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w' fmd' i' ^Wiia fm<& ixhqla; .Ks;h kj úIh ks¾foaYh 2017 jif¾ isg
Tn oek isáh hq;= uQ,sl lreKQ
1'1 ùcSh m%ldYk m%idrKh
3322babababa
2cba
1'2 ùcSh m%ldYkj, idOl
333322 bababa
ùc .Ks;h
1'3 ùcSh m%ldYk iq¿ lsrSu
1'4 iólrK úi|Su
003 332 axxx
123
532
yx
yx
1'5 o¾Yl iy ,>q m%ldYk
nmmn
mnmn
mnmn
aa
aaa
aaa
xnx
y
xyx
xyyx
an
a
aaa
aaa
loglog
logloglog
logloglog
a
xx
b
ba
log
loglog
1'6 wkqmd; ms<sn| wjfndaOh
fuh u kus muKla f,i lshjuq' d
c
b
adcba ::
2'1 cHdï;sl m%fush
mhs;.riaf.a m%fushh
b
a
c
222 cba
cHdï;sh
iq¿ fldaKSl m%fushh
ABC hkq iq¿ fldaKsl ;s%fldaKhla hehs .ksuq'
B C
A
D
BDBCBCABAC ..2222
uyd fldaKSl m%fushh
BDBCBCABAC ..2222
ABC hkq uyd fldaKsl ;s%fldaKhla hehs .ksuq'
C
A
B D
wemf,dakshia m%fushh
;s%fldaKhl TskEu mdo foll j¾.hkays ftlHh" f;jeks mdofhys wvl j¾.h iy f;jeks mdoh iupsfPaokh lrk uOHia:fhys j¾.fhys ftlHh fuka fo.=Khls'
ABC hkq ;s%fldaKhla hehso D hkq BC mdofhys uOH ,laIHh hehso .ksuq.
C
A
B D
2222 2 BDADACAB
2'2 mhs;.ria m%fushfha fhoSus
2'3 ;%sfldaKhl fldaK iupsfPaol iy fhoSus
B
C
A
D
c
b
b
c
AD hkq A fldaKfhys wNHka;r fldaK iupsfPaolh jk úg
.:: bcDCBD
.mn
m
c
b
AN hkq A fldaKfhys ndysr fldaK iupsfPaolh jk úg
B C
A
N m
b
c
n
fuu fldaK iupsfPaolh iusuqL mdoh b : c wkqmd;hg ndysrj fnohs. tkus ,
2'4 iurEmS ;%sfldaK ms<sn| wjfndaOh iy fhoSus
2'5 ;%sfldaK yd iusnkaê; jD;a; iy flakaø
mrsjD;a;h iy mrsflakaøh
tla tla mdofha ,usNn iupsfPaol yuq jk fmd¥ ,laIHh
,usNjD;a;h iy ,usNflakaøh
tla tla YS¾Ifha isg iusuqL mdohg we|s ,usN yuq jk fmd¥ ,laIHh
wka;:jD;a;h iy wka;: flakaøh
tla tla fldaKfha wNHka;r iupsfPaol yuq jk fmd¥ ,laIHh
ixhqla; .Ks;h fldgia follska iukaú;hs'
( 1 ) fldgi - Y=oaO .Ks;h ixrplh
ùc .Ks;h
l,kh
LKavdxl cHdï;sh
;%sfldaKï;sh
( 2 ) fldgi - jHjydrsl .Ks;h ixrplh
ia:s;slh
.;slh
iusNdú;djh
ixLHdkh
( 1 ) fldgi
Y=oaO .Ks;h ixrplh
ùc .Ks;h
1. ;d;a;aúl ixLHd
2. Y%s;
3. j¾.c Y%s;h
4. nyqmo Y%s;h
5. mrsfush Y%s;h
6. o¾Yl iy ,>q
7. wiudk;d
19. .Ks; wNHqykh
20. fY%aKs iy tajd wdl,kh
21. wmrsï; fY%aKs
22. oaúmo m%idrKh
23. ixlS¾K ixLHd
24. ixlrK iy ixfhdack
25. kHdi
ùc .Ks;h
l,kh
13. iSudj
