Mathematics - essential learning concepts

w;HjYH bf.kqï ixl,am
1.Ks; fomd¾;fïka;=j cd;sl wOHdmk wdh;kh
j¾I 2016 § yd bka bÈßhg meje;aùug kshñ;
w' fmd' i'^idudkH fm<& úNd.fha .Ks;
m%Yak m;%h 1 i|yd wdjrKh úh hq;= úIh ikaOdrh
^10 iy 11 fY%aKs úIh ks¾foaY wkqj&
.Ks; fomd¾;fïka;=j
úoHd yd ;dlaIK mSGh
cd;sl wOHdmk wdh;kh
Y%S ,xldj
.Ks;h
www.nie.lk

(Essential Learning Concepts)
w' fmd' i' îdudkH fm<& úNd.fha § isiqka f;dard.; hq;= yr úIhka w;r m%Odk ;ekla ysñjkafka .Ks;h úIhg h' óg m%Odk fya;=j
jkafka w' fmd' i' îdudkH fm<& úNd.h iu;aùu r|d mj;skqfha .Ks;h úIhfha iu;aùu u; h' w' fmd' i' ^Wiia fm<& l=ula fyda
úIh Odrdjla Tiafia yeoEÍfï isyskh h:d¾;hla njg m;a lr .; yelafla fuu wksjd¾h jQ .Ks; úIh iu;aùu u; h'
w' fmd' i' ^Wiia fm<& l,d fyda jdKsc úIh Odrdjka Tiafia yeoEÍug Wkkaÿj fuka u yelshdj we;s orejdg w' fmd' i' îdudkH fm<&
.Ks; úIhh wiu;aùfuka mdi,a moaO;sh yer hdug isÿfõ'
fï ms<sn| j jeäÿrg;a fidhd neÆ wOHdmk wud;HdxYh" w' fmd' i' îdudkH fm<& úNd.fha § YsIHhskaf.a .Ks; ld¾h idOkh by<
kexùu msKsi iqÿiq ks¾foaY bÈßm;a lsÍu i|yd jQ úfYaI WmfoaYl lñgqjla m;a lr ta ms<sn| j fidhd neÆ w;r tu WmfoaYl lñgq
jd¾;dj ;=, i|yka j ;snQ ks¾foaY w;=ßka lsysmhla my; iqúfYaIS j olajuq'
1' oaú;Shl wOHdmkh i|yd bÈßm;a lrkq ,nk .Ks; úIh wka;¾.;h"
^w& mdi,a .Ks;h Ydia;%Sh fyda m¾fhaIKd;aul .Ks;g iudk fkdúh hq;= nj'
^wd& oaú;Sh mdi,a uÜgfï .Ks;h fmkS isákafka" isiqka ±kqj;a mqrjeishka njg m;aùug bv i,id Tjqkaf.a we;eï Ôj l=i,;d
ixj¾Okh msKsi Wmldr lsÍug nj'
^we& .Ks;h úIhh wfkl=;a úIhkays § wjYH jk WmldÍ úIhla ùu'
^wE& jvd;a M,odhS bf.kqula i|yd .Ks; ixl,am y|kajd§fï m%uqL;d wkqms<sfj,la iys; ùu'
hk lreKq flfrys ie,ls,su;a úh hq;=ùu
2' j¾;udkfha ieufokd úiska u tlu .Ks;hla bf.k .ekSug isÿj ;sîfï ;;ajhg iqÿiq m%;sld¾h úi÷ula f,i 10 iy 11
fY%aKsj, w;HjYH bf.kqï ixl,am" (Essential Learning Concepts) y÷kdf.k we;' fuh .Ks; idlaIr;djfhka hq;a mqrjeisfhl=
f,i ie,lSu i|yd wjYHfhka u bf.k .; hq;= fldgila f,i ks¾jpkh l< yels w;r Tjqkag .Ks;fha iudÔh Wmfhda.S;d
úpdrd;aul j ;lafiare lsÍug o yelsjkq we;'

3' w;HjYH bf.kqï ixl,amj,g wh;a .eg¨ úi£fï l%ñl yd ixl,amSh ±kqu wdo¾Ykh lsÍug yelsùu f,i ks¾jpkh l<yels
wfmalaIs; uQ,sl ^wju& idOk uÜgu [Basic (Lowest) Achievement Level (BAL) ] ms<sn| tl`.;djlg t<öug o ks¾foaY lrkq
,efí'
4' w;HdjYH bf.kqï ixl,am (ELC) ms<sn| by;ska i|yka lrk ,o ks¾foaYhkag wkql+, j w' fmd' i' ^idudkH fm<& úNd.fha .Ks;h
m%Yak m;%fhys ixhq;sh my; i|yka mßÈ m%;sjHqy.; l< yels h'
• m<uqjeks m;%fhys ^meh foll ld,h& wka;¾.; jkq we;af;a úIh ks¾foaYfhys w¾: ±lajQ w;HjYH bf.kqï ixl,am wh;a jHqy.;
m%Yak iy flá ms<s;=re iys; m%Yak muKs' th ish¨ úNd. wfmalaIlhskaf.a yelshd mrdih ;=<g jefgk w;r wjidk m%;sM,fhka
50]lg odhl fõ'
• fojeks m%Yak m;%fhys ^meh fol yudrl ld,h& wka;¾.; jkq we;af;a iïmQ¾K úIh ks¾foaYfhka tk jHqy.; rpkduh m%Yak fõ'
fuh ilia lrkq ,nkafka jvd Ydia;%Sh yelshdjkA we;s isiqka i|yd h' by< idud¾:hka n,dfmdfrd;a;= jkakka iy Wiia wOHdmk
Odrdjkag fhduqùug wfmalaId lrk wh b,lal lrf.k fuh ilia lrkq ,efí' wjidk idud¾:hg fojk m;%fhka ,efnk
odhl;ajh 50]ls'
• fï wkaoug iudkH fm< .Ks; m%Yak m;%fha iu;aùfï ,l=K 35]la f,i ie<fla kï m<uq m;%hg 70]la ^fuh w;HjYH bf.kqï
ixl,amj, uQ,sl idOk uÜgu f,i ie<lsh yels h& ,nd .kakd ´kEu YsIHfhl=g fojeks m;%hg lsisÿ ,l=Kla ,nd fkdf.k
jqj;a .Ks;h iu;aùug yels fõ'
• by; i|yka lreKq o wdpd¾h Wmd,s udïmsáh m%uqL úoaj;a msßila úiska j¾I 2005 § ilia lrk ,o w;HjYH bf.kqï ixl,am keu;s
f,aLKh o ie<ls,a,g .ksñka 11 fY%aKsfhka miq Wiia fm< wOHmkhg msúfik orejl= ;=, ;sìh hq;= .Ks; ixl,am ms<sn| cd;sl
wOHdmk wdh;kfha .Ks; fomd¾;fïka;=j úiska y÷kd.kakd ,o fuu "w;HjYH bf.kqï ixl,am"" úoHd mSG lÓldpd¾hjreka"
.=re WmfoaYljreka yd .=reNj;=kaf.ka ieÿï,;a lKavdhula iu`. idlÉPd lrñka hï hï ;srKj,g t,eöfuka miq ilia lrk
,o w;HjYH bf.kqï ixl,amj, 10 yd 11 fY%aKs úIh ks¾foaYj,g wod< úIh wka;¾.;h yd bf.kqïm, my; i|yka lr we;'
fuu úIh fldgi" isiqka ,`.d lr.kafka o hkak mÍlaId lsÍu j¾I 2016 § y÷kajdfokq ,nk w' fmd' i' ^idudkH fm<& .Ks;h m;%h - I
u`.ska isÿ lsÍug kshñ; h'

