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Teacher's Instruction ManualGrade 12(Sinhala)
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i jHdmdr ixLHdkh .=re udf.damfoaY ix.%yh
12 jk fYa%Ksh
jHdmdr wOHhk fomd;fka;=joHd yd ;dlaIK mSGh
cd;sl wOHdmk wdh;kh
uyr.u
ii
ixLHdkhixLHdkhixLHdkhixLHdkhixLHdkh
12
iii
fmrjokfmrjokfmrjokfmrjokfmrjok
iv
ix{dmkhix{dmkhix{dmkhix{dmkhix{dmkh
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iii
fufyhu yd WmfoaYl;ajh ( uydpdh ,d,a fmfrd uhd, wOHCI ckrd,a, cd;sl wOHdmk wdh;kh
WmfoaYl;ajh yd wCIKh ( wdpdh whs t,a .sksf.a h, iyldr wOHCI ckrd,a, cd;sl wOHdmk wdh;kh
Ihud,d kdhl;ajh ( ta isjfkairdcd uhd, m%Odk jHdmD;s ks,Od, jHdmdr wOHdmk fomd;fka;=j, cd;sl wOHdmk wdh;khIhud,d lgqj (
f,aLl uKav,h (
m.Kl joka ieliqu ( hQ ux.,sld fr;ak h, jHdmdr wOHdmk fomd;fka;=j, cd;sl wOHdmk wdh;kh
iageka,s is,ajd uhd, fcHIaG lldpdh,iudc ixLHdk wOHhk wxYh,Y%S chjOk mqr Yaj oHd,h
tia fla wd is,ajd uhd,fcHIaG lldpdh,iudc ixLHdk wOHhk wxYh,Y%S chjOk mqr Yaj oHd,h
'tia'mS' chiQh uhd"fcHIaG lldpdh,;SrK oHd wOHhk wxYh,Y%S chjOk mqr Yaj oHd,h
tia' isjrdcisxy uhd"fcHIaG lldpdh"wdl oHd wOHhk wxYh,fmardfoKsh Yaj oHd,h
rejka w;a l=udr uhd,iyldr jHdmD;s ks,Od,jHdmdr wOHdmk fomd;fka;=j,cd;sl wOHdmk wdh;kh'
ixch r;akj uhd,iyldr jHdmD;s ks,Od,jHdmdr wOHdmk fomd;fka;=j,cd;sl wOHdmk wdh;kh'
ta isjfkairdcd uhd, m%Odk jHdmD;s ks,Od,jHdmdr wOHdmk fomd;fka;=j,cd;sl wOHdmk wdh;kh
ta'' fiQh uhd, m%Odk jHdmD;s ks,OdjHdmdr wOHdmk fomd;fka;=j,cd;sl wOHdmk wdh;kh'
mS l=iqudj;S h, jHdmD;s ks,Odks,jHdmdr wOHdmk fomd;fka;=j,cd;sl wOHdmk wdh;kh
t'ta'whs' m;aKS fmfrd h,jHdmD;s ks,Odks,jHdmdr wOHdmk fomd;fka;=j,cd;sl wOHdmk wdh;kh'
tia'fla' m%Ndyrka uhd" jHdmD;s ks,Od,jHdmdr wOHdmk fomd;fka;=j,cd;sl wOHdmk wdh;kh'
jhs chisxy uhd, kd,kao oHd,h,fld
viii
mgqk
y bf.kq - b.eka l%shdj,sh 1
10 jHdmdr ixLHdkh Ihfhys Ih m:h iy tys iajNdjh .fIKh lrhs 2
20 jHdmdr f;dr;=re ikaksfokh lrhs 9
30 jHdmdr o;a; Yaf,aIKh lrhs 32
40 p,Hh w;r mj;sk inkaO;d .fIKh lr mqfrdal:kh lrhs 48
50 jHdmdl wjodkug uqyqK ug we;s iQodku m%oYkh lrhs 77
y bf.kq - b.eka - we.hS ie,iq 116
1ksmqK;dj 1'0 ( jHdmdr ixLHdkh Ih m:h iy tys iajNdjh .fIKh lrhs'ksmqK;d ugu 1'1 ( jHdmdr ixLHdkh iy tys iSudjka uYkh lrhs'ld,fo ixLHdj ( 04
bf.kq M,y ixLHdkfhys iajNdjh bka bgq lrkq ,nk ldhh wkqj fmkajd fohs'y ixLHdkfhka Wmu M, ,eu i|yd tys jdis" wjdis fjka lr olajhs'y ixLHdkh i|yd O ksjpk f.dvk.d" jvd;a iqiq ksjpkh f;darhs'y uQ,dY% mYS,kh lrka wjYH f;dr;=re ,nd .kshs'y Yla;Ska yd iSud ms
2bf.kqu i|yd fhda; Wmfoia (y my; i|yka Wmfoia isiqkag ,nd foka Tjqka bf.kqfuys fhdojkak y my; lafjk ud;Dld j,g wkqj isiqka lKavdh j,g fjka fldg ,nd fok ud;Dldj flfrys wjOdkh fhduq lrjkak'
y o;a; /ia lsu y o;a; ixOdkh lsu yd bm;a lsu y o;a; Yaf,aIKh y ks.ukj,g t
3 y "Intelligent business decision makers use statistics to plan, control and reduce the uncertainty involved in business decisions."
^nqoau;a ;Srlhka iska jHdmdr ;SrK .ekSf ie,iq lsug" md,khg iy
wjodku wju lsug ixLHdkh Nd; lrhs'&
y my; i|yka m%Yakj,g ms
4ksmqK;d ugu 1 ' 2 (jHdmdr lafIa;%h ;=< ixLHdkfhys odhl;ajh Yaf,aIKh lrhs'
ld,fo ixLHdj ( 06
bf.kq M, (y ixLHdkh jHdmdr lafIa;%hg jeo.;a jk wjia:d m%ldY lrhs'y ixLHdkh ;=< fhdod .kq ,nk Ys,amSh l%u k lrhs'y jHdmdr wjia:djkag iqiq ixLHdk Ys,am l%u ksjerj .
5y my; i|yka lreKq u;= lrka idlPdjla fufyhjkak'y oYkh jQ mska;+rj,ska m%;sY; w.hka" l%udkql+, j f.dvke.=Kq f.dvke.s,a,la"
m%ia;drhla" j.=jla oDYHudk jk nj'
y oDYHudk jQ rEmigyka O Ys,amSh l%u u; bm;a lr we;s nj'y tajdfha l%udkql+, njla fuka u is;a weo .kakd iq njla o mj;sk nj'y jHdmdl lghq;=j, m%.;sh iudf,dapkh lsug fuu igyka Nd; lrk nj'y tjeks igyka iy rEmigyka o" ixLHd;aul kq o f.dvke.Su ;=
Ih lreKq meye,s lr .ekSug w;aje,la (y jHdmdr lafIa;%fha my; wjia:dj, ;SrK .ekSu i|yd ixLHdk Ys,amSh l%u fhdod
.kshs'
y wjia:dy wf, mfhaIK ilaIKy kj m%jK;d yd mqfrdal:ky ie,iq lsu yd ;;a;aj md,khy msjehlrKh yd .Kkhy udkj im;a l
7wNHdih 1
1' jHdmdr lghq;=j, ixLHdkh fhdod.; yels wji:d olajka ta tla tla wjia:dj,
Nd; l< yels ixLHdk Ys,amSh l%u i|yka lrkak'
2' ixLHdk oHdf Nd; lrk my; i|yka fh flfhka ia;r lrkak'
i. ia;rd;aul ixLHdkh yd wkq;sl ixLHdkhii. ix.ykh iy kshehiii. ilaIK yd mlaIKiv. ,dlaIKslhv. p,Hh
3' " iEu oHdjla i|yd u ixLHdkh wksjdh f'" by; m%ldYfha i;H wi;H;djolajd Tf ms
8ksm qK;dj 2'0 ( jHdmdr f;dr;=re /ialr ikaksfokh lrhs'ksmqK;d ugu 2 ' 1 ( O uQ,dY% fhdod .kska o;a; /ia lrhs'ld,fo ixLHdj ( 15
bf.kq M,y jHdmdl o;a; O wdldrj,g j. lrhs'y m%d:l yd oa;shsl o;a; uQ,dY% ykajd foka tajdfha jdis iy wjdis u;=lr olajhs'y m%d:l o;a; uQ,dY% u.ska o;a; /ia lsu i|yd O WmlrK ksudKh lrhs'y j.SlrK m%fNao i,ld n,ka fhda.H;u m%fNaoh f;darhs'y wksYa;;dj wju lr .ekSu i|yd ie,iq ilihs'
bf.kq- b.eka ls%hdj,sh (msiquy f;a ludka;fha kshef,k llrejkaf.a jk hou ms
9y flgqm;a l< m%Yakdj,sh$ Wmf,aLkh o;a; /ia lsug n,dfmdfrd;a;= jk wh w;=frka lsysmfofkl=g ,nd ksjer m%;spdr ,ef hs mlaId lrkak' ^mQj mlaIdj is
lrkak'&
y ,efnk m%;spdr mok lrf.k m%Yakdj,sh$ Wmf,aLkh kej; ixfYdaOkh lrkak'y ixfYda; m%Yakdj,sh bm;a lrkak'y ix.Kkh yd kshe ilaIKh w;r fjki myokak'y Tf wkdjrK ksudKYS,Sj yd iduQysl j iuia; mka;shg bm;a lsug iQodk
jkak'
Ih lreKq meye,s lr .ekSug w;aje,la (y tla/ia lrkq ,nk o;a; m%d:l- oa;shsl" m%udKd;aul- .=Kd;aul" wNHka;r- ndysr
f,i j. l< yels nj'
y wruqKg wod< j uq,ajrg ,nd .kakd o;a; m%d:l o;a; nj'y m%d:l o;a; fndfyda g YajdikSh;ajfhka by< h yels w;r" hdj;ald,Sk o jk nj'
y uqs; fyda oHq;a yd bf,lafg%daksl udOHj,ska o o;a; /ia l< yels w;r tajdieug u oa;shsl o;a; jk nj'
Wod( wka;cd,h
y oa;shsl o;a; ,nd .ekSu myiq yd blauka jqjo iuyrg hdj;ald,Sk fkdjk nj'y o;a; /ia lsf O l%uj, jdis yd wjdis .
10
ksmqK;d ugu 2'2 ( jHdmdr o;a; ixOdkh lrhs'ld,fo ixLHdj ( 15
bf.kq M, (y o;a; je,a yd jDka; m;% igyka ms
11
bf.kqu i|yd fhda; Wmfoia (y my; i|yka Wmfoia isiqkag ,nd foka Tjqka bf.kqfuys fhdojkaky o;a; ixOdkh l< yels my; i|yka l%uj,ska Tf lKavdhug ,efnk l%uh flfrys
wjOdkh fhduq lrkak'
y iuqys; ixLHd; jHdma;shy idfmalaI ixLHd; jHdma;shy .=rejrhd$ .=rejh iska imhkq ,nk ly,l fiajlhska 100la miq.sh udih ;=q Nd;fhka .Kkh ir, lr.; yels nj'
=
=n
jjLogn
G1
1log
y rdYSka foll wkqmd; uska lafjk wiudk yrhka iys; p,Hhkays idudkHksrEmKh lsug yrd;aul uOHkH iqiq jk nj'
y ta i|yd my; iQ;%h fhdod.; yels nj'
==
n
iix
nH
1
1
38
ksmqK;d ugu 3'3 ( idfmalaI msysf Kq Nd;fhka o;a;j, msysu .%y lrhs'
ld,fo ixLHdj ( 12
bf.kq M,y ifmalaI msysf Kq k lrhs'y o;a; msysu idfmalaI Kq weiqka ia;r lrhs'y jHdma;shl iajrEmh ykd .ekSug p;=:l" oYul iy m%;sY;l Nd; lrhs'y mlaIKhl ,l=Kq wdYs%; j ;udg ysjk ia:dkh uekka jgyd .kshs'y iudcfha ;udg ysjk ;ek wka wh iu .
39
y Tf wkdjrK ksudKYS,Sj o" iduQyslj o fldgq fl igykla weiqka o iuia;mka;shg bm;a lsug iQodk jkak'
Ih lreKq meye,s lr .ekSug w;aje,la (y o;a; je,la iudk fldgia y;rlg fnfok ia:dk ;=fka w.h p;=:l f,i ykajk
nj'
y tajd 321 ,, QQQ jYfhka wxlkh lrk nj'y o;a; je,la iudk fldgia oyhlg fnfok w.hka" kjh oYul f,i ykajk nj'y tajd 9321 ..........,, DDDD jYfhka wxlkh lrk nj'y o;a;je,la iudk fldgia ishhlg fnfok w.hka wkQkjh m%;sY;l f,i ykajk
nj'
y tajd 99321 ..........,, pppp jYfhka wxlkh lrk nj'y idfmalaI msysf Kq ,nd .ekSu i|yd my; wdldrfha iQ;% fhdod.; yels nj'
CF
FLQ
CF
FLQ
CF
FLQ
Q
n
Q
n
Q
n
c
c
c
+=
+=
+=
3
43
13
2
42
12
411
1
y fldgq fl igykla weiqka idfmalaI msysf Kq .Kkh l< yels nj'
CFp
FLp
CFp
FLp
CFp
FLP
CFd
FLD
CFd
FLD
CFd
FLD
c
c
c
c
c
c
n
n
n
n
n
n
+=
+=
+=
+=
+=
+=
90
10090
90
50
1050
50
10
10010
8
108
8
5
105
1
10
1
1
110
1
15
11
40
ksmqK;d ugu 3'4 ( jHdmdr o;a; wmlsrK Kq u.ska Yaf,aIKh lrhs'ld,fo ixLHdj ( 16
bf.kq M,y o;a; iuQyhl wmlsrK Kq k lr W; iQ;% brsm;a lrhs'y ;SrK .ekSu i|yd O wmlsrK Kq .Kkh lrhs'y idfmalaI wmlsrK Kq fhdodf.k o;a; iuQyj, me;srSu ikaikaokh lrhs'y p,Hhka ksjerj weia;fka;= lr fydka ;SrK .kshs'y uOHl Kq jvd;aa w:j;a lsu i|yd wmlsrK Kq Nd; lrhs'
bf.kq- b.eka ls%hdj,sh (msiquy tlsfklg fjkia Wiska hq;= isiqka 7 fofkl= mka;sh bhg le|jkak'y Wfiys wkqms
41
Ih lreKq meye,s lr .ekSug w;aje,la (y o;a; iuQyhl isu ykd .ekSug wmlsrK Kq wjYH jk nj'y mrdih o;a; je,l ueo w.hla ie,ls,a,g fkd.kakd Kqula fnj'y wka; p;=:l mrdih iy wO wka; p;=:l mrdih ^ p;=:l wm.ukh& jHdma;shl
we;s o;a;j,ska 50] wmlsrKh muKla ksrEmKh lrk nj'
y o;a; iuQyhl uOHkHfhys isg tla tla o;a;hg we;s ksrfmalaI wm.ukhkaf.a idudkHhuOHkHh wm.ukh jk nj'
y tla tla w.hfhys isg uOHkHhg we;s wm.uk j.hkaf.a idudkHh " p,;dj" jknj'
y p,;djfha j.uQ,fhys Ok w.h iu; wm.ukh jk nj'y ksrfmalaI wmlsrKh uOHkHhg idfmalaI j bm;a l< g th idfmalaI wmlsrK
Kqula jk nj'
y jHdma;Skays wmlsrKhla ieiug fhdod.; hq;af;a idfmalaI wmlsrK Kq nj ydth iu; wm.uk ix.=Klh yd p,kh ix.=Klh jk nj'
y iu; wm.uk ix.=Klfha m%;sY; w.h p,k ix.=Klh jk nj'y iu; wm.uk ix.=Klh yd p,kh ix.=Klh tall j,ska iajdh;a; neka o;a; ldKAv lsysmhl p,kh ieiu myiqjk nj
y by; i|yka wmlsrK Kq ish,a, iuqys; jHdma;s i|yd o .Kkh l< yels nj'y wmlsrK Kq .Kkh lsu i|yd my; iQ;% fhdod.; yels nj'
mrdih } ixLHd iuQyfha jeu w.h - ixLHd iuQyfha wvqu w.h
R = H - L
wO wka; p;=:l mrdih
^p;=:l wm.ukh&
uOHkH wm.ukh
wiuqys; o;a; i|yd
iuQys; o;a; i|yd
213 QQ =
=
=
=
=
=
k
ii
k
ii
n
ii
f
XXfiMD
n
XXMD
1
1
1
42
p,;djh - ^S2&
iu; wm.ukh - ^S&p,;djfha j.uQ,h iu; wm.ukh f'
ksmqK;d ugu 3'5 (jHdmdr o;a; l=l;dj iy jlS%u Kq u.ska Yaf,aIKh lrhs'
wiuqys; o;a; i|yd
iuqys; o;a; i|yd
kslaIs; o;a; ta weiqka u
Wml,ams; uOHkH weiqka
fla;k l%uh Nd;fhka
Cdu
Cfi
fiufi
fiuS
AXd
fifidi
fifidi
S
fiXXfi
S
nXX
S
ii
ii
ii
i
i
/
)(
)(
222
2
222
22
22
=
=
=
=
=
=
43
ld,fo ixLHdj ( 06
bf.kq M, (((((y l=l;dj iy jlS%uh Kq k lr meye,s lrhs'y jHdma;sj, iajrEmh wkqj l=l;dj yd jlS%uh fhdod .kakd wdldrh ia;r lrhs'y l=l;dj yd jlS%uh Kq .Kkh lrhs'y m%dfhda.sl p,Hhkays iu;sl" wiu;sl iajrEmhka ms
44
y A wdh;kfha je fofkl= wvq jegqma ,nk njy tjeks iajrEmhla ykajkq ,nkafka Ok l=l;djla f,i nj'y B wdh;kfha je fofkl= je jegqma ,nk nj'y tjeks iajrEmhla y+kajkq ,nkafka iDK l=l;djla f,i hy C, D yd E wdh;k" jegqma jHdma;sj, fYaI keUqrejla olakg fkdue;s nj'y tu iajNdjh " iu;sl iajrEmh" jk nj'y iu;sl iajrEmhkays o O;d we;s nj'y jHdma;shl uqka jf m%udKh jlS%uh f,i yekafjk nj'
bf.kqu i|yd fhda; Wmfoia (y my; i|yka Wmfoia isiqkag ,nd foka isiqka bf.kqfuys fhdojkaky my; i|yka jHdmdr wdh;k ;=fka ffoksl l=Kqj,ska Tf lKavdhug ,efnk
jHdmdr wdh;kh ffoksl l=Kq flfrys wjOdkh fhduq lrkak'
l=Kq jkdlu l=Kq jkdlu l=Kq jkdlu l=Kq jkdlu l=Kq jkdlu k .Kk k .Kk k .Kk k .Kk k .Kk
^remsh,a^remsh,a^remsh,a^remsh,a^remsh,a oyia&oyia&oyia&oyia&oyia& A B C10 - 20 5 26 4
20 - 30 10 30 5
30 - 40 20 20 8
40 - 50 30 10 10
50 - 60 20 8 23
60 - 70 10 4 32
70 - 80 5 2 18
100 100 100
y jHdmdrfha ffoksl l=Kq ms
45
;=kajk p;=:lh )( 3Q 55 39'5 67'81
10 jk m%;sY;lh )( 10P 25 13'84 31'25
90 jk m%;sY;lh )( 90P 65 55 74'44iu; wm.ukh )(S 14'5 15'2 15'9
l=l;d ix.=Klh
( )( ) ( )( ) ( )( ) ( )109021 501090
21
213
2
21
2
2
3
43
PPPPPSK
QQQQQSK
SMdxSK
SMxSK
p
Q
+=
+=
=
=
jlS%u Kqu1090
1321 )(
PPQQK
=
y Tng wod< jHdma;sfha cd, fLh ksudKh lrkak'y tys iajrEmh ms> nj'y iDK l=l jHDdma;shl 0MMX d
46
y iDK l=l jHdma;shl 2312 QQQQ > jk nj'y iu;sl jHdma;shl iajrEmh ixLHd;aul j m%ldY lsug jlS%u ix.=Klh fhdod.;
yels nj'
y jlS%u ix.=Klh 0263 k th iu jls%uhla (Mesokurtic) jk nj'y jlS%u ix.=Klh 0'263g je jk l+g jlS%uhla (Leptokurtic) f,i yekafjk nj'y jlS%u ix.=Klh 0'263g wvq jk g "msg" jls%uhla (Platykurtic) f,i yekafjk
nj'
47
ksm qK;dj 4'0 ( p,H w;r mj;sk inkaO;d .fIKh lrka mqfrdal:kh lrhs'
ksmqK;d ugu 4'1 ( p,H wdldr ksYaph lrhs'ld,fo ixLHdj ( 02
bf.kq M, iajdh;a;" mrdh;a; jYfhka p,Hhka w;r fjkial u;= lrhs'
kEu p,Hhla wjia:dj wkqj iajdh;a; fyda mrdh;a; h yels nj WodrK u.ska
meye,s lrhs'
is ;s;a igyk wOHhkh lrka p,H i|yd iqiq wlaI f;darhs'
w:l:kh myiq lr .ekSug kslaIK fhdod .kshs'
wjia:dfjda;j ksjerosj f;a lrhs'
bf.kq- b.eka ls%hdj,sh (msiqu l=Kq , hk moh mqjref f,dl= wl=rska ,shkak'
l=Kq , ;SrKh ug n,mdk p,H iy l=Kq , u; ;SrKh jk p,H
ykdf.k l=Kq ,g wE|Sug isiqkag wjia:dj fokak
my; wdldrfha igykla f.dvk.d f.k bka Tfnys we;s lreKq u;= lrka
idlPdjla fufyhjkak'
wuq jH , iemhq m%udKh
l=Kq , b,a m%udKh
jegqma l=Kq m%udKh
jmi oelafjk p,Hh fjkia jk g l=Kq , fjkia jk nj'
l=Kq , fjkia jk g ol=Kq mi p,Hh fjkia jk nj'
tla p,Hhla u; ;j;a p,Hhla fjkiau O wdldrfhka ish yels w;r" fjd
m%ia;dlj o ksrEmKh l< yels nj'
48
bf.kqu i|yd fhda; Wmfoia ( my; i|yka Wmfoia isiqkag ,nd foka isiqka bf.kqfuys fhdojkak
my; i|yka isrs ;s;a igyka ;=fkka Tf lKavdhug ,efnk igyk fj; wjOdkh
fhduq lrkak'
tu igykg w,j my; i|yka ldhhka ys ksr; jkak'
m%ia;drfha iajNdjh uYkh lrkak'
x wCIhg yd y wCIhg .e
49
(1) (2)(3)
(4) (5)
ksm qK;d uguksm qK;d uguksm qK;d uguksm qK;d uguksm qK;d ugu 4 ' 24 ' 24 ' 24 ' 24 ' 2 ((((( isrs ;s;a igyka ksrSCIKh lsrSfuka inkaO;d wdldr ksYaph lrhs
ld,fo ixLHdj ( 02
bf.kq M,y we;s kslaIK iuQy fhdod .kska is ;s;a igyka ksudKh lrhs'y wk ,o is ;s;a igyk wOHhkh lr p,H fol w;r mj;sk fh inkaO;d
jrKh lrhs'
y tu fh inkaO;djh fyda thg wdikak fjkia fh inkaO;d mj;sk p,Hbm;a lrhs'
y kslaIK ;=
50
bf.kqu i|yd fhda; Wmfoia ( my; i|yka Wmfoia isiqkag ,nd foka isiqka bf.kqfuys fhdojkak
Tf lKavdhug ,efnk jHdmdl o;a; we;=
51
Ih lreKq meye,s lr .ekSug w;aje,la ( O inkaO;d j. ykd .ekSug is ;s;a igyka fhod .; yels nj'
is ;s;a igyka u.ska ykd .kakd fh inkaO;d" Ok inkaO;d fyda iDK
inkaO;d h yels nj'
mQK fh fjkqjg fndfyda g ykd .; yelafla m%n, fyda n, fh inkaO;d
nj'
iyinkaO;d fkdmj;sk wjia:d o fujeks is ;s;a igyk u.ska ykd .; yels
w;r" tajd Yaf,aIK i\yd fhdod .; fkdyels nj'
52
ksmqK;d ugu 4'3( p,H folla Yaf,aIKhg iyinkaO;d ixl,amh Nd;lrhs'
ld,fo ixLHdj ( 02
bf.kq M,y fokq ,nk p,Hhka m%udKd;aul yd .=Kd;aul f,i j. lrhs'y p,H folla w;r iyinkaO;df Ydj yd tys m%n,;ajh kslaIKfhka fyda is;s;a
igyka Nd;fhka m%ldY lrhs'
y p,H folla w;r mj;sk iyinkaO;dfjys m%n, nj fyda n, nj o< jYfhkaixLHd;aul j m%ldY lrhs'
y o;a; hq., kslaIKh lsfuka ;SrK .kshs'y ldhhka myiq lr .ekSug iyinka; p,Hhka Nd; lrhs'
bf.kq- b.eka ls%hdj,sh (msiquy my; i|yka mqj;am;a isia;, mka;sh bfha m%oYkh lrkak'
mqj;am;a isria ;,
y i,a , by
53
y p,H folla w;r O wdldrfha iyinkaO;d ;sfnk nj'bf.kqu i|yd fhda; Wmfoia (y my; i|yka j.= lKavdh j,g fnod ta ms
54
j.= wxl 5j.= wxl 5j.= wxl 5j.= wxl 5j.= wxl 5
wdh;khl ldh uKav,fha fiajd
ld,h iy ,nk udisl jegqm
fiajd ld,h ^wjq& udisl jegqm^re oyia&
10 12
8 20
7 7
8 6
12 8
15 18
j.= wxl 6j.= wxl 6j.= wxl 6j.= wxl 6j.= wxl 6
cE ksIamdok wdh;k myl cE l=Kq , yd udisl l=Kq m%udK
wdh;k , ^re& udisl l=Kq ^oyia&
A 90 60B 85 80C 92 60D 95 50E 88 48
j.= wxl 4j.= wxl 4j.= wxl 4j.= wxl 4j.= wxl 4
wdh;khla hka;% w;ajehdjg fhojQ
fiajl ixLHdj iy thg .;jQ ld,h
fiajl ixLHdj .;jQ ld,h
12 3
6 6
9 4
55
j.= wxl 7j.= wxl 7j.= wxl 7j.= wxl 7j.= wxl 7
wdh;klhl hka;% kv;a;= msjeh iy hdka;s %l fodaI we;s jQ jdr .Kk
kv;a;= msjeh hdka;s%l fodaI
^re' oyia& we;s jQ jdr .Kk
25 2
12 3
20 1
18 2
23 2
28 1
y my; i|yka Wmfoia isiqkag ,nd foka isiqka bf.kqfuys fhdojkaky Tng ,e w;s p,H m%udKd;aul p,Hhka o" ke;fyd;a .=Kd;aul p,Hhka o
hkak meye,s lr tfia i|yka lsug fya;= olajkak'
y o;a; kslaIKh lsfuka fyda is ;s;a igyka wefuka iajdh;a; p,Hh u; mrdh;a;p,Hh fjkiau meye,s lrkak'
y tu iyinkaO;dj ixLHd;aul j o< jYfhka m%ldY lrkak'y jHdmdr ldhlaIu lr .ekSu i|yd p,H w;r iyinkaO;dj Nd; l< yels
wjia:d folla olajkak'
y Tf wkdjrK ksudKYSS,Sj o" iduQyslj o iuia; mka;shg bm;a lsug iQodkjkak'
Ih lreKq meye,s lr .ekSug w;aje,la (y p,Hhka m%udKd;aul fyda .=Kd;aul f,i j. l< yels nj'y iajdh;a; p,Hfha o;a;j,g wkqrEm j mrdh;a; p,Hfha o;a; wkqf,dau$ m%;sf,dau
wdldrfhka fjkiah yels nj iy p,Hhka w;r iyinkaOh ksrEmKhg fLdjla
.e
56
ksmqK;d ugu 4'4 ( .=Ks; >QK iyinkaO;d ix.=Klh m%udKkh lrhsa'ld,fo ixLHdj ( 04
bf.kq M,y we;s o;a;" iyinkaO;d ix.=Klh fiug myiq jk m msqK iyinkaO;d ix.==Klhg ,efnk w.hka u.ska fh inkaO;djfha
m%n,;ajh yd Ydj jrKh lrhs'
y ffoksl ;fha yuqjk O p,Hhka myiqfjka ikaikaokh lsug tallj,skaf;dr kq fhdod .kshs'
y we;e by< iyinkaO;dj, o ksr:l inkaO;d ;sh yels nj'
bf.kq- b.eka ls%hdj,sh (msiquy my; lafjk foni iafjPdfjka isiqka fofofkl= ,jd mka;shg bm;a lrjkak'
lqK ,laIHh ^uOH ,laIHh& f,i ),( YX ,laIHh mok lrf.k .=Ks; >qK
iyinkaO;d ix.=Klh .Kkh lrk nj '
57
bf.kqu i|yd fhda; Wmfoia (y my; i|yka j.= lKavdh j,g fnod tajd flfrys wjOdkh fhduq lrjkak'
j.=j 1
m%pdrK l=Kq
hou ^re' oyia& wdodhu ^re' oyia&
20 30
18 20
20 28
30 35
25 35
j.=j 2
jdykhl jdykfha
jld,h jkdlu
^wjq'& ^re' ,shk&
5 1'0
3 2'5
2 3'2
4 1'5
3 1'8
j.=j 3
fiajd ld,h udisl jegqqm
wjq' ^re' oyia&
3 7
10 12
7 7
8 20
12 8
58
j.=j 4
, ^re'& l=Kq
m%udKh ^ oyia&
5 7
6 10
8 10
4 12
10 7
y iajdh;a; p,Hh X f,io" mrdh;a; p,H Y f,i o k fldg tu j.=j ;jrg;a > lrka ;Sr 22 ,, YXXY imQK lr .kak'y .=Ks; >qK iyinkaO;d ix.=Klh r .Kkh lrkak'y r i|yd ,efnk w.hg tallhla mj;S o@y r .Kkh fldg ,efnk m%;sM, jrKh lrkak'y .=Ks; >QK iyinkaO;d ix.=Klfhys ,eh yels ms
59
lsh jH.=Ks; >qK iyinkaO;d ix.=Klh (Product moment correlation cofficient) fifuka
wmg ta p,Hhka w;r mj;sk inkaO;dj, osYdj iy m%udKh uek .kak mqjka
Product moment ^ .=Ks; >QK& f ix.=Klh fydhkafk ta p,Hhka fofla uOHkHhka^ YX , & f. isg we;s wm.uk j, .=Ks;hka f. ftlHh tajd fh iu; wm.ukj,.=Ks;hkag orK wkqmd;hla hghs. t;fldg >QK ,CIH ^uOH ,CIH& ;uhs ^ YX , &LKAvdxlh fuh my; lafjk isrs ;s;a igyfkys oelafjkj
>QK ,CIH u; isg wm.uk .=Ks;hka iQK
iyinkaO;d ix.=Klh f,i ykaj, ;sfnkafk'
f ix.=Kl .Kkh lrkafk fldfyduo@
ta i|yd f.dvk, ;sfnk iQ ;% Nd ;d lr, .Kl hka;% fyda mrs.Kl Nd;fhka b;du
blauKska ms
60
ksmqK;d ugu 4'5( ;rd iyinkaO;d ix.=lKlh m%udKkh lrhs'ld,fo ixLHdj ( 04bf.kq M,y we;s o;a; ksjer j ;rd .; lrhs'y iQ;%h Nd;fhka ;rd iyinkaO;d ix.=Klh .Kkh lrhs'y ;rd iyinkaO;d ix.=Klh Nd;fhka .=Kd;aul$ m%udKd;aul p,Hhka folla w;r mj;sk inkaO;df m%n,;ajh iy Ydj jrKh lrhs'
y fm
61
j.= wxl 2
mrSCIKhloS fmkS is Ihhka i|yd isiqka
fofofkl= ,nd .;a ,l=Kq
Ihhka A f.a ,l=Kq B f.a ,l=Kq.Ks;h 80 58
oHdj 70 60
isxy, 55 85
iudc wOHhkh 65 50
bx.%Sis 70 70
wd.u 85 60
;dCIKh 45 90
fi!kaoh 50 70
j.=j msgm;a lrf.k tla tla p,Hfha we;s ,l=Kq i|yd ;rdjka fhdokak
tla tla w.h i|yd ,e we;s ;rdjka w;r fjki ^d& ,nd .kak ^d2& ,nd .kak my; oelafjk iQ;%h fhd f.k ;rd iyinkaO;d ix.=Klh r .Kkh lrkak
( )161 22
=nn
dr
d = p,H foflys ;rd w.hka w;r fjki
,efnk m%;ssM,h wkqj p,H fol w;r iyinkaO;dj ms
62
ksmqK;d ugu 4'6 ( m%;smdhk fLdj wkqiSykh lsug wkqmldr l%uh Nd; lrhs'ld,fo ixLHdj ( 02
bf.kq M,y is ;s;a igykg .e
63
y tu wjia:d fol wkqudksl inkaO;d jk nj'y by; lS ish inkaO;d oelaug .Ks;uh ilrKhla f.dvke.Su W; nj'y th m%;smdhk ilrKh f,i k lrk nj'y m%;smdhk ilrKh ,nd .ekSug O l%u mj;sk nj'
bf.kqu i|yd fhda; Wmfoia ( my; lafjk is ;s;a igyka isiq lKavdh j,g ,nd tu igyka fol fj; isiq
wjOdkh fhduq lrjkak
^1& ^2&
^1& ^2&
tla tla isrs ;s;a igyk fyd|ska ksrSCIKh fldg p,H fol w;r inkaO;dj
meyeos,s lsrSug fhda.Hhehs Tn is;k ir, fLdj ir, rhla Nd;fhka w|skak
w|sk ,o fLdj mok lrf.k tys nEjqu ^wkql%uKh& ,nd .kak th m%;smdhk
ix.=Klh f,i k lrkak
Tn w|sk ,o fLdj Y wCIh fPokh lrk ,CIHfhys Y LKavdxlh ^wka;#LKavh& ,nd .kak
w|sk ,o fLdjg iqiq ilrKh ,shkak
tu.ska iajdh;a; p,Hfha fjkia u u; mrdh;a; p,Hh p,kh f m%udKh
meyeos,s lrkak
64
Tn ,nd .;a ilrKh wod< p,H hq.,h w;r inkaO;dj meyeos,s lssrSug flf;larg
m%udKj;a o@
y Tf wkdjrK ksudKYS,S j yd iduQysl j iuia; mka;shg bm;a lsug iQodkjkak'
Ih lreKq meye,s lr .ekSug w;aje,la (y my; lreKq u;= lrka iudf,dapkhl fhfokak'y p,H fol w;r inkaO;dj o< jYfhka muKla ia;r lsug ir, fLdjla
wNsu; m weu wkqmldr l%uh jk nj'
y p,H fol w;r inkaO;dj meye,s lsug .Ks;uh ilrKhla ksudkh l< yels nj iy ta i|yd += baY fyda 110 xY
+= jeks ilrKhla Nd; l< yels nj'
y ;s;a kslaIKh lsfuka wkq ,nk fLdj wkkH fkdjQ mqoa., ks(Ys%; jQjla nj'y fuh blauka ;SrKj,g u.mdok" ir, fh inkaOhla f.dvke.sh yels myiq
l%uhla nj'
65
ksmqK;d ugu 4'7 ( wvq;u j. l%uhg m%;smdhk ilrKh wkqiSykh lrhs'ld,fo ixLHdj ( 06
bf.kq M,y wkqmldr l%ufha mj;sk fodaI u.yrjd .ekSug iqiq l%uhla fhdackd lrhs'y fok ,o o;a; ksjerj ilia lr .kska wvq;u j. m%;smdhk ilrKh ,nd .kshs'y m%;smdhk ilrKh Nd;fhka iajdh;a; p,H u; mrdh;a; p,H .Kkh lrhs'y fodaI wju jk wdldrhg ldhhka is lrhs'y .Kkhka myiq lr .; yels fjk;a l%ufo fidhd n,hs'
bf.kq- b.eka ls %hdj,sh (msiquy my; olajd we;s rEmigyka y;r m%oYkh lrkak'
ixy 10 += exy i ++= 10
ixy 10 = exy i += 10
y my; i|yka lreKq biau;= jkfia idlPdjl fhfokak'y wkqmldr l%ufha mj;sk j,;d u.yrjd .ekSu i|yd fodaI wju jk l%uhla
Nd; lrk nj'
y fuu l%uh wvq;u j. l%uh nj'y wdkqudksl inkaO;d mj;sk g m%;smdhk wdlD;sh ieY ++= 10 u.ska lafjk
nj'
y ie hkq m%;smdhk ilrKfhka meyeos,s fkdlrk n,mEu we;=,;a jk moh nj'
66
y m%;smdhk ilrKh weia;fka;= lsug ie wju l< hq;= nj'y p,H w;r inkaO;dj meye,s lsug fodaI j. ftlHh wju jk wvq;u j.
m%;smdhk ilrKh jvd;a fhda.H nj'
f.kqu i|yd fhda; Wmfoia (y isiq lKavdh j,g o;a; j.= ,nd my; i|yka ls%hdldrlfuys fhdojkak'
j.= wxl 1 j.= wxl 2
jdykfha jhi kv;a;= msrsjeh re.oyia wuq jH 1kg l , re b,a m%udK2 5 2 25
4 6 4 20
6 7 4 25
3 5 3 24
5 8 5 28
8 7 8 10
Tng imhd we;s o;a; j.=j msgm;a lrf.k mrdh;a; p,H Yi f,io iajdh;a;p,H Xi f,io k lr .kak'
tu j.=j ;j rg;a m%idrKh lrka X2, yd XY ;Sre .Kkh lrkak iEu ;Srejlu ftlHh o ,nd .kak tajd XYXYX ,,, 2 f,i k lrkak tu w.hka my; oelafjk iu.d ilrKhg wdfoaY lr th i|Sfuka 0 iy
1 fidhkak th ilrKhg wdfoaY lrkak'
iy ykajkak'
by; ldh ish,a, lrk ,oafoa l=ula i|yd oehs meyeos,s lrkak
0 iy 1 fiug my; olajd we;s m%u; ilrK Nd;d lrkak'
y Tf wkdjrK ksudKYS,Sj yd iduQysl j iuia; mka;shg bm;a lsug iqodk jkak'
je r wOHhkh i|yd(-
wvq;u j. m%;smdhk ilrKh .Kkh lsrSug Nd;d l< yels fjk;a iQ;% ms
67
Ih lreKq meye,s lr .ekSug w;aje,la ( my ; lreKq u ;= lrka iudf,dapkhl fhfokak'
/ia lr.;a o;a; ldKav j, iajdh;a; p,Hh u; mrdh;a; p,Hfhys yeisrSu
.Ks;uh ilrKhla u.ska meyeos,s l< yels nj'
fodaI j. ftlHh wju jk wdldrhg m%;smdhk ilrKh ksudkh lrk nj'
faIhka wju jk neka th o;a; i|yd jvd;a .e,fmk ir, fLdj nj'
1 m%;smdhk ix.=Klh f,i ye|skafjk nj' .Kkh lrk ,o ilrKfhys 1 ys w.h fhd f.k iajdh;a; p,H u;
mrdh;a; p,Hh fjkiajk m%udKh iy osYdj jrKh l
68
lsh jH m%;smdhk wdlD;sh fhdod f.k m%;smdhk ilrKh ksudkh lsu m%;smdhk wdlD;sh fhdod f.k m%;smdhk ilrKh ksudkh lsu m%;smdhk wdlD;sh fhdod f.k m%;smdhk ilrKh ksudkh lsu m%;smdhk wdlD;sh fhdod f.k m%;smdhk ilrKh ksudkh lsu m%;smdhk wdlD;sh fhdod f.k m%;smdhk ilrKh ksudkh lsu
m%;smdhk wdlD;sh (-
ieY ++= 10
ei hkq fodaI mohhs tys ksudklh f f
ei
ta wkqj mrdh;a; p,Hfhys ishu w.hka i|yd jQ m%;smdhk wdlD;shg by; fldkafoais
fol wdfoaY lsfuka fuys jk neka
^1&
m%;smdhka wdlD;sh Xi j,ska .=K lsfuka fuys jk neka
^2&
fuu ^1& iy ^2& ilrK hq.,h m%u; ilrK f,i i
69
ksmqK;d ugu 4'8 ( wkqiSykh lrk ,o wvq;u j. m%;smdhk fLdjl fyd|lu mlaId lrhs'
ld,fo ixLHdj ( 06
bf.kq M,y wkqiSykh lrk ,o m%;smdhk ilrKh Nd;fhka mrdh;a; p,Hfha w.hka weia;fka;= lrhs'
y ksKk ix.=Klh .Kkh lrhs'y ksKk ix.=Klh fhdodf.k m%;smdhk fLdf .e
70
y tu p,khka mok lrf.k ksKk ix.=Klh ^ 2R &.Kkh lsfuka m%;smdhk ilrKfhys wkqiSykfha fyd|lu jrKh lrk nj'
bf.kqu i|yd fhda; Wmfoia (y isiq lKavdh j,g my; we;s j.= ,nd ta flfrys wjOdkh fhduq lrjkak'
j.= wxl 1
jdykfha jhi kv;a;= msjeh
wjq( re' oyia
x y2 5
4 6
6 7
3 5
5 8
8 7
j.= wxl 2
wuqo%jH 11111kg , b,a m%udKre'
x y2 25
4 20
4 25
3 24
5 28
8 10
y my; Wmfoia isiqkag ,nd isiqka bf.kqfuys fhdojkaky Tf lKavdhug ,efnk o;a; j.= iy .Kkh lrk ,o m%;smdhk ilrKh mok
lr .kak'
y m%;smdhk ilrKh weiqfrka tla tla w.hkag wod< j .Kkh lrkak'
y fidhkak'
71
y fidhkak
y fidhkak
y Nd;fhka
ksKk ix.=Klh fidhkak'
y m%;smdhkfhka meye,s jk p,kh mrdh;a; p,Hfhys uq p,kfhka lsk m%;sY;hla o hkak meye,s lrkak'
y m%;smdhkfhka meye,s fkdjk p,kh i|yd woyia olajkak'y .Kkh lrk ,o m%;smdhk ilrKfha wkqiSykfha fyd|lu ms
72
ksmqK;d ugu 4'9 ( p,H w;r mj;sk inkaO;d olska mqfrdal:k lrhs'ld,fo ixLHdj ( 02
bf.kq M,y wka; ksfYk iy nys ksfYk mqfrdal:k w: olajhs'y fok ,o m%;smdhk ilrKh fhdodf.k iajdh;a; p,Hfha w.hg wkqrEm mrdh;a; p,Hfha w.h .Kkh lrhs'
y iajdh;a; p,Hfhys w.h ;sfnk uug jvd by< ouka mrdh;a; p,Hfha w.h weia;fka;= lrhs'
y jHdmdr lfIa;%fha m%Yia; ;SrK .ekSug mqfrdal:k Nd; l< yels wjia:d i|yd WodyrK imhhs'
bf.kq- b.eka ls %hdj,sh (msiquy my; oelafjk foni N+ld rx.khla f,i mka;shg bm;a lrkak'
N+ld rx.khN+ld rx.khN+ld rx.khN+ld rx.khN+ld rx.kh
miq.sh mej;s Y%shd isrs wdh;kfha l
73
f isrs ;s;a igyk u; we|sh yels fyd|u m%;smdhk fLdj
ixLHdk Ys,amSh l%u wkqj f.dv k., ;sfhkafk. ta
ilrKh ;uhs f ;sfhkafk.^m%;smdhk ilrKh ,shQ
ldm; m%oYkh lrka& f fLdj remsh,a ,shk j,ska
f.dvk., ;sfhkafk. ^ jeks m%;smdhk
ilrKhla ldm;l ,shd .kak.&
l
74
bf.kqu i|yd fhda; Wmfoia (my; lafjk j.= isiq lKavdh w;r fnod tajd flfrys wjOdkh fhduq lrjkak'
j.= wxl 1
jdykfha jhi kv;a;= msjeh
wjq( re' oyia
x y2 5
4 6
6 7
3 5
5 8
8 7
j.= wxl 2
wuqo%jH 1kg1kg1kg1kg1kg , b,a m%udK
re'
x y2 25
4 20
4 25
3 24
5 28
8 10
y my; lafjk Wmfoia isiqka g ,nd foka isiqka bf.kqfuys fhdojkaky x=7 g Yys w.h weia;fka;= lrkak'y x=10 g Yys w.h weia;ka;= lrkak'y fok ,o w.h mrdih ;=< j.=fjys fkdue;s kEu x w.hla i|yd Yys w.h ,nd .kak'y fok ,o w.h mrdifhka msg; j.=fjys fkdue;s kEu x w.hla i|yd Yys w.h ,nd .kak'
y jHdmdr lafIa;%fha ;SrK .ekSu i|yd mqfrdal:k fhdod.; yels wdldrh ksoiqkla iys; j ia;r lrkak'
75
Ih lreKq meye,s lr .ekSug w;aje,la (y we;s o;a; ldKav foflys iajdh;a; p,H m%;smdhk ilrKhg wdfoaY lsfuka mrdh;a; p,Hhl w.h weia;fka;= l< yels nj'
y mqfrdal:kh wka; ksfYk mqfrdal:kh yd nys ksfYk mqfrdal:kh jYfhka j. l< yels nj'
y jHdmdr lafIa;%fha b jIh i|yd b,lal weia;fka;= lsug nys ksfYk mqfrdal:kh fhdod.; yels nj'
y m%;smdhk Yaf,aIKfha fodaI .Kkh lsug wka; ksfYk mqfrdal:kh fhdod.; yels nj'
76
ksmqK;dj 50 ((((( jHdmdrsl wjodkug uqyqKoSug we;s iQodku m%oYkh lrhsksmqK;d ugu51 ( ( ( ( ( jHdmdrsl wksYa; ;d weiqka iNd;d ixl,amh .%y lrhsld,fPo ixLHdj ( 03bf.kq M, ( h yelshdj wkqj is j.SlrKh lrhs
tla tla j.hg wod< is fhdackd lrka tajdfha hyelshdj ;SrKh lrk idOl
f.dkq lrhs
tu is i|yd iNd;d w.hla wkqudk lrhs
hyelshdj mslaiSfuka wjodk mej;sh yels w.h mrdih olajhss wksYa;;dj uek lah hq;= isoa ;SrKh lrhss
bf.kq-b.eka l% shdj,sh ( msiqu my; kafjk isoa mka;shg fhduqlr isiq woyia uikak
bfnla mshdir lsu fyg jeis we;su fyg;a kef.kyska ysre Wod u
u;= lafjk lreKq biau;= jk fia idlPdjla fufyh jkak
f;wdldrhl isoa by; ia;r lr ;sfnk nj
fjd ksYa; is, wksYa; is iy lsisfia;a h fkdyels is f,i ykajk nj
tfkod ;fha yuqjk fujeks is j,ska fndfyduhla wksYa; is nj
bf.kqu i|yd fhdacs; Wmfoia ( my; i|yka ud;Dld isiq lKavdhj,g ,nd we;s Wmfoia wkqj isiqka bf.kqfuys fhdojkak ksYa; is wksYa; is lsisfia;a h fkdyels is Tng ,e we;s ud;Dldj meye,s lsug WodyrK 5 la ,shkak jHdmdr is ta w;r ;sfk tajd ykd .kak jHdmdr is .Kk my olajd jelsug fjk;a is ,ehsia;=jg tl;= lrkak ffoksl ;fha tlS jHdmdr is j, iq,N;dj uYkh lrkak ^Analysis of Frequency& Tn bm;a fldg we;s is j, hyelshdj uek laug iqiq w.hla fyda w.h mrdihla fhdackd lrkak Tf wkdjrK ksudKYS,Sj iy iduQyslj iuia; mka;shg bsm;a lsug iQodk
jkak
Ih lreKq meye,s lr.ekSug w;aje,la ( jHdmdr yd nef|k wksYa; is iq,N nj ,dN$w,dN, wf, u $fkdu, weKjq ,eu$fkd,eu jHdmdr yd ne is lsysmhla nj jHdmdr wjodku wju lr .ekSf Ys,am l%uhla f,i wksYa; isoa ixLHdkuh jYfhka Kqug ,la flfrk nj fuu Ys,am l%uh iNd;dj f,i k flfrk nj ksYa; isoahl iNd;dj 1 jk w;r lsisfia;a is fkdjk isul iNd;dj 0 jk nj wksYa; isoahl iNd;dj 0 ;a 1 ;a w;r w.hla .kakd nj
77
ksmqK;d ugu 52 ( O mCIK w;ka iiNd mCIK fjka lr olajhsld,fPo ixLHdj ( 03bf.kq M, ( iiNd iy ksKdhk mCIK i|yd ksjpk bm;a lrhs
tla tla mCIK j.h i|yd jHdmdr fCIa;%fha WodyrK u;= lr olajhs
mCIK foj.fha fjki ikd: lsug WodyrK fhdod .kshs
jk wNsfhda. j,g fkdie,S uqyqK u i|yd iiNd is ykd .ekSf iQodku
m%oYkh lrhss
WodyrK u;= lrka lKavdh idlPd fmdaIKh lrhs
bf.kq-b.eka l% shdj,sh ( msiqu my; i|yka m%Yak mka;shg fhduqlrkak
ue.akSish mhla oykh lsf ,efnk m%;sM,h l=ulao @
remshf,a ldishla by, f ,efnk m%;sM,h l=ulao @
my; lreKq u;=lrka idlPdjla fufyhjkak
ue.akSish mhla oykfha ,efnk m%;sM,h ksYa;j lsj yels nj
ldishla by, f ,efnk m%;sM,h ksYa;j lsj fkdyels nj
f wkqj ksKhk mCIK iy iiNd mCIK hkqfjka mCIK
foj.hla we;s nj
bf.kqu i|yd fhdacs; Wmfoia ( my; i|yka mCIK wjia:d fol isiq lKavdh j,g ,nd my; we;s isoawOHhkh weiqfrka isiqka bf.kqfuys fhdojkak
ksKdhk mCIK
iiNd mCIK
tu mCIK wjia:dj isf;ys r|jdf.k my; i|yka isoah wOHhkh lrkak
kl ;udg ,efnk meKs,s Yaf,aIKh lrk ksIamdok wdh;khl l
78
Ih lreKq meye,s lr.ekSug w;aje,la ( m%;sM, fmr lsj fkdyels mCIK iiNd mCIK k jk nj
m%;sM, fmr lsj yels mCIK ksKdhk mCIK jk nj
jHdmdr fCIa;%h ;=< fuu mCIK ish,a,u is lrk w;r jvd;a iq,Nj we;af;a
iiNd mCIK nj
iNd;d ixl,amh iiNd mCIK j, jeo.;a jk nj
79
ksmqK;d ugu 53 ( kshe wjldYhg iy isoa wjldYhg wh;a wjhj l=,l wdY%s;j ksrEmKh lrka isoa ixhqla; lr jHdmdl wjodkug
uqyqK ug iQodk fjhs
ld,fPo ixLHdj ( 10bf.kq M, ( iiNd mCIKhl oS ,eh yels ish m%;sM, ksrEmKh l< yels O l%u k lrhs
kshe wjldYh O l%u u.ska ksrEmKh lrhs
kshe wjldYh ;=, tla tla isoag wh;a m%foaYh fjka lr olajhs
O wjia:d ixhqla; lrka ixhqla; isoa m%oYkh lrhs
ixhqla; isoaka f.a Wm fldgia j, wjodku flfrys ie
80
A is fkdjk g B isu B is fkdjk g A isu A fyda B fyda hk foflka tllaj;a isfkdu A g yd B g wh;a fkdjk isoa isu Tf wkdjrK ksudKYS,Sj iy iduQyslj iuia; mka;shg bsm;a lsug iQodk
jkak
Ih lreKq meye,s lr.ekSug w;aje,la ( iiNd mCIKhlska ,eh yels ish m%;sM, O l%u u.ska ksrEmKh l