14. wjl,kh
15. wjl,kh Ndú;fhka Y%s;hl yeisrSu
16. ksYaÉ; iy wksYaÉ; wkql,kh
LKavdxl cHdï;sh
17. LKavdxl ;,h
18. ir, f¾Ldj
26. jD;a;h
27. jD;a;hl cHdï;sl .=K
;%sfldaKï;sh
8. fldaKsl ïkqu
9. ;%sfldaKï;sl Y%s;
10. ;%sfldaKï;sl i¾jiduHh
11. ihska kS;sh iy fldaihska kS;sh
12. m%;sf,dau ;%sfldaKï;sl Y%s;
ixhqla; .Ks;h Y=oaO .Ks; ixrplh - ùc .Ks;h
1 ;d;a;aúl ixLHd
1'1 ;d;a;aúl ixLHd j¾.SlrKh úfYaIs; Wml=,l" m%dka;r iy cHdï;sl ksrEmKh
1'2 ;d;a;aúl ixLHdjl oYu ksrEmKh iy lrKs
2 Y%s;
2'1 tla úp,Hhla iys; Y%s; Y%s;hl w¾: oelaùu" jiu" iyjiu" kS;sh" mrdih iy m%;sìusnh
2'2 úfYaIs; Y%s; ksh;" tall" udmdxl" nyqmo" lvukska" tlg-tl" u;g iy m%;sf,dau Y%s;
3 j¾.c Y%s;h
3'1 j¾.c Y%s;fha .=K ye|skaùu" j¾. mQrKh" úfjsplh" wvq;u fyda jeä;u w.h" uQ,j, iajNdjh iy m%ia;drh
3'2 j¾.c iólrKhl uQ, uQ, ftlHh" .=Ks;h" uQ, we;=<;a iuï;sl m%ldYk iys; uQ, iys; j¾.c iólrK f.dv ke.Su" úfjsplh" mrsKduk
4 nyqmo Y%s;h
4'1 ye|skaùu 4'2 ftlHh" wka;rh" .=Ks;h iy fnoSu 4'2 fYaI m%fushh iy idOl m%fushh
5 mrsfush Y%s;h
5'1 Nskak Nd. fkdokakd ksh; 4la olajd
6'1 o¾Yl kshu iy ,>q kshu
6 o¾Yl iy ,>q
7 wiudk;d
7'1 wiudk;d ms<sn| uQ,sl ixl,am wiudk;d ixLHd f¾Ldfjs ksrEmKh
19'1 .Ks; wNHqyk uQ,O¾uh ye|skaùu iy tys fhoSus
19 .Ks; wNHqykh
7'2 ùcSh wiudk;d ùcSh f,i iy m%ia;drslj wiudk;d úi|Su
7'3 udmdxl wiudk;d úi|Su iy m%ia;drsl ksrEmKh
20 fY%aKs iy tajd wdl,kh
20'1 mrsï; fY%aKs iy tajdfha ,laIK 20'2 uQ,sl (mrsï;) fY%aKs iy ftlHh iudka;r fY%aKs" .=fKda;a;r fY%aKs iy iud-.=fKda;a;r fY%aKs
idOkh iy fhoSus
n
r
n
r
n
r
rrr
1
3
1
2
1
20'3 uQ,sl (mrsï;) fY%aKs wdl,k l%u wka;r l%uh" .Ks; wNHqyk uQ,O¾uh iy Nskak Nd. Ndú;h
21'1 wdxYsl ftlHh
wmrsï; fY%aKshl wNsidrs;djh/wmidrs;djh
21 wmrsï; fY%aKs
22 oaúmo m%idrKh
22'1 Ok ksÅ,uh o¾Yl i|yd oaúmo m%idrKh
m%idrKfha ,laIK iy idOkh
22'2 oaúmo m%idrKfha .=K
m%idrKfha mo iy ix.=Kl
23 ixlS¾K ixLHd
23'1 ixlS¾K ixLHd ye|skaùu
23'2 ixlS¾K ixLHd ùch
ixlS¾K ixLHd i|yd .Ks; l¾u
23'2 ixlS¾K m%;snoaOh
23 ixlS¾K ixLHd
23'4 ixlS¾K ixLHdjl udmdxlh iy tys ,laIK
23'5 wd¾.ka igyk iy ixlS¾K ixLHd ksrEmKh
23'6 o uqjdj¾ m%fushh
m%fushh ye|skaùu" idOkh iy ir, fhoSus
ninin
sincossincos n hkq ksÅ,hla jk úg
2n jk úg
cossin22sin
sincos2cos 22
nz ys úia;drh
23'7 úp,H ixlS¾K ixLHdjl m:h iy wd¾.ka igyfkys m%foaY
24 ixlrK iy ixfhdack
24'1 l%udfrdams; wxlkh
24'2 .Kka lsrSfus uQ,sl m%fush
24'3 ixlrK iy fhoSus
24'4 ixfhdack iy fhoSus
25 kHdi
25'1 kHdi ye|skaùu iy ,laIK
25'2 úfYaIs; kHdi
25'3 kHdihl fmr¿u iy kHdihl m%;sf,dauh
25'4 iu.dó iólrK kHdi Ndú;fhka úi|Su
ixhqla; .Ks;h Y=oaO .Ks; ixrplh - l,kh
13 Y%s;hl iSudj
13'1 iSudj ye|skaùu
13'2 iSudj ms<sn| m%fush
13'3 m%;sM,h 1
nnn
nna
ax
axLim
idOkh iy fhoSus
13'4 m%;sM,h 1sin
0
x
xLimn
idOkh iy fhoSus
13 Y%s;hl iSudj
13'5 tla w;a iSudj ol=K;a iSudj iy ju;a iSudj
13'6 wkka;fhaoS iSudj iy mrsfush Y%s;j, iSudj
;sria iam¾fYdakauqL
13'7 iSudj fkdmej;Su
isria iam¾fYdakauqL (tla w;a iSudj fhoSfuka)
13'8 Y%s;hl ika;;sl;djh
14 wjl,kh
14'1 Y%s;hl jHq;amkakh ms<sn| woyi
14'2 m%uQ, O¾uh
14'3 wjl,kh i|yd kS;s
14'4 m%;sf,dau ;%sfldaKï;sl Y%s; wjl,kh
14'5 m%lD;s >d;Sh Y%s;h iy th wjl,kh
14'6 m%lD;s ,>q Y%s;h iy th wjl,kh
14'7 wOHdND; Y%s;/mrdï;sl Y%s; wjl,kh
14'8 by< .Kfha wjl,k ix.=Kl
15 wjl,kh Ndú;fhka Y%s;hl yeisrSu
15'1 yereus ,laIH iy wjl,k ix.=Klh
15'2 k;sj¾;k ,laIH
15'3 jl% wkqf¾Lkh
15'4 m%fhda.sl wjia:d i|yd wjl,kh Ndú;h
16 wksYaÉ; iy ksYaÉ; wkql,kh
16'1 wksYaÉ; wkql,h
16'2 wkql,k kS;s
16'3 l,kfha uQ,sl m%fushh iy ksYaÉ; wkql,h
16'4 wkql,k l%u
16'5 i¾jiduH weiqfrka ;%sfldaKï;sl Y%s; wkql,kh
16'6 fldgia jYfhka wkql,kh
16'7 im¾hka; fmfoil j¾.M,h i|yd wkql,kh
16'8 jl% N%uKfhka ;efkk fmfoil mrsudj i|yd wkql,kh
ixhqla; .Ks;h Y=oaO .Ks; ixrplh - LKavdxl cHdï;sh
17 LKavdxl ;,h
17'1 ,laIH folla w;r ÿr
17'2 f¾Ld LKavhla wkqmd;hlg fnoSu
18 ir, f¾Ldj
18'1 ir, f¾Ldjl iólrKh
18'2 f¾Ld foll fPaok ,laIH Tiafia we;s fmdÿ f¾Ldjl iólrKh
18'3 f¾Ldjla wkqnoaOfhka ,laIH foll idfmalaI msysgqu
18 ir, f¾Ldj
18'4 f¾Ld folla w;r fldaKh
18'5 ,laIHhl isg f¾Ldjlg ÿr
26 jD;a;h
26'1 jD;a;hl iólrKh
27 jD;a;hl cHdï;sl .=K
27'1 jD;a;hla wkqnoaOfhka f¾Ldjl msysgqu
27'2 ndysr ,laIHhl isg jD;a;hlg we|s iam¾Yl
27'3 jD;a;hl iy f¾Ldjl fPaok ,laIH Tiafia we;s fmdÿ jD;a;hl iólrKh
27'4 jD;a;h foll idfmalaI msysgqu
27'5 jD;a; m%,usnj fPaokh
( 2 ) fldgi
jHjydrsl .Ks;h ixrplh
2 tal;, n,
1 ffoYsl ia:s;slh
3 p,s;h i|yd ksjsfgdakshdkq wdlD;sh
.;slh
4 wyUq isÿùus i|yd .Ks;uh wdlD;sh
iusNdú;djh
5 ;SrK .ekSu i|yd .Ks;uh wdlD;sh
ixLHdkh
ixhqla; .Ks;h jHjydrsl .Ks; ixrplh - ia:s;slh
1 ffoYsl
1'1 ffoYsl ye|skaùu
1'2 ffoYsl ùch
1'3 msysgqus ffoYsl
1'4 wosY .=Ks;h iy ffoYsl .=Ks;h
2 tal;, n,
2'1 wxY=jla u; n,
2'2 wxY=jla u; n, foll iusm%hqla;h
2'3 wxY=jla u; n, moaO;shl l%shdldrs;ajh
2'4 n, ;=kl l%shdldrs;ajh hgf;ys wxY=jl iu;=,s;;djh
2'5 oDv jia;=jla u; tal;, moaO;shl iusm%hqla;h
2'6 jia;=jla u; iudka;r n, foll l%shdldrs;ajh
2'7 oDv jia;=jla u; l%shd;au; n, moaO;shla úYaf,aIKh
2 tal;, n,
2'8 jia;=jla u; n, ;=kl iu;=,s;;djh
2'9 >¾IKh
2'10 ikaêhl iu;=,s;;djh i|yd n, moaO;sl ie,lSu
2'11 rduq iels,s
2'12 iuï;sl jia;=j, ialkaO flaka
2'13 wkql,kh fhoSfuka jia;=j, ialkaO flaka
2'14 ixhqla; jia;=j, ialkaO flaka
2 tal;, n,
2'15 .=re;aj flaka h
2'16 iu;=,s;;djfha we;s jia;=jl ia:dhs;djh
2'17 t,a,d we;s jia;=jl iu;=,s;;djh
3 p,s;h i|yd ksjsfgdakshdkq wdlD;sh
3'1 f¾Çh fm;l p,kh jk jia;=jla i|yd m%ia;dr
3'2 m%.;sl iólrK
3'3 idfmalaI p,s;h
3'4 ;,hla u; jia;=jl p,s;h
3'5 ;,hla u; jia;= foll idfmalaI p,s;h
3'6 idfmalaI p,s;fha m%dfhda.sl fhoSus
3'7 m%laIsma;
3 p,s;h i|yd ksjsfgdakshdkq wdlD;sh
3'8 wjia:s;sl rduqjloS ksjsgksf.a kshu
3'9 hdka;%sl Yla;sh
3'10 laIu;djh
3'11 wdfjs.h
3'12 m%;Hdia: .egqus
3'13 f¾Çh .uH;d ixia:s;s uQ,O¾uh
3'14 jD;a;dldr fm;l p,kfhaoS m%fjs.h iy ;ajrKh
3 p,s;h i|yd ksjsfgdakshdkq wdlD;sh
3'15 ;sria jD;a;dldr fm;l p,kh
3'16 issria jD;a;dldr fm;l p,kh
3'17 ir, wkqj¾;S p,s;h
3'18 ;sria f¾Çh fm;l isÿ jk ir, wkqj¾;S p,s;h ú.%y lsrSu
3'19 issria f¾Çh fm;l isÿ jk ir, wkqj¾;S p,s;h ú.%y lsrSu
ixhqla; .Ks;h jHjydrsl .Ks; ixrplh - iusNdú;djh
4 wyUq isÿùus i|yd .Ks;uh wdlD;sh
4'1 iiusNdù mrSlaIK
4'2 wyUq isÿùus i|yd iusNdú;d wdlD;s
4'3 wiusNdú iusNdú;djh
44 iajdh;a; isÿùus
4'5 fnshiaf.a m%fushh
ksheos wjldYh úNd.kh" uq¿ iusNdú;d m%fushh (idOkh iu.)
fnshiaf.a m%fushh
5 ;SrK .ekSu i|yd .Ks;uh wdlD;sh
5'1 ixLHdkh ye|skaùu
5'2 flakaˉsl m%jK;d ïkqus
5'3 ixLHd; jHdma;s
54 úisrSfus ïkqus
5'5 l=ál;djh