• j¾.uQ,h
• ikaksl¾IKh ^m<uq
ikaksl¾IKh muKs&
• iudka;r fY%aÎ
• ye¢kaùu
• n jk moh
• Nd. wdY%s; ir, .eg¨
úi£u
• m%;sf,dau iudkqmd;
ye¢kaùu
• m%;sf,dau iudkqmd; wdY%s;
.eg¨
• jev yd ld,h
• wkqhd; mQ¾K j¾. ixLHd folla w;r msysá mQ¾K j¾.hla fkdjk
ixLHdjl j¾.uQ,h i|yd o< w.hla fidhhs'
• mQ¾K j¾.hla fkdjk mQ¾K ixLHdjl j¾.uQ,h m<uq
ikaksl¾IKhg fidhhs'
• mQ¾K j¾.hla fkdjk mQ¾K ixLHdjl j¾.uQ,h oYu ixLHdjla jk
nj ms<s.kshs'
• wkqhd; mo folla w;r wka;rh ksh;hla jk ixLHd wkql%uhla
iudka;r fY%aÎhla f,i y÷kd .kshs'
• iudka;r fY%aÎ wdY%s; mdßNdIsl mo y÷kd .kshs'
• ( 1)nT a n d   iQ;%h Ndú;fhka iudka;r fY%aÎhl n jk moh fidhhs'
• iudka;r fY%aÎhl n jk moh ^ nT & § we;s úg n ys w.h iQ;% Ndú;fhka
fidhhs'
• tÈfkod Ôú;fha Nd. Ndú; jk wjia:d ú.%y lrhs'
• BODMAS kS;sh o we;=<;a j" Nd. weiqßka tÈfkod Ôú;hg iïnkaO
ir, .eg¨ úi|hs'
• rdYs folla w;r iïnkaOh ú.%y lrñka m%;sf,dau iudkqmd;sl y÷kd
.kshs'
• m%;sf,dau iudkqmd; ms<sn| ±kqu Ndú;fhka jev yd ld,h wdY%s; ir,
.eg¨ úi|hs'
úIh wka;¾.;h bf.kqï m, igyka
100g wvq mQ¾K j¾.hla fkdjk
ixLHd muKs'
a yd d ksÅ, muKs'
jryk iu`. .Ks; l¾u 3la
we;=<;a m%ldYk muKs'

• jßmkï nÿ, ;Sre nÿ, wdodhï nÿ yd tl;= l< w.h u; noao hk
nÿ j¾. y÷kd .kshs'
• jßmkï nÿ wdYs%; .Kkh lsÍïj, fhfohs'
• ;Sre nÿ wdYs%; .Kkh lsÍïj, fhfohs'
• wdodhï nÿ wdYs%; .Kkh lsÍïj, fhfohs'
• tl;= l< w.h u; nÿ wdYs%; .Kkh lsÍïj, fhfohs'
• nÿ wdYs%; .eg¨ úi|hs'
• uq,a uqo,;a ld,h;a fmd,S wkqmd;slh;a ie,ls,a,g .ksñka .Kkh
lrk fmd,ssh, iq¿ fmd,ssh f,i y÷kd .kshs'
• hï uqo,la i|yd tlu fmd,S wkqmd;slh hgf;a iudk ld, mrdihka
;=< § ,efnk fmd,sh iudk nj y÷kd.kshs'
• uqo,la i|yd § we;s ld,hg yd fmd,S wkqmd;slhg wkqj fmd,sh
.Kkh lrhs'
• wjYH f;dr;=re § we;s úg fmd,ssh fyda fmd,SS wkqmd;slh fyda ld,h
fyda uqo, fyda fiùfï .eg¨ úi|hs'
• ixLHdjla o¾Yl wdldrfhka oS we;s úg tu ixLHdfõ ,>q.Klh,
mdoh weiqfrka úia;r lrhs'
• o¾Yl wdldrfha m%ldYkhla ,>q.Kl wdldrhg fyda ,>q.Kl
wdldrfha m%ldYkhla o¾Yl wdldrhg fyda mßj¾;kh lrhs'
• nÿ j¾. ^;Sre nÿ" wdodhï
nÿ" jßmkï nÿ yd tl;=
l, w.h u; noao&
• ye¢kaùu
• .Kkh lsÍï
• iq`M fmd,sh
• fmd,S wkqmd;slh
• jd¾Isl$udisl
• fmd,S .Kkh
• o¾Yl yd ,>q.Kl w;r
iïnkaOh
• ,>q.Kl n, mßj¾;kh
nÿ m%;sY;h mQ¾K ixLHdjla jk
mßÈ jQ o ms<s;=r ixLHd;aul w.hla
jk mßÈ jQ o .Kkh lsÍï muKla
we;=,;a h'
^ùcSh mo fyda m%ldYk Ndú; jk
.eg¨ wfmalaId fkdflf¾'&
fmd,S m%;sY;h mQ¾K ixLHdjla jk
mßÈ jQ o ms<s;=r ixLHd;aul w.hla
jk mßÈ jQ o .Kkh lsÍï muKla
we;=,;a h'
^ùcSh mo fyda m%ldYk Ndú;d jk

• mohla yd Bg fmr moh w;r wkqmd;h ksh; jQ ixLHd wkql%u .=fKda;a;r
fY%AVs f,i y÷kd .kshs'
• a yd r ys w.h ksÅ, jk mßÈ jQ .=fKda;a;r fY%AVshl fmdÿ wkqmd;h (r)
fidhhs'
• a yd r ys w.h ksÅ, jk mßÈ jQ .=fKda;a;r fY%AVshl n jk moh (Tn
)
fidhhs'
• je,afmd,S l%uh y÷kd .kshs'
• je,afmd,sh wdY%s; .Kkh lsÍï isÿ lrhs'
• fldgia wdfhdackfha § nyq;r wdfhdaclhska ixLHdjla jHdmdrhg
iïnkaO lr.; yels nj ms<s.kshs'
• iSudiys; iud.ï m%d.aOkh iïmdokh lr.kqfha f l d g i a k s l = ; a
lsÍfuka nj ms<s.kshs'
• fldgia fj<| fmdf,ys .Kqfokqùfï §" iud.ul fldgia i|yd
mj;sk ñ," fldgil fj<| fmd, ñ, f,i kï lrhs'
• fldgil fj<| fmd, ñ, fldgia .Kkska .=K lsÍfuka fldgiaj,
jákdlu ^wdfhdackh l< uqo,& ,efnk nj m%ldY lrhs'
• .=fKda;a;r fY%aÎ
• ye|skaùu
• n jk moh
• je,afmd,sh
• je,afmd,sh .Kkh
^jdr folla f;la&
• iSudiys; iud.ï
• fldgia
wjidk ms,s;=r o¾Yl wdldrfhka
;sîu m%udKj;a h'
fmd,S m%;sY;h mQ¾K ixLHdjla jk
mßÈ jQ jdr folla f;la jQ .Kkh
lsÍï muKs'
^ùcSh mo fyda m%ldYk Ndú;d jk

• wdfhdackh l< yels uqo, ^fldgiaj, jákdlu& fldgil fjf<|
fmd, ñf,ka fn§fuka ñ, § .;yels fldgia .Kk ,efnk nj m%ldY
lrhs'
• fldgilg hï ld,iSudjla i|yd f.jk ,dNdxYh" fldgia .Kkska
.=K lsÍfuka wdfhdaclhdg ,efnk ,dNdxY wdodhu .Kkh lrhs'
• wdfhdackh l< uqo, ^fldgiaj, jákdlu&" fldgil fj<| fmd,
ñ," m%d.aOk ,dNh yd fldgil ,dNdxYh we;=<;a .eg¨ úi|hs'
• flakaøsl LKavj, mßñ;sh fidhhs'
• flakaøsl LKav we;=<;a ixhqla; ;, rEmj, mßñ;sh wdY%s; .eg¨ úi|hs'
• mßñ;sh
• flakaøsl LKav
• ñkqï mQ¾K ixLHdjla jk mrsos jQ
iup;=ri%h" RcqfldaKdi%h"
RcqfldaKS ;%sfldaKh" ;%mSishu
hk ;, rEm w;=rska Wmrsu
jYfhka ;, rEm 2la yd flakaøsl
LKav 1la muKla we;=,;a ixhqla;
;, rEmj, mßñ;sh muKs'
• flakaø fldaKh 450
, 900
fyda
1800
jQo wrh 7 ys .=Kdlrhla jQ o
flakaøsl LKavj, mßñ;sh muKs'

• j¾.M,h
• flakaøsl LKav
• flakaøsl LKavj, j¾.M,h fidhhs'
• flakaøsl LKav we;=<;a ixhqla; ;, rEmj, j¾.M,h wdY%s; .eg¨
úi|hs'
• pdm È. yd mßñ;sh §
we;s úg wrh fiùu iy wrh
yd mßñ;sh § we;súg pdm È.
fiùu muKs'
• flakaø fldaKh 450
, 900
fyda
1800
jQo wrh 7 ys .=Kdlrhla jQ
o flakaøsl LKavj, j¾.M,h
muKs'
• ñkqï mQ¾K ixLHdjla jk mrsos
jQ iup;=ri%h" RcqfldaKdi%h"
RcqfldaKS ;%sflaKh" ;%mSishu
hk ;, rEm w;=rska Wmrsu
jYfhka ;, rEm 2la yd
flakaøsl LKav 1la muKla
we;=,;a ixhqla; ;, rEmj,
j¾.M,h muKs'
^flakaøsl LKavfha j¾.M,h §
we;s úg" wrh fyda flakaø
fldaKh fiùu wfmalaId
fkdflf¾'&

• 2
2 2A r rh   iQ;%h Ndú;fhka r ys w.h mQ¾K ixLHdjla yd 7ys
.=Kdldrhla jk mßÈ jQ o hys w.h mQ¾K ixLHdjla jQ o Rcq jD;a;
is,skavrhl mDIaG j¾.M,h .Kkh lrhs'
• Rcq jD;a; is,skavrhl mDIaG j¾.M,h § we;s úg hys w.h fidhhs'
• ;%sfldaKdldr yrialvla iys; Rcq m%siauhl uqyqK;aj, yev y÷kd .kshs'
• 2
V r h iQ;%h Ndú;fhka jD;a; is,skavrhl mßudj .Kkh lrhs'
• Rcq jD;a; is,skavrhl Vys w.h § we;s úg hys w.h fidhhs'
• Rcq jD;a; is,skavrhl Vys w.h § we;s úg rys w.h fidhhs'
• mDIaG j¾.M,h
• is,skavrh ^>k&
• mDIaG j¾.M,h
• ;%sfldaKdldr yrialvla
iys; Rcq m%siauh
• mßudj
• is,skavrh
• r ys w.h 7ys .=Kdldrhla jQ o
hys w.h mQ¾K ixLHdjla jk
mßÈ jQ o >k Rcq jD;a; is,skavr
muKS'
• Ays w.h mQ¾K ixLHdjlao r ys
w.h 7ys .=Kdldrhla jQ o hys
mQ¾K ixLHd;aul w.hka jQ o
>k Rcq jD;a; is,skavr
muKs'
(mDIaG j¾.M,h fiùu
wfmalaId fkdflf¾')
• r ys w.h 7ys .=Kdldrhla jk
mßÈ jQ o hys w.h mQ¾K
ixLHdjla jQ o Rcq jD;a;
is,skavr muKS'
• r ys w.h 7ys .=Kdldrhla jk
mßÈ jQ o Vys w.h mQ¾K
ixLHdjla jQ o Rcq jD;a;
is,skavr muKs'
• hys w.h mQ¾K ixLHdjla jQ o
Vys w.h mQ¾K ixLHdjla jk
mßÈ jQ o Rcq jD;a; is,skavr
muKs' ( r ys w.h mQ¾K j¾.hla
jk mßÈ úh hq;=hs' )

• yrialv ;%sfldaKhla jQ Rcq m%siauhl mßudj .Kkh lrhs'
• ld,h wkqnoaOfhka ÿr fjkiaùfï iS>%;dj fõ.h f,i y÷kd .kshs'
• ÿr" ld,h yd fõ.h w;r iïnkaOh ,shhs'
• ÿr yd ld,h we;=<;a f;dr;=re m%ia;drhl ksrEmKh lrhs'
• ÿr-ld, m%ia;drhl wkql%uKh u`.ska fõ.h ,efnk nj y÷kd .kshs'
• ÿr" ld,h yd fõ.h iïnkaO .eg¨ úi|hs'
• mßudj yd ld,h iïnkaO ir, .eg¨ úi|hs'
• wjfrdayK fldaKh y÷kd .kshs'
• wdfrdayK fldaKh y÷kd .kshs'
• wjfrdayK fldaKh yd wdfrdayK fldaKh weiqßka jia;=jl msysàu úia;r
lrhs'
• RcqfldaKS ;%sfldaKhl hï fldaKhl ihska wkqmd;h " tys iïuqL mdofha
È. yd l¾Kfha È. w;r wkqmd;fhka ,ndfok nj wkdjrKh lr .kshs'
• RcqfldaKS ;%sfldaKhl hï fldaKhl fldaihsk wkqmd;h" tys noaO mdofha
È. yd l¾Kfha È. w;r wkqmd;fhka ,nd fok nj wkdjrKh lr
.kshs'
• mßudj
• ;%sfldaKdldr yrialvla
iys; Rcq m%siauh
• ÿr yd ld,h
• ÿr-ld, m%ia;drhl
ksrEmKh ^taldldr fõ.h
we;s wjia:d&
• m%ia;drfhys wkql%uKh =
ld,h
ÿr
= fõ.h
• mßudj yd ld,h
• wdfrdayK fldaKh yd
wjfrdayK fldaKh
• ;%sfldaKñ;sl wkqmd;
• ihskh
• fldaihskh
• gexckh
• yrialv j¾.M,h fok ,o Rcq
m%siau muKs' ^mßudj § we;sjg"
yrialv j¾.M,h fyda m%siaufha
Wi fiùu wfmalaId fkdflf¾'&
• tall m¾j¾;k we;=,;a fkdjk
wjika ms<s;=r mQ¾K ixLHd;aul
jk mßÈ jQ .eg¨ muKs'
• 
ÿr
fõ.h
ld,h
ys rdYs folla §
we;s wjia:d muKs'
iS>%;dj 
mßudj
ld,h
ys rdYs folla §
we;s" k, ;=,ska øj .,d hk wjia:d
muKs'
• fok ,o rEm igykla weiqßka
msysàu fiùu wdY%s; .eg¨ we;=,;a h'
^mßudK rEm we|Su wfmalaId
fkdflf¾'&
• RcqfldaKS ;%sfldaKhl ´kEu mdo
foll È. § we;súg" ;%sfldaKñ;sl
wkqmd; fiùu wdY%s; .eg¨
wka;¾.;h'

• idOl fiùu
• 2
ax bx c  wdldrh
• ùÔh m%ldYkj, l=vdu fmdÿ
.=Kdldrh ^mo ;=klg fkdjeä
w{d; follg yd o¾Ylh
follg fkdjeä&
• ùÔh Nd.
• tl;= lsÍu
• wvq lsÍu
• ùÔh Nd. iys; talc iólrK
• úi£u
• RcqfldaKS ;%sfldaKhl hï fldaKhl gexck wkqmd;h" tys iïuqL
mdofha È. yd noaO mdofha È. w;r wkqmd;fhka ,nd fok nj wkdjrKh
lr .kshs'
• 2
ax bx c  wdldrfha m%ldYkj, idOl fidhhs'
• ùÔh mo lsysmhlska fnÈh yels l=vdu ùÔh moh tu ùÔh moj, l=vdu
fmdÿ .=Kdldrh nj y÷kd .kshs'
• fokq ,nk ùÔh mo lsysmhl l=vdu fmdÿ .=Kdldrh fidhhs'
• ùÔh Nd. tl;= lsÍfï § fyda wvq lsÍfï § ;=,H Nd.j, wjYH;dj
y|qkd.kshs'
• ùÔh mo we;=<;a iïnkaê; yr iys; ùÔh Nd. tl;= lr iq`M lrhs'
• ùÔh mo we;=<;a iïnkaê; yr iys; ùÔh Nd. wvq lr iq`M lrhs'
• ùÔh mo we;=<;a iïnkaê; yr iys; ùÔh Nd. iq`M lrhs'
• ùÔh Nd. iys; ir, iólrK úi£fï § ùÔh Nd. iq`M lsÍfï l%ufõo
fhdod .; yels nj y÷kd .kshss'
• yrfha ùÔh mo we;=<;a ùÔh Nd. iys; ir, iólrK úi|hs'
• ;%sfldaKñ;sl wkqmd;hla yd tu
wkqmd;hg wod< mdo foflka
tll È. § we;súg" wfkla mdofha
È. fiùu wdY%s; .eg`M wka;¾.; h'
• 2
0 5, 4a b ac   mQ¾K
j¾.hla jk yd , ,a b c z jk
mßÈ fõ'
• 2
,2 ,3x xy y jeks wdldrfha mo
;=klg fkdjeä w{d; follg
yd o¾Ylh follg fkdjeä mo
we;=,;a wjia:d muKs'
• yrj, tlu w{d;h yd o¾Ylh
follg fkdjeä yrh iudk
fkdjQ ùcSh Nd. ;=klg fkdjeä
wjia:d muKs' ^yrfha ùcSh
m%ldYk we;=,;a fldflf¾'&
• yrj, tlu w{d;h yd yrh
iudk fkdjQ ùcSh Nd. folla
we;=,;a wjia:d f;la we;=,;a h'
^yrfha ùcSh m%ldYk we;=,;a

• tlsfklg fjkia jQ ix.=Kl iys; iu.dó iólrK úi|hs'
• j¾.c iólrKhg wod< j¾.c m%ldYkh idOlj,g fjka lrhs'
• m%ldYk foll .=Ks;h Y+kH ùug wju jYfhka tla m%ldYkhla fyda
Y+kHh úh hq;= nj yqkd .kshs'
• idOl Ndú;fhka j¾.c iólrK úi|hs'
• y mx c  wdldrfha ir, f¾Ldjla u; msysá ,laIH foll LKavdxl §
we;s úg tys wkql%uKh .Kkh lrhs'
• y mx c  wdldrfha ir, f¾Ldjl m%ia;drh § we;súg tys wKql%uKh
.Kkh lrhs'
• ir, f¾Ldjl wKql%uKh yd wka;#LKavh weiqßka úp,H fol w;r
iïnkaO;dj fidhhs'
• ùÔh mo we;=<;a ùÔh Nd. .=K lrhs'
• ùÔh Nd.hl mriamrh fidhhs'
• ùÔh mo we;=<;a ùÔh Nd. fnohs'
• iu.dó iólrK
• úi£u
• j¾.c iólrK úi£u
• idOl Ndú;fhka
• y mx c  wdldrfha ir,
f¾Ldjl wkql%uKh yd
wka;#LKavh .Kkh lsÍu
^LKavdxl weiqßka&
• ùÔh Nd.
• .=K lsÍu
• fn§u
• w{d; folla iy mQ¾K
ixLHd;aul ix.=Kl iys;
ix.=Kl iudk fkdjQ yd úi÷ï
mQ¾K ixLHd;aul w.hhka jk
mßÈ jQ .eg¨ muKs'
• 2
0,ax bx c  
2
0 5, 4a b ac   mQ¾K
j¾.hla jk mßÈ jQ wjia:d muKs'
• m<uq jD;a; mdolh ;=< fyda tys
wlaI u; msysá mQ¾K ixLHd;aul
LKavdxl iys; ,laIH folla §
we;s wjia:d muKs'
• m<uq jD;a; mdolh ;=< msysá
f¾Ld fldgi we| ;sìh hq;=h'
^uQ, ,laIH yryd .uka lrk
wjia:d o we;=<;a h"&
• yrfhys fyda ,jfhys fyda
,jfhys yd yrfhys w{d; 2la
wvx.= ùcSh Nd. muKs'

• ; ; ;ax b c ax b c ax b c ax b c        ,
; ;ax b cx d ax b cx d      ;ax b cx d ax b cx d    
wiudk;dj, ksÅ,uh úi÷ï l=,lh fidhhs'
wiudk;dj, ksÅ,uh úi÷ï l=,lh" ixLHd f¾Ldjla u; ksrEmKh
lrhs'
wiudk;dj, úi÷ï m%dka;r fidhhs'
wiudk;dj, úi÷ï m%dka;r" ixLHd f¾Ldjla u; ksrEmKh lrhs'
• fma<s yd ;Sr weiqfrka f;dr;=re bÈßm;a lsÍfï l%uhla f,i kHdi
y÷kd .kshs'
• kHdihl fma<s .Kk yd ;Sr .Kk u.ska tys .Kh olajk nj y÷kd
.kshs'
• fma<s kHdi" ;Sr kHdi" iup;=ri% kHdi" tall kHdi iy iuñ;s
kHdi y÷kd .kshs'
• kHdi folla tl;= lsÍfï § yd wvq lsÍfï § tajdfha .Kh iudk úh
hq;= nj m%dfhda.sl wjia:d weiqßka úia;r lrhs'
• wiudk;d
• úi£u yd úi÷ï ixLHd
f¾Ldjl ksrEmKh
• ax b c wdldrh
• ax b cx d  wdldrh
( , , , )a b c d z
• kHdi
• ye¢kaùu ^3 3 olajd&
0 , , ,a a b c d z yd jQ
wjia:d muKs'
• kHdi .=K lsÍfï § wjhj
ksÅ,uh jQ wjia:d muKs'
><
><

• fma<s kHdi folla tl;= lrhs¦ wvq lrhs'
• ;Sr kHdi folla tl;= lrhs¦ wvq lrhs'
• .Kh 3 3 f;la jQ kHdi folla tl;= lrhs¦ wvqlrhs'
• .Kh 3 3 f;la jQ kHdihla ksÅ,hlska .=K lrhs'
• tl;= lsÍu" wvq lsÍu" ksÅ,hlska .=K lsÍu hk .Ks; l¾u fhdod
.ksñka kHdi we;=,;a m%ldYk iqM lr olajhs'
• kHdi folla .=K lsÍu i|yd m<uq kHdifha ;Sr .Kk fojk
kHdifha fma<s .Kkg iudk úh hq;= nj y÷kd .kshs'
• .Kh 2 2 f;la jQ kHdi folla .=K lrhs'
• ;%sfldaKhl wNHka;r fldaK ;=fkys ftlHh 1800
la fõ hk m%fïhh
Ndú;fhka .Kkh lsÍïj, fhfohs'
• ;%sfldaKhl mdohla Èla lsÍfuka iEfok ndysr fldaKh tys wNHka;r
iïuqL fldaK foflys ftlHhg iudk fõ hk m%fïhh Ndú;fhka
.Kkh lsÍï lrhs'
• tl;= lsÍu yd wvq lsÍu
^3 3 olajd&
• ksÅ,hlska .=K lsÍu
^3 3 olajd&
• ksÅ,hlska .=K lsÍu
^ 2 2 olajd&
• ;%sfldaKhl wNHka;r fldaK
1800
la fõ hk m%fïhh wdY%s;
.Kkh lsÍï'
• ;%sfldaKhl mdohla Èla
lsÍfuka iEfok ndysr
fldaKh tys wNHka;r iïuqL
fldaK foflys ftlHhg
iudk fõ hk m%fïhh wdY%s;
.Kkh lsÍï
• my< fY%aKsj,§ W.;a cHdñ;sl
ixl,am o 10 fyda 11 fY%aKsfha§
W.;a úIh lreKq wdY%s; .Kkh
lsÍï i|yd fhdod .; yels h'
^wkqfïhhka idOkh wfmalaId
fkdflf¾'&

• tlsfklg iumd;jk ;,rEm folla wx.iu rEm f,i y÷kd .kshs'
• wx.iu ;,rEmj, ,laIK y÷kd .kshs'
• ;%sfldaK 2la wx.iu ùu i|yd wksjd¾h yd m%udKj;a wjYH;d we;=<;a
wjia:d f,i md' flda' md'" flda' flda' md'" md' md' md' iy l¾K md' wjia:d
y÷kd .kshs'
• ;%sfldaKhl mdo folla iudk fõ kï tu mdoj,g iïuqL fldaK o iudk
fõ hk m%fïhh y÷kd .kshs'
fõ hk m%fïhh Ndú;fhka .Kkh lsÍïj, fhfohs'
fõ hk m%fïhfhys úf,dauh Ndú;fhka .Kkh lsÍïj, fhfohs'
• iudka;rdi%hl iïuqL mdo iudk fõ; iïuqL fldaK iudk fõ; tla tla
úl¾Kh u`.ska iudka;rdi%fha j¾.M,h iuÉfþokh lrhs hk m%fïhh
y÷kd .kshs'
• iudka;rdi%hl iïuqL mdo iudk fõ; iïuqL fldaK iudk fõ; tla tla
úl¾Kh u`.ska iudka;rdi%fha j¾.M,h iuÉfþokh lrhs hk m%fïhh
Ndú;fhka ir, .Kkh lsÍïj, fhfohs'
• wx.iduHh
• ;%sfldaK folla wx.iu
ùfï wjia:d y÷kd .ekSu
• md' flda' md
• flda' flda' md
• md' md' md'
• l¾K md'
• iu oaúmdo ;%sfldaK
• ;%sfldaKhl mdo folla
iudkfõ kï tu mdoj,g
iïuqL fldaK o iudk fõ hk
m%fïhh wdY%s; .Kkh lsÍï
• ;%sfldaKhl mdo folla iudk
fõ kï tu mdoj,g iïuqL
fldaK o iudk fõ hk
m%fïhfha úf,dauh wdY%s;
.Kk lsÍï
• .=K
• iudka;rdi%hl iïuqL mdo
i udk f õ; iïuqL fldaK
iudkfõ; tla tla úl¾Kh
u`.ska iudka;rdi%fha j¾.M,h
iuÉfþokh lrhs hk

