,yf;dk; epd;w el;rj;jpughjk; fhz:
Xh; ,uhrpapy; xd;gJ ghjq;fs; cs;sd.
nfhLf;fg;gl;l cjhuz [hjfj;jpy;. ,yf;dk; mike;j ,uhrp fd;dpahFk;. fd;dpapYs;s 9
el;rj;jpu ghjq;fs;> cj;jpuk; - 2>3 kw;Wk; 4 > `];jk; - 1>2>3>
kw;Wk; 4> rpj;jpiu -1 kw;Wk; 2 MFk;.
,e;j xd;gJ ghjq;fspy; ve;jg; ghjj;jpy;
,yf;dk; mike;Js;sJ vd;gijNa ehk; fzf;fpl Ntz;Lk;. vq;qdk;; fzf;fPL nra;tJ ? –vd;gJ kpf vspjhdJ. fd;dpuhrpapd; nkhj;j ,uhrp ghpkhzj;ij tpdhbahf;fp 9
My; tFf;f tUk; tpilia>fd;dp ,uhrpapy; nrd;w ghpkhzj;jpypUe;J xt;nthU ghj
,uhrpkhdj;ijf; fopj;Jtu>ve;j ghjrhuj;jpy; fopf;f Kbahj epiy
Vw;gLfpwNjh>mJNt ,yf;dk; epd;w ,uhrpghjkhFk;. Ghpe;jjh ? md;gh;fNs! re;Njfkwg;
Ghpe;Jnfhs;Sq;fs;. ,d;p nray;Kiwf;F tUNthkh ?
மதுரையின் nkhj;j ,uhrp ghpkhzk; 4.58;
,ij> tpdhbahf khw;w 60 My; ngUf;fp : 4 × 60 + 58 = 298
÷ 9 = 33 .tp.1 ghj msT ;xd;gjhy; tFf;fTk;.
,e;j xU ghj msthd 33 tpdhbfisf; fd;dpapy; nrd;w ghpkhzj;jpypUe;J
fopf;fTk;.
fd;dpapy; nrd;w ghpkhzk; = 2 -51
Kjy; ghjk; - cj;jpuk; - 2 f;F = 0 -33 (--)
|
2 - 18
|
2 Mk; ghjk; - cj;jpuk;-3 f;F = 0 –33 (--) ;;
1 --45
|
3 Mk; ghjk;- cj;jpuk; -4 f;F = 0 –33 (--)
1 - 12
4 ஆம் பாதம் அஸ்தம்-1 0 - 33
0 - 39
5Mk; ghjk; --`];jk; --2 f;F = 0—33
0 –06
|
,jd;gb> mLj;j 0.33 tpdhb
fopf;f KbahJ vd;gjhy; `];jk; -2 f;Fg; gpwF tUk; `];jk; -- 3 y; yf;dk; mikfpwJ.
khztu;fs; Rygkhf Ghpe;Jnfhs;sNt ,g;gb fzpjk; nra;aglgl;lJ. ,ijNa RUf;fkhfr;
nra;a 2×60 = 120 + 51 = 171 ÷ 33 = 5.18 .
/ 5 Mk; ghjk; fle;J 6 k; ghjkhd `];jk; - 3 Mk; ghjk; te;J tpl;ljy;yth ?
Mjpae;j guk ehopif:
xU ehspd; 60 ehopiff;Fk; xNu el;rj;jpuk;
tpahgpj;J ,Ug;gjpy;iy. xU [hjfh; gpwe;j md;W vd;d el;rj;jpuk; ,Uf;fpwJ. vt;tsT
Neuj;jpw;F mUf;fpwJ vd;gij gQ;rhq;fj;jpd; %yk; mwpe;J nfhs;fpNwhk;.Mjp vd;why;
Muk;gk;>me;jk; vd;why; KbT.xU el;rj;jpuk; njhlqfp>KbAk;tiu cs;s fhyNk
Mjpae;j ghuk ehopifahFk;. ,jd; cjtpahy; [hjfu;pd; gpwe;j el;rj;jpu
ghjj;ijAk;>fu;g;gr; nry; ePf;fp> jprhGj;jp ,Ug;igAk; fhzyhk;.
[hjfu; gpwe;j Kjy; ehspy; xU
el;rj;jpuj;jpd; Kd;gFjpAk; ,uz;lhk; ehspy; gpd;gFjpAk; tpahