ª' \uf aflx/ lgsfNof] eg] pSt 9ª' u\ f slt
lsnf]uf| dsf] /x]5, kQf nufpgx' f;] \ .

;dfwfg efu u//] x]/f},F

22000 ÷ 1000

1000 )22000( 22

- 2000 1000 u|fd = 1 ls=u|f=

2000

- 2000

0

∴ct pSt 9'ª\uf 22 ls=u|f=sf] /x5] .

pbfx/0f 3

tnsf j:t'x¿sf] tf}n gfKg uf| d cyjf lsnf]u|fd sg' s'g PsfO pko'St xG' 5, cgd' fg
ugx{' f;] \ .

olb ;ftcf]6f cgf/sf] tf}n 2 ls=u|f= 500 u|fd eP uf| ddf slt xfn] f <

;dfwfg

(i) lsnfu] f| d (ii) uf| d (iii) lsnf]uf| d (iv) u|fd

;ftcf6] f cgf/sf] tfn} = 2 ls=u|f= 500 uf| d

= (1000 x 2) u|fd + 500 u|fd

= 2000 u|fd + 500 uf| d

= 2500 u|fd

ul0ft M sIff $ 119

cEof;

1. ¿kfGt/0f ugx{' f];\ M uf| d
(i) 3 ls=uf| = Ö

(ii) 3 ls=u|f= 250 u|fd Ö u|fd

(iii) 1400 uf| d Ö ls=u|f= u|fd

(iv) 7 ls=uf| = 500 u|fd Ö uf| d

2. u|fddf ¿kfGt/0f ugx{' f];\ M (ii) 1 ls=uf| = 300 u|fd
(i) 6 ls=u|f=

(iii) 20 ls=uf| = 500 uf| d (iv) 25 ls=uf| = 700 u|fd

(v) 7 ls=uf| = 530 uf| d (vi) 8 ls=u|f= 900 u|fd

3. lsnf]u|fd / u|fddf nV] gx' f;] \ M (ii) 18300 uf| d
(i) 7500 uf| d

(iii) 8770 u|fd (iv) 5100 u|fd

(v) 2600 uf| d (vi) 5555 u|fd

4. lzNkfsf] lstfa /fvs] f] Aofu 3 ls=u|f= 250 uf| d /x5] eg] slt u|fd /x]5 .
5. ljBfnosf] k':tsfnodf /xs] f] cªu\ ]|hL zAbsf]ifsf] tfn} 2300 u|fd /x5] eg]

slt ls=uf| = /x]5 .

kl/of]hgf sfo{ (Project work)
s'g} kfFrcf6] f ;fdu|Lx¿sf] ;ª\sng ug{'xf;] \ . ltgLx¿sf] kl/df0f gfKgsf lgldQ uf| d
cyjf lsnf]u|fd s] k|of]u ul/G5, nV] gx' f;] \ .

;fdfgsf] gfd
PsfO

120 ul0ft M sIff $

3.5.3 lsnf]uf| d / uf| d;DaGwL hf8] / 36fp (Addition and subtraction

related to kilogram and gram)
lj|mofsnfk 1
Pp6f l8lh6n t/fh' lng'xf];\ . Pp6f emfn] fdf sx] L ;fdu|Lx¿
/fv]/ tf}n gfKgx' f];\ . o;df c¿ ;fdu|Lx¿ yKb} hfg'xf];\ . t/fh'n]
bv] fPsf] tfn} slt 5, l6kf]6 ug{'xf;] \ . emfn] fsf] ;fduL| ;lxtsf]
tfn} u|fddf 5 ls lsnfu] |fddf 5, Tof] klg l6kf6] ug{'xf;] \ .

ljm| ofsnfk 2
tn lbOPsf j:t'x¿sf] tf}nsf cfwf/df 9s;Fu hf]8f ldnfpg'xf];\ M

(i) (i)

(ii) (ii)

(iii) (iii)

(iv) (iv)

(v) (v)
ul0ft M sIff $ 121

pbfx/0f 1

(a) sfFj|mf] / nfs} fsf] hDdf tf}n slt xfn] f <
(b) nfs} f / ufFh/sf] hddf tf}n slt xf]nf <
(c) nf}sfsf] tf}n ufh/sf] eGbf sltn] a9L xf]nf <

;dfwfg tf}n lgsfNgsf
-s_ sfj|mf] / nfs} fsf] hDdf tf}n slt xf]nf < nflu s] ug{'knf{ <

sfj|mf] / nf}sfsf] hDdf tfn} lgsfNg hf]8\gk' 5{ .

ls=u|f= u|fd ls=u|f= / u|fd Pp6f Pp6f nx/df

2 260 /fVg'xf;] \ . ls=u|f= / ls=uf| = clg uf| d
/ u|fd hf8] \gx' f;] \ . 1000 u|fd Ö 1
+ 4 800 ls=uf| = xg' ] ePsf]n] 1060 uf| d Ö 1
ls=u|f= 60 u|fd xG' 5 .
6 ls=uf| = 1060 u|fd

1
7 ls=uf| = 60 uf| d

hDdf tf}n 7 ls=uf| = 60 uf| d /x]5 .

-v_ nfs} f / ufh/sf] hDdf tfn} f slt xf]nf <

;dfwfg

ls=u|f= u|fd

3 500

+ 2 260

5 ls=u|f= 760 uf| d

o;df nfs} f / ufh/sf] hDdf tf}n 5 ls=u|f= 760 uf| d /x]5 .

122 ul0ft M sIff $

-u_ ufh/sf] tf}n nf}sfsf] eGbf sltn] a9L xf]nf <

;dfwfg

tf}nsf] km/s lgsfNgsf nflu 36fp ugk'{ b{5 .

ls=u|f= u|fd tfn} df ls=u|f= / u|fdsf] 5'6\6f5'66\ }
nx/df /fv]/ uf| daf6 u|fd /
4 800 ls=uf| = af6 ls=uf| = 36fcf}F .

- 3 500

1 ls=u|f= 300 uf| d

ufh/sf] tf}n nfs} fsf] eGbf 1 ls=uf| = 300 uf| dn] a9L /x]5 .

pbfx/0f 2

Pp6f efF8fdf 5 ls=uf| = lrgL c6\5 . t/ To; ef8F fdf clxn] 3 ls=u|f= 420 u|fd lrgL
5 eg] slt lrgL yKg ;lsG5 <
;dfwfg

ls=uf| = uf| d

5 0

- 3 420

o;nfO{ ldnfP/ ;dfwfg ubf{,

ls=u|f= u|fd

5 4 1000

- 3 420

1 ls=u|f= 580 uf| d

5 ls=u|f= lrgLsf] ef8F f] eg{ 1 ls=u|f= 580 uf| d yKg ;lsG5 .

cEof; (b) ls=uf| = u|fd

1. hf]8 ug'x{ f];\ M 7 600
(a) ls=u|f= uf| d + 5 200

5 420
+ 4 100

ul0ft M sIff $ 123

(c) ls=u|f= uf| d (d) ls=uf| = u|fd

17 525 51 152
+ 13 663 + 27 275

2. 36fp ug{'xf;] \ M

(a) ls=uf| = uf| d (b) ls=uf| = uf| d

7 500 32 826
- 3 300 - 15 527

(c) ls=uf| = uf| d (d) ls=uf| = u|fd

12 88 524
- 10 616
+ 69 811

3. cfdfn] ahf/af6 3 ls=u|f= 500 u|fd bfn / 2 ls=uf| = 750 u|fd cf6f lsg/]
Nofpg'eof] eg] logLx¿sf] hDdf tf}n slt xf]nf <

4. ;/nfn] 1 ls=uf| = ;G' tnf ahf/af6 lsg]/ NofOg\ . olb 750 uf| d ;'Gtnf laluP| sf]
eP slt ;'Gtnf /fd|f lyP xf]nfg\ <

5. Ps hgf t/sf/L Jofkf/Ln] 24 ls=uf| = cfn', 20 ls=uf| = 300 u|fd Kofh / 15
ls=uf| = 700 uf| d s/] fp xfn] ;n] k;naf6 lsg]/ NofP eg] hDdf slt t/sf/L
lsg5] g\ <

6. lgdfsf] 7 ls=u|f= 300 u|fd tf}n a9]/ 50 ls=uf| = 500 uf| d ku' 5] eg] pgsf]
klxn]sf] tfn} slt lyof] xfn] f <

7. /fhs' f] tf}n 47 ls=uf| = 300 uf| daf6 a9/] 50 ls=uf| = 500 uf| d k'u]5 eg] pgsf]
a9]sf] tf}n slt /x]5, kQf nufpgx' f;] \ .

kl/of]hgf sfo{ (Project work)
ljBfnosf] glhs} /x]sf] ls/fgf k;ndf uP/ s'g} kfFrcf6] f j:t'x¿sf] tfn} sf] gfk
;f]Wgx' f;] \ / o;nfO{ l6kf]6 ug'x{ f];\ . lsnfu] |fd / uf| ddf /x]sf] tfn} nfO{ hf]8g\ x' f];\ .
sIffsf]7fdf k|:tt' ug{x' f];\ .

124 ul0ft M sIff $

3.6 kl/ldlt / Ifq] kmn (Perimeter and Area)

3.6.1 kl/ldlt (Perimeter)

ljm| ofsnfk 1

bfofFsf] lhofa] f8] {sf] cjnfs] g ug{'xf];\ / tnsf

k|Zgx¿df 5nkmn ugx{' f];\ .
(i) /ftf,] lgnf] / kx]Fnf] /ªsf] /a/AofG8af6

agfOPsf] cfotx¿sf] 3]/fsf] hDdf
nDafO slt xfn] f < logLx¿dWo] ;ae} Gbf
nfdf] sg' xfn] f <

(ii) xl/of] / KofhL /ªsf] /a/AofG8af6

agfOPsf] cfotsf] 3]/fsf] hDdf nDafO

slt xf]nf < logLx¿df ;ae} Gbf 5f6] f]

s'g xfn] f < lhof]af]8{ KnfOp8df lsnf 7f]sL

(iii) olb Pp6f lsnfaf6 csf{] lsnf;Ddsf] /a/AofG8sf] ;xfotfn] ljleGg
t;] f{] jf 7f8f] nDafO a/fa/ 3 ;]=ld= HofldtLo cfsl[ tx¿ b]vfpg k|of]u
eP cfotx¿ / ju{x¿sf] 3/] fsf] hDdf ul/g] z}lIfs ;fduL| xf] .
nDafO slt slt x'G5 <

ljm| ofsnfk 2

bfofFsf] uf| kmaf8] {sf] cjnf]sg u/L tnsf k|Zgx¿sf] pQ/ vfH] gx' f];\ M

(i) cfot ABCD, XYZM / PQRS sf] 3]/fsf] A D M
hDdf nDafO slt xfn] f < X Z
B
(ii) cfot LMNO sf] 3]/fsf] hDdf nDafO slt P CY O
xfn] f < S N
R
(iii) uf| kmdf ePsf] ju{sf] nDafO 1 ;]lG6ld6/ ePdf Q
k|To]s cfsl[ tsf] 3/] fsf] hDdf nDafO slt L

xf]nf < M

(iv) ;ae} Gbf nfdf] 3/] f sg' cfsl[ tsf] /x]5 <

ul0ft M sIff $ 125

ljm| ofsnfk 3

pko'St ;ª\Vofdf ;dx" sf] lgdf{0f ugx'{ f;] \ . x/s]
;dx" n] Pp6f Pp6f u|fkmaf]8{ lngx' f;] \ . u|fkmaf]8{df
km/s km/s gfk / cfsf/sf cfotsf/ 1 ;]=ld= sf
jufs{ f/ sf7] fx¿ uGg'xf;] \ . slt kfpg'eof] < x/s]
;d"xn] k|:t't ugx'{ f;] \ .
lbOPsf] lrqdf Pp6f cfotsf/ cfsl[ t b]vfOPsf]
86af8] d{ f ag]sf] pSt cfsl[ tdf 1 ;]=ld= x 1 ;=] ld=
sf ;fgf sf]7fx¿ 5g\ . o;sf] rf/}lt/ j/k/sf nDafO
/ rf}8fOlt/sf ;fgf sf7] fx¿ uGgx' f;] \ . o;sf] nDafOdf 7 cf6] f sf7] fx¿ /xs] f 5g\ .
o;n} ] pSt cfsl[ tsf] kl/ldlt = 5 + 5 + 7 + 7
= 24 ;]=ld=
s'g} klg cfsl[ tsf] aflx/L 3/] fsf] gfknfO{ kl/ldlt elgG5 .
3.6.2 Ifq] kmn (Area)

lj|mofsnfk 4

(i) /ftf] / lgnf] /ªsf /a/AofG8af6 ags] f cfotx¿
leq sltcf6] f jufs{ f/ sf7] fx¿ 5g\ .

(ii) kxnF] f] / xl/of] /ªsf /a/AofG8af6 ags] f
cfotx¿ leq sltcf6] f jufs{ f/ sf7] fx¿ 5g\ .

(iii) olb Pp6f jufs{ f/ sf7] fsf] Ifq] kmn 1 ju{
PsfO ePdf ;a} cfotx¿sf] Ifq] kmn slt
slt xfn] f <

(iv) kl/ldltsf] lj|mofsnfk 2 df ePsf] lrq x/] L
cfotx¿ ABCD, XYZM, PQRS / LMNO leq slt sltcf]6f juf{sf/x¿
/xs] f 5g\ <

(v) uf| kmdf Pp6f jus{ f] Ifq] kmn 1 ju{ ;=] ld= xbF' f ;a} cfotx¿sf] Ifq] kmn slt slt xG' 5 <

cfoptbfxle/0qf e1Psf PsfO jux{ ¿sf] ;ªV\ of g} pSt cfotsf] If]qkmn xf] . Ps PsfO
nDafO ePsf] ju{sf] Ifq] kmn Ps ju{ PsfO xG' 5 .

126 ul0ft M sIff $

tnsf] uf| kmsf] cWoog u/L k|Zgx¿sf] pQ/ lbg'xf;] \ M

(i) sf]7f ug]/ cfot ABCD sf] Ifq] kmn kQf nufpgx' f];\ .
(ii) cfot MNOP df sltcf]6f ju{ PsfOx¿ 5g\ <
(iii) IJKL sf] kl/ldlt sf]7f ug/] kQf nufpg'xf;] \ .
(iv) UVWX df nDafOdf slt / rf8} fOdf sltcf]6f sf7] fx¿ 5g\ <
;dfwfg

AD I LU X
W
BC J V
MP K

NO

(i) nDafOlt/ ePsf ju{ PsfOx¿ = 5

rf}8fOlt/ ePsf ju{ PsfOx¿ = 2

cfot ABCD sf] If]qkmn = 5 × 2 = 10 ju{ PsfO

o;nfO{ o;/L klg ;dfwfg ug{ ;lsG5 .

cfotleq /x]sf sf7] fsf] ;ª\Vof = 10

ABCD sf] Ifq] kmn = 10 ju{ PsfO

(ii) MNOP df 16 cf]6f ju{ PsfOx¿ 5g\ .

(iii) IJKL sf] aflx/ nDafO / rf8} fOdf /xs] f] sf7] fsf] ;ªV\ of = 9 + 8 + 9 + 8 = 34 cf6] f

kl/ldlt = 34 PsfO

(iv) UVWX df, nDafOdf ePsf] sf7] f = 7
rf8} fOdf ePsf] sf7] fsf] ;ªV\ of = 4

ul0ft M sIff $ 127

pbfx/0f 2

tn lbOPsf] lrqdf nDafO / rf8} fOlt/sf juf{sf/ sf7] fx¿ ugL cfsl[ tsf] Ifq] kmn /
kl/ldlt kQf nufpg'xf];\ .
;dfwfg
nDafOlt/sf] jufs{ f/ sf7] fsf] ;ªV\ of = 14
rf8} fOlt/sf] jufs{ f/ sf7] fsf] ;ªV\ of = 10
hDdf sf7] fsf] ;ª\Vof = 14 × 10 = 140
o;sf/0f If]qkmn = 140 ju{ PsfO
jl/kl/sf] rf}3]/fsf] sf]7fsf] ;ªV\ of = 14
+ 14 + 10 + 10 = 48 PsfO
kl/ldlt = 48 PsfO

pbfx/0f 3

nDafO 10 ;]=ld= / rf}8fO 6 ;=] ld= ePsf] Pp6f cfot lvRg'xf];\ . juf{sf/ sf7] f
agfP/ pSt cfotsf] kl/ldlt / If]qkmnsf] juf{sf/ kQf nufpg'xf];\ .

;dfwfg

cfotleq nDafO 1 ;=] ld= / rf}8fO 1

;]=ld= ePsf] ju{ agfcfF} . nDafOlt/ 10

cf6] f sf7] fx¿ eP eg] rf8} fOlt/ 6 cf]6f

sf7] fx¿ 5g\ . 6 ];=ld=

hDdf sf7] fx¿ = 10 × 6 = 60 eP 10 ;]=ld=
To;}n] cfotsf] Ifq] kmn 60 ju{ ;=] ld=
eof] .

o:t} u/L nDafOdf /xs] f] sf7] fsf] ;ª\Vof = 10 sf7] f + 10 sf]7f = 20 sf7] f

rf8} fOdf /xs] f] sf]7fsf] ;ªV\ of = 6 sf]7f + 6 sf]7f = 12 sf]7f

hDdf sf7] f = 10 + 10 + 6 + 6 = 32

o;n} ] kl/ldlt = 32 ;]=ld= eof] .

128 ul0ft M sIff $

cEof;
1. tnsf cfotx¿df ePsf jufs{ f/ sf7] f ug]/ Ifq] kmn kQf nufpg'xf];\ M

(i) (ii)

(iii) (iv)

2. tnsf kT| o]s cfotsf/ cfsl[ tsf] kl/ldlt / Ifq] kmn kQf nufpg'xf;] \ . -k|Tos]
sf]7fsf] Ifq] kmn 1 ju{ ;]=ld= 5 ._

(i) (ii)

(iii) (iv) 129
ul0ft M sIff $

3. uf| kmkk] /df tn lbOPcg';f/ gfksf cfoft lvRg'xf];\ . juf{sf/ sf7] f ug]/
kl/ldlt / If]qkmn kQf nufpgx' f];\ .

(i) (ii)
9 cm

4 cm 8 cm 7 cm 6 cm
(iii) (iv)

5 cm

5 cm 4 cm

4. tnsf] cfsl[ tsf] kl/ldlt / If]qkmn slt xG' 5 < sf]7f ug/] kQf nufpgx' f;] \ .

130 ul0ft M sIff $

kl/of]hgf sfo{ (Project work)

(i) sIff $ sf] ul0ft k':tssf] dflyNnf] ;txsf] If]qkmn / kl/ldlt juf{sf/ sf]7f
agfP/ kQf nufO{ sIffsf7] fdf k:| tt' ug{x' f;] \ .

(ii) cfcfˆgf] gfdsf] klxnf] cIf/nfO{ k|Zg g= 3 sf] h:t} u/L u|fkmkk] /df To;sf] kl/
ldlt / If]qkmn kQf nufpg'xf];\ / sIffsf]7fdf k|:t't eof] .

ldl>t cEof;

1. vfnL 7fpdF f plrt zAb nV] g'xf];\ M

(i) 1 jifd{ f lbg xG' 5 .

(ii) 2 306fdf ldg]6 xG' 5 .

(iii) 5 ?lkofF eg]sf] k;} f xf] .
(iv) 3 ld6/df ;]lG6ld6/ x'G5 .

(v) 2000 ld6/ egs] f] lsnfl] d6/ xf] .

(vi) 50 ln6/df ldlnln6/ xG' 5 .

(vii) 3 ls=u|f=df uf| d x'G5 .

2. ¿kfGt/0f ug{x' f;] \ M
(i) 5 jif{ 3 dlxgfnfO{ dlxgfdf
(ii) 4 306f 45 ldg]6nfO{ ldg]6df
(iii) 140 306fnfO{ lbg / 306fdf
(iv) 25100 ld6/nfO{ lsnfl] d6/df kl/jt{g ugx{' f;] \ .
(v) 9 ln6/ 280 ldlnln6/nfO{ ldlnln6/df nV] gx' f;] \ .
(vi) 55 ls=uf| =df slt u|fd x'G5 .