• jD;a; pdmhlska flakaøh u; wdmd;kh lrk fldaKh" tu pdmh u`.ska
jD;a;fha b;sß fldgi u; wdmd;kh lrk fldaKh fuka fo.=Khla
• jD;a; pdmhlska flakaøh u; wdmd;kh lrk fldaKh" tu pdmh u`.ska
jD;a;fha b;sßa fldgi u; wdmd;kh lrk fldaKh fuka fo.=Khla
fõ hk m%fïhh Ndú;fhka .Kkh lsÍïj, fhfohs'
• jD;a;hl cHdhl uOH ,laIHh flakaøhg hd lrk f¾Ldj cHdhg ,ïn
• jD;a;hl cHdhl uOH ,laIHh flakaøhg hd lrk f¾Ldj cHdhg ,ïn
fõ hk m%fïhh Ndú;fhka .Kkh lsÍï lrhs'
• jD;a;hl flakaøfha isg cHdhlg w¢k ,o ,ïnfhka cHdh iuÉfþokh
• jD;a;hl flakaøfha isg cHdhlg w¢k ,o ,ïnfhka cHdh iuÉfþokh
fõ hk m%fïhh Ndú;fhka .Kkh lsÍï lrhs'
• jD;a;hl tlu LKavfha fldaK iudk fõ hk m%fïhh y÷kd .kshs'
• jD;a;hl tlu LKavfha fldaK iudkfõ hk m%fïhh Ndú;fhka
.Kkh lsÍïj, fhfohs'
• fldaK
• jD;a; pdmhlska flakaøh u;
wdmd;kh lrk fldaKh" tu
pdmh u`.ska jD;a;fha b;sß
fldgi u; wdmd;kh lrk
fldaKh fuka fo.=Khla fõ
hk m%fïhh wdY%s; .Kkh
lsÍï
• cHd
• jD;a;hl cHdhl uOH
,laIHh flakaøhg hd lrk
f¾Ldj cHdhg ,ïn fõ hk
• jD;a;hl flakaøfha isg
cHdhlg w¢k ,o ,ïnfhka
cHdh iuÉfþokh fõ hk
• jD;a;hl tlu LKavfha fldaK
iudk fõ hk m%fïhh wdY%s;
.Kkh lsÍï

• w¾O jD;a;hl msysá fldaKh RcqfldaKhla fõ hk m%fïhh y÷kd
.kshs'
• w¾O jD;a;hl msysá fldaKh RcqfldaKhla fõ hk m%fïhh Ndú;fhka
.Kkh lsÍïj, fhfohs'
• wp, ,laIHhlg ksh; ÿßka p,kh jk ,laIHhl m:h ljlgqj yd
ir, odrh Ndú;fhka ks¾udKh lrhs'
• wp, ,laIH follg iuÿßka p,kh jk ,laIHl m:h ljlgqj yd ir,
odrh Ndú;fhka ks¾udKh lrhs'
• ir, f¾Ldjlg ksh; ÿßka p,kh jk ,laIHhl m:h ljlgqj yd ir,
odrh Ndú;fhka ks¾udKh lrhs'
• fþokh jk ir, f¾Ld follg iu ÿßka p,kh jk ,laIHhl m:h
ljlgqj yd ir, odrh Ndú;fhka ks¾udKh lrhs'
• uQ,sl m: ms<sn| ±kqu fhdod .ksñka cHdñ;sl msysgqï ,nd .kshs'
• RcqfldaKS ;%sfldaKhl l¾Kh iy RcqfldaKfha wvx.= mdo fjk fjk u
kï lrhs'
• mhs;.ria m%fïhh y÷kd .kshs'
• mhs;.ria m%fïhh Ndú;fhka .Kkh lsÍïj, fhfohs'
• w¾O jD;a;hl msysá fldaKh
RcqfldaKhla fõ hk m%fïhh
wdY%s; .Kkh lsÍï
• ir, odrh yd ljlgqj
Ndú;fhka
• uq,sl m: y;r ks¾udKh
• mhs;.ria m%fïhh
Ndú;fhka .Kkh lsÍï
• Wmßu jYfhka m: folla
,efnk wdjia:dj, § tla m:hla
§" wfkla m:h weiqßka cHdñ;sl
msysgqï ,nd .ekSu wfmalaId
flf¾'
• mhs;.ria ;%s;aj muKla we;=,;a
.eg¨ wfmalaId flf¾'

• ;%sfldaKhl mdo foll uOH ,CIH hd lrk f¾Ldj iy b;sß mdoh fjk
fjk u kï lrhs'
• uOH ,CIH m%fïhh y÷kd .kshs'
• uOH ,CIH m%fïhh Ndú;fhka .Kkh lsÍïj, fhfohs'
• uOH ,CIH m%fïhfha úf,dauh y÷kd .kshs'
• uOH ,CIH m%fïhfha úf,dauh Ndú;fhka .Kkh lsÍïj, fhfohs'
• jD;a; p;=ri%hl iïuqL fldaK hq., ,shd olajhs'
• jD;a; p;=ri%hl iïuqL fldaK mßmQrl fõ hk m%fïhh y÷kd .kshs
• jD;a; p;=ri%hl iïuqL fldaK mßmQrl fõ hk m%fïhh Ndú;fhka
.Kkh lsÍï lrhs'
• jD;a; p;=ri%hl mdohla Èla lsÍfuka iEfok ndysr fldaKh iy Bg
wNHka;r iïuqL fldaK y÷kd .kshs'
• jD;a; p;=ri%hl mdohla Èla lsÍfuka iEfok ndysr fldaKh wNHka;r
iïuqL fldaKhg iudk fõ hk m%fïhh y÷kd .kshs'
• jD;a; p;=ri%hl mdohla Èla lsÍfuka iEfok ndysr fldaKh wNHka;r
iïuqL fldaKhg iudk fõ hk m%fïhh Ndú;fhka .Kkh lsÍï lrhs'
• ika;;sl o;a; iy úúla; o;a; y÷kd .kshss'
• mka;s m%dka;rhl uOH w.h y÷kd .kshs'
• mka;s m%dka;rhl uOH w.h fidhhs'
• uOH ,CIHh m%fïhh
Ndú;fhka .Kkh lsÍï
• uOH ,CIHh m%fïhfha
úf,dauh Ndú;fhka .Kkh
lsÍï
• jD;a; p;=ri%
• jD;a; p;=ri%hl iïuqL fldaK
mßmQrl fõ hk m%fïhh Ndú;h
• jD;a; p;=ri%hl mdohla Èla
lsÍfuka iEfok ndysr fldaKh
wNHka;r iïuqL fldaKhg
iudk fõ hk m%fïhh
Ndú;fhka .Kkh lsÍï '
• o;a; j¾.
• ika;;sl
• úúla;
• iuQys; ixLHd; jHdma;sh
• uOH w.h
• mka;s m%dka;rhl udhsï foflys
tl;=j 100g wvq jQ o uOH w.h
mQ¾K ixLHdjla jk mßÈ jQ o
mka;s m%dka;r muKs'
• my< fY%aKsj,§ W.;a cHdñ;sl
ixl,am o 10 fyda 11 fY%aKsfha§
W.;a úIh lreKq wdY%s; .Kkh
lsÍï i|yd fhdod .; yels h'
^wkqfïhhka idOkh wfmalaId
fkdflf¾'&