3. Pp6f emfn] fdf ePsf tLgcf6] f lstfasf] tfn} 4 ls=uf| = 5 . olb bO' c{ f]6f
lstfasf] tfn} 1 ls=uf| = 200 u|fd eP afsF L Pp6f lstfasf] tfn} slt xf]nf <

ul0ft M sIff $ 131

4. Pp6f kfgLsf] aft] nsf] dN" o 80 ?lkofF 75 k;} f kb5{ eg] To:t} 9 cf6] f af]tnsf]
dN" o slt knf{, kQf nufpgx' f;] \ .

5. ;]ljsf / ;fl] jtsf] pd/] sf] of]ukmn 20 jif{ 10 dlxgf 5 . ;]ljsfsf] clxns] f]
pd]/ 8 jif{ 11 dlxgf 5 eg] ;f]ljtsf] pd]/ slt xfn] f <

6. ;u/dfyfsf] prfO 8848 ld6/ 86 ;l] G6ld6/ 5 eg] ;]lG6ld6/df ¿kfGt/0f ubf{
slt xfn] f <

7. Ps Kofs]6 rgfsf] tf}n 2 ls=uf| = 600 uf| d 5 eg] 5 Kofs6] rgfsf] tfn} slt
xfn] f <

8. 11 ln6/ 727 ldlnln6/df 20 ln6/ 840 ldlnln6/ yKbf slt ln6/
xf]nf, kQf nufpg'xf;] \ .

9. tn lbOPsf] cfs[ltsf] If]qkmn / kl/ldlt lgsfNgx' f;] \ M

10. lzjn] ?= 100 lnP/ ahf/ uof] . p;n] 25 ?lkofF 50 k};f kg]{ snd, 30 ?lkofF
25 k};f kg{] sfkL / 10 ?lkofF 50 k};fdf bO' c{ f]6f l;;fsnd lsGof] eg] pm;Fu
slt ?lkofF / k;} f afFsL /xs] f] xfn] f, kQf nufpgx' f;] \ .

11. 12 af]tn h;' sf] dN" o ?= 1806 k5{ eg] Ps af]tn h;' sf] dN" o slt k5{ xfn] f,
kQf nufpg'xf;] \ .

132 ul0ft M sIff $

4. ;d"x (Set)

4.1 kf7;uF ;DalGwt sx] L zAbjnLsf] vf]hL

tn n]lvPsf zAbx¿n] xfd|f] b}lgs hLjgdf s] cy{ /fVb5g\ < ;fyLx¿;uF 5nkmn

u/L zAbsf] cy{ nV] g] k|of; ugx'{ f];\ .

(i) x'n (ii) ayfg (iii) emG' 8

(iv) u88\ L (v) tfFtL (vi) uR' 5f

tn lrqdf oL zAbx¿;Fu dn] vfg] lrqx¿nfO{ 5\of;ld; u/L lbOPsf] 5 . zAbsf]

cy{ ldNg] u/L hf]8f ldnfpg'xf];\ .

(i) xn' 1

(ii) ayfg 2

(iii) emG' 8 3

(iv) u8\8L 4
(v) tfFtL 5
(vi) u'R5f 6
ul0ft M sIff $
133

4.2 sx] L j:t'x¿sf] ;ªs\ ng (Collection of some objects)

lrqdf lbOPsf s]xL j:t'x¿sf] ;ª\sngnfO{ xg] '{xf;] \ / s] a‰' g'eof,] ;fyL;uF 5nkmn

ug'x{ f];\ . (B)

(A)

(C) (D)

aei ou

ca lgDglnlvt kZ| gsf] pQ/ lbg'xf;] \ M
1. (i) dflysf] ;ªs\ ng (A) df s] s] j:t'x¿ 5g\ <
(ii) ;ªs\ ng (A) df ;'Gtnf 5 ls 5}g <
(iii) ;ªs\ ng (A) nfO{ gfdfs/0f ug'k{ bf{ s] eGg plrt xG' 5 <
2. (i) dflysf] ;ªs\ ng (B) df s] s] j:tx' ¿ 5g\ <
(ii) ;ªs\ ng (B) df v';fg{ L k5{ ls kb}{g <
(iii) ;ª\sng (B) nfO{ gfdfs/0f ubf{ s] eGbf plrt xG' 5 <
3. (i) ;ªs\ ng (C) df s] s] j:t'x¿ 5g\ <
(ii) ;ªs\ ng (C) df kl] G;n k5{ ls kbg{} <
(iii) ;ª\sng (C) nfO{ gfdfs/0f ubf{ s] eGg ;lsPnf <

134 ul0ft M sIff $

4. (i) ;ªs\ ng (D) df s] s] cIf/x¿ 5g\ <
(ii) ;ªs\ ng (D) df b k5{ ls kb}{g <
(iii) ;ªs\ ng (D) nfO{ gfdfs/0f ug'{ kbf{ s] eGg' knf{ <
(iv) dflysf] ;ª\sng (D) nfO{ æ:j/ j0fÆ{ eg]/ gfdfs/0f ug{ ldN5 <
cEof;

1. tn lbOPsf] kT| os] ;ªs\ ngdf x/]s ;ª\sngsf] ;uF } lbPsf] j:t' ;ªs\ ngdf
k5{ eg] √ / × kb}g{ eg] nV] gx' f];\ .

(i) (ii)

rDrf sDkf;
ss] kl] G;n

(iii) (iv) ;f]daf/
cfOtaf/ cfOtaf/
sfutL
;'Gtnf aw' af/ ;fd] af/

(v) laxLaf/

1, 3, 5, 7 (vi)

9 la/fnf ]
11 af3

ul0ft M sIff $ 135

kl/ofh] gf sfo{ (Project work)
xf], xfO] g vn] (Yes/No Game) sIffsf7] f aflx/ v]Ng]

b'O{ hgf ;fyLx¿dWo] Pp6f ;fyLn] j:tx' ¿sf] ;ª\sngsf sx] L gfd eG5g\ . csf]{
;fyLn] Tof] ;ª\sngdf kg]{ jf gkg{] Pp6f j:ts' f] gfd eG5 . nfOgdf a;]sf ;fyLx¿dWo]
;aeGbf cufl8sfn] k5{ jf kb}g{ dWo] Pp6f dfq zAb atfpgx' 'G5 . olb ;xL eP
cufl8sf] uf]nfdf uO{ a:g] unt eP nfOgsf] k5fl8 pleP/ kfnf] sg' {] ug'k{ 5{ . ha
;a} ;fyL uf]nf]df cfO{ a:g' x'G5 . ta vn] ;dfKt x'G5 . pbfx/0fsf nflu ;fyL …sÚ
n] /ftf], lgnf], xl/of], kx]Fnf] eGg'x'G5 . ;fyL …vÚ n] sfnf] eGgx' 'G5 . ca nfOgdf a:g]
;fyLn] k5{ eg] uNtL xG' 5 k5fl8 uP/ pleg'k5{ kb{}g eg] ;xL xG' 5 / ufn] f] 3/] fleq
uO{ a:g kfOG5 .

136 ul0ft M sIff $

4.3 ;d"xsf] kl/ro (Introduction of sets)

tnsf] ;ª\sngnfO{ xg] {x' f];\ M

 of] ;ª\sngdf v/fof] 5 .
v/fof] of] ;ªs\ ngsf] Pp6f
;b:o xf] .

 of] ;ªs\ ngdf d';f] 5g} .
d';f] of] ;ªs\ ngsf] ;b:o
xf]Og .

of] Pp6f ;d"xsf] pbfx/0f
xf] . of] pbfx/0fsf cfwf/df
xfdLn] ;dx" nfO{ tn lbOPcg';f/
kl/eflift ug{ ;S5f}F .

sg' } j:t' k5{ ls kbg}{ eg/] olsg ug{ ;Sg] u/L ul/Psf] j:t'x¿sf] ;ª\sngnfO{
;d"x elgG5 . ;d"xdf ;ªs\ lnt j:t'x¿ Tof] ;dx" sf ;b:ox¿ x'g\ .

pbfx/0f 1

tn lbOPsf k|Tos] ;d"xx¿df ;d"x;uF lbOPsf j:t'x¿ Tof] ;dx" df k5g{ \ eg] √
/ kb}{gg\ eg] × ug{x' f];\ .

(i) (ii)

z'j|maf/, zlgaf/, cfOtaf/ 2, 4, 6, 8

cfOtaf/ 4

;fd] af/ 10

ul0ft M sIff $ 137

(iii) (iv)

abcd

e
f

(v) cªu\ ]|hL snd
O/]h/

(vi) o;fb] f
/fwf
ul0ft g]kfnL

;fdflhs

cªu\ |]hL
lj1fg

(vii) (viii)

j}zfv, h]7, ;fpg, ebf}

8f8' c;f/
Kn]6 c;f]h

of] pbfx/0fsf cfwf/df xfdL tnsf] lgisifd{ f kU' g ;S5f}F .
s'g} klg ;d"x hgfpg] ;ª\sngdf s'g} j:t' kb{5 eg] Tof] j:t' pSt ;d"xsf] ;b:o
xf] . kb}{g eg] ;b:o xf]Og .

138 ul0ft M sIff $

lj|mofsnfk 1
gldNg] x6fcfF} (ODD ONE OUT)

 of] 6fs] /Ldf ePsf :ofp, s]/f, cfFk,
gl/jn / nf}sfsf] ;ª\sngdf nf}sf ldNb}g .
To;n} ] nfs} f cfp6 (out) ubf{ kmnk"mnsf]
Pp6f ;dx" aGb5 .

tnsf kl/ofh] gfx¿ k"/f ug{x' f;] \ M
sIffsf]7fdf ePsf ;a} j:t' ;ª\sng u/L ldNg] j:ts' f] ;dx" lgdf{0f ug{x' f];\ .
/Ltfn] u/]sf] ;d"x lgdf{0fdf sIffsf7] fsf lgDglnlvt ;fduL| x¿ k/s] f /x]5g\ .

(i) s] ldNb}g <
(ii) gldNg] j:t' x6fpFbf Tof] ;ªs\ ng hgfpg] Pp6f gfd lbg ldN5 <
(iii) pko'St gfd lbO{ ;dx" df lgdf0{ f u/L bv] fpg'xf];\ .

o:t} lj|mofsnfk ljBfnosf] v]Ng] rp/df ePsf ;fdfuL| ;ªs\ ng u/L u0' fsf cfwf/df j:t'
5gf6] u/L ;dx" gdf{0f ug{'xf;] \ .

ul0ft M sIff $ 139

pbfx/0f 2

gldNg] j:t' x6fO{ (Odd one out
u/L) afFsL /x]sf j:t' hgfpg]
;d"xsf] gfdfs/0f ugx'{ f;] \ .

pQ/ M of] ;ª\sngdf ;fOgkg] odd
5 . To;n} ] ;fOgkg] nfO{ x6fpFbf k|f6] \
ofS6/, ;]6:Sjfo;,{ ;fOgkg] , sDkf;,
l8efO8/ / ?n/ ;dfj]z ePsf] Pp6f
;d"x aGb5 . of] ;dx" nfO{ æHofldlt
aS;sf HofldtLo cf}hf/Æ sf] ;d"x
eg]/ gfdfs/0f ug{ ;lsG5 .

cEof;
gldNg] j:tn' fO{ x6fO{ (odd one out u/L) afsF L /xs] f j:tn' fO{ hgfpg] ;dx" sf] gfd
n]Vg'xf;] \ .

1.

x6fpg]

;d"xsf] gfd

140 ul0ft M sIff $

2. x6fpg]
3.
4. ;dx" sf] gfd

5. x6fpg]
6.
ul0ft M sIff $ ;d"xsf] gfd

x6fpg]

;dx" sf] gfd

x6fpg]

;d"xsf] gfd

;dx" sf] gfd x6fpg]

141

7.

x6fpg ]

;dx" sf] gfd

8. 2,4,5,6 ;dx" sf] gfd x6fpg]
;dx" sf] gfd x6fpg]
9. jz} fv ;dx" sf] gfd x6fpg]
cfOtaf/ c;f/
h]7

10.

11.

x6fpg]

;dx" sf] gfd

142 ul0ft M sIff $

4.4. ;dx" nv] g (Writing set)
lj|mofsnfk 1

lrqdf lbOPsf j:tx' ¿af6 aGg] ;d"xnfO{ ;d"x n]Vg] ljlwcg;' f/ { } leq ;b:onfO{
sdf (,) n] 5'6\ofO{ n]Vg ;Sg'xG' 5 <

{ , , ,}

oxfF ;fl] wPsf lj|mofsnfkdf ;ªs\ lnt j:t'x¿nfO{ d‰ofn} f sfi] 7leq sdf -,_ n]
5'6\ofO{ nV] g elgPsfn] tnsf] h:t} u/L nV] g' kb{5 .

lj|mofsnfk 2 143
tn ;dx" nv] g ljlwaf6 Pp6f ;d"x n]v/] bv] fOPsf] 5 .

{cfOtaf/, ;fd] af/, dª\unaf/}

ul0ft M sIff $