• fok ,o o;a; iuqyhla jg m%ia;drhlska ksrEmKh lrhs'
• f;dr;=re ld¾hlaIu j yd M,odhs j ikaksfõokh i|yd jg m%ia;dr
fhdod .kshs'
• jg m%ia;dr wdYs%; ir, .eg¨ úi|hs'
• fok ,o iuQys; o;a;j, uOHkHh, uOH w.h weiqfrka .Kkh lrhs'
• fok ,o iuQys; o;a;j, uOHkHh, Wml,ams; uOHkHh weiqfrka .Kkh
lrhs'
• fok ,o iuQys; o;a;j, uOHkHh fiùu i|yd jvd;a myiq l%uh
y÷kd .kshs'
• o;a; w¾:l:kh i|yd flakaøsl m%jK;d ñkqï w;=ßka uOHkHh .Kkh
lsÍfï jdis$wjdis m%ldY lrhs'
• ffoksl wjYH;d m%udKd;aulj ksudkh lr .ekSu i|yd uOHkHh
iïnkaO lr.; yels nj y÷kd .kshs'
• ffoksl wjYH;d i|yd uOHkHh Ndú;fhka mqfrdal:k isÿlrhs'
• ixLHd; jHdma;shl mka;s iSud yd mka;s udhsï y÷kd .kshs'
• ixLHd; jHdma;shl mka;s iSud yd mka;s udhsï w;r fjki meyeÈ,s
lrhs'
• ixLHd; jHdma;shl mka;s iSud yd mka;s udhsï fidhhs'
• mka;s m%dka;r iudk ika;;sl o;a; we;+<;A ixLHd;
jHdma;shlg wod< f;dr;+re cd, f¾Lhlska ksrEmKh lrhs'
• cd, f¾Lfha tla tla ;Srfha j¾.M,h u.ska ixLHd;h (f) oelafjk nj
m%ldY lrhs'
• o;a; ksrEmKh
• jg m%ia;dr
• o;a; w¾:l:kh
• iuQys; ixLHd; jHdma;shl
uOHkHh
• uOH w.h Ndú;fhka
• Wml,ams; uOHkHh
weiqfrka
• o;a; ksrEmKh
• mka;s iSud iy mka;s
udhsï
• cd, f¾Lh ^mka;s ;ru
iudk$wiudk&
• mka;s m%dka;rhl udhsï foflys
tl;=j 100g wvq jQ o uOH w.h
mQ¾K ixLHdjla jk mßÈ jQ o
mka;s m%dka;r muKs'

• wiudk mka;s m%dka;r iys; ixLHd; jHdma;shl" wiudk mka;s
m%dka;rhl ;ru tu ixLHd; jHdma;sfha l=vd u mka;s m%dka;rfha ;ru
fuka lS .=Khla o hkak u.ska ,nd .kshs'
• wiudk mka;s m%dka;r iys; ixLHd; jHdma;shlg wod< cd, f¾Lh
we£fï § mka;s m%dka;rhlg wod< cd, f¾Lfha Wi
f
n
u.ska ,nd .kshs
• wiudk mka;s m%dka;r iys; ika;;sl o;a; we;+<;A ixLHd; jHdma;shlg
wod< f;dr;=re cd, f¾Lhlska ksrEmKh lrhs'
• úúla; o;a; we;=<;a ixLHd; jHdma;shl tla tla mka;s m%dka;rhg wod<
mka;s udhsï ms<sfh, lrhs'
• úúla; o;a; we;=<;a ixLHd; jHdma;shlg wod< f;dr;=re cd, f¾Lhla
u.ska ksrEmKh lrhs'
• cd, f¾Lh weiqßka ixLHd; nyqwi%h w¢hs'
• ixLHd; nyq wi%fha j¾.M,h" cd, f¾Lfha j¾.M,hg iudk nj ms<s.kshs
• mka;s m%dka;rj, uOH w.h yd tla tla mka;s m%dka;rhg
wkqrEm ixLHd;h Wmfhda.s lr.ksñka ixLHd; nyq wi%h w¢hs'
• o;a; ksrEmKh
• ixLHd; nyqwi%h
wod< mka;sfha ;ru
l=vd mka;sfha ;ru
= n
• wiudk mka;s m%dka;rj, §
f
n
 cd, f¾Lfha Wi" mQ¾K
ixLHdjla jk mßÈ jQ ixLHd;
jHdma;s muKs'

• ixLHd; nyq wi%h we£fï § ixLHd; jHdma;sfha m<uqjk mka;s m%dka;rhg
fmr mka;s m%dka;rfha uOH w.hg yd wjika mka;s m%dka;rhg miq mka;s
m%dka;rfha uOH w.hg wfkla ;Srej, uqÿkays uOH ,CIH iïnkaO l<
miq ;sria wCIh;a iu`. nyq wi%h iïmq¾K jk nj m%ldY lrhs'
• ixLHd; jHdma;shl ixLHd; ;Srfha w.hhka by< isg my<g fyda my<
isg by<g tl;= lsÍfuka iuqÉÑ; ixLHd; ;Srh ,nd .kshs'
• tla tla mka;s m%dka;rfha by< udhsu yd tu mka;s m%dka;rhg wod<
iuqÉÑ; ixLHd;h fhdod .ksñka iuqÉÑ; ixLHd; jl%h w¢hs'
• ixLHd; jHdma;shla iudk fldgia y;rlg fnok w.hhka f,i
p;=¾:l meyeÈ,s lrhs'
• wdfrdayK l%uhg ms<sfh, l< o;a; n we;s iuQyhl
 
1
n 1
4
 jk ia:dkfha wh .Kk m<uqjk p;=¾:lh
^ 1 & f,i y÷kd .kshs'
 
1
1
2
n  jk ia:dkfha wh .Kk fojk p;=¾:lh  2 f,i y÷kd
.kshs'
• o;a; ksrEmKh
• iuqÉÑ; ixLHd; jl%h
• o;a; w¾:l:kh
• p;=¾:l yd wka;Ya p;=¾:l
mrdih ye¢kaùu

3
( 1)
4
n  jk ia:dkfha wh .Kk ;=kajk p;=¾:lh ( )3 f,i y÷kd
.kshs'
• o;a; iuQyhl fojk p;=¾:lh  2 tu o;a; iuQyfha uOHia:hg
iudk nj fmkajd fohs'
• o;a; iuQyhl ;=kajk p;=¾:lh  m<uqjk p;=¾:lh ( )3 1  wka;Ya
p;=¾:l mrdih f,i y÷kd .kshs'
• o;a; iuQyhla wdfrdayK ms<sfj,g ilia l< úg my< 25] iy by< 25]
bj;a l< úg ,efnk w.h mrdih" wka;Ya p;=¾:l mrdih f,i
y÷kd .kshs'
• ixLHd;h n jk úg"
1
4
n ia:dkhg wod< wh .Kk m<uq jk p;=¾:lh
^ 1 & f,i iuqÉÑ; ixLHd; jl%h weiqßka fidhhs'
1
2
n ia:dkhg wod< wh .Kk fojk p;=¾:lh
( )2 f,i iuqÉÑ; ixLHd; jl%h weiqßka fidhhs'
3
4
n ia:dkhg wod< wh .Kk ;=kajk p;=¾:lh
( )3 f,i iuqÉÑ; ixLHd; jl%h weiqßka fidhhs'
• m<uqjk yd ;=kajk p;=¾:l fhdod.ksñka wka;Ya p;=¾:l mrdih .Kkh
lrhs'
• ffoksl Ôú;fha .eg¨ úi£ug p;=¾:l yd wka;Ya p;=¾:l mrdih
Wmfhda.S lr .kshs'
• iuqÉÑ; ixLHd; pl%h
^wiuQys; yd iuqys; o;a;
i|yd&
• p;=¾:l
• wka;Ya p;=¾:l mrdih
• nys w.h" 4ys .=Kdldrhla
jk mßÈ úh hq;=hs'

• l=,l wxlk l%u y÷kd .kshs'
• l=,lhla" úia;r lsÍula f,i" wjhjj, tl;=jla f,i" fjka rEmhla
weiqßka yd l=,l ckk iajrEmfhka ,shd olajhs'
• l=,l wxlk l%u Ndú; lrhs'
• Ayd B mßñ; l=,l folla úg ( )n A B hkak ( ), ( ), ( )n A n B n A B
weiqßka m%ldY lrhs'
• mßñ; l=,l folla fjka rEm igyklska ksrEmKh lrhs'
• fok ,o l=,l l¾uj,g wod< j fjka rEmhl m%foaY ,l=Kq lrhs'
• l=,l l¾uj,g wod< f;dr;=re we;=<;a fjka rEmhl m%foaY jpkfhka
úia;r lrhs'
• fjka rEm igyk weiqrska l=,l folla wdYs%; .Kkh lsÍï lrhs'
• mßñ; l=,l folla wdYs%; .eg¨   ( ) ( ) (A )=n A B n A n B n B   
iQ;%h Ndú;fhka úi|hs'
• ir, isoaê yd ixhqla; isoaê fjka fldg y÷kd .kshs'
• A hkq S ksheÈ wjldYfhys jQ iufia NjH isoaêhla jk úg A isÿùfï
iïNdú;dj
 
 
( )
n A
P A
n S
 nj m%ldY lrhs'
• ixhqla; isoaêhl iïNdú;dj m%ldY lrhs'
• l=,l wxlkh
• úiaa;r lsÍula f,i
• wjhjj, tl;=jla f,i
• fjka rEmhla weiqßka
• l=,l ckk iajrEmfhka
• l=,l wdYs%; .eg¨ úi£u
• fjka rEm igyka weiqfrka
mrsñ; l=,l folla i|yd
iQ;%h Ndú;h
( )
(A) (B) (A B)
n A B
n n n
 
  
• isoaê
• ir,
• ixhqla;
• tla l=,l wxlk l%uhlska §"
fjk;a l=,l wxlk l%uhlska
±laùu wfmalaId flf¾'
• l=,l 2la wdY%s; .eg¨ muKs'

• iiïNdù mÍlaIKhl
^iajdh;a; isoaê we;=<;a&
ksheÈ wjldYh
• fldgq oe,l ksrEmKh
• rela igyklska ksrEmKh
• fldgq oe, fyda rela igyk
fyda weiqßka iajdh;a; isoaê
we;=<;a .eg¨ úi£u
• iiïNdù mÍlaIKhl
^mrdh;a; isoaê we;=<;a&
ksheÈ wjldYh
• fldgq ±,l ksrEmKh
• rela igykl ksrEmKh
• fldgq ±, fyda rela igyk
fyda weiqßka mrdh;a; isoaê
we;=,;a .eg¨ úi|Su'
• iajdh;a; isoaê i|yd kso¾Yl imhhs'
• iajdh;a; isoaê we;=<;a iiïNdù mÍlaIKhl ksheÈ wjldYh fldgq oe,l
ksrEmKh lrhs'
• wjia:d follska hq;a iajdh;a; isoaê we;=<;a ls%hdj,shl ish¨ iu fia NjH
m%;sM, rela igykl ksrEmKh lrhs'
• fldgq oe, yd rela igyk weiqßka iajdh;a; isoaê we;=,;a .Kkh lsÍï
lrhs'
• mrdh;a; isoaêhl iajNdjh úia;r lrhs'
• mrdh;a; isoaê i|yd kso¾Yl imhhs'
• mrdh;a; isoaê yd iajdhka; isoaê fjkafldg y÷kd .kshs'
• mrdh;a; isoaê we;=<;a iiïNdù mÍlaIKhl ksheÈ wjldYh fldgq±,l
ksrEmKh lrhs'
• mrdh;a; isoaê we;=<;a iiïNdù mÍlaIKhl ksheÈ wjldYhg wod<
fldgq ±, wiqßka fok ,o isoaêhlg wod< iïNdú;dj ,shd olajhs'
• wjia:d follska hq;a mrdhka; isoaê we;=<;a iiïNdù mÍlaIKhl § úh
yels ish¨ isÿùï rela igykla u`.ska olajhs'
• fldgq ±, yd rela igyk weiqßka mrdh;a; isoaê we;=,;a .Kkh lsÍï
lrhs'
• wjia:d 2lg fkdjeä l%shdj,s
muKs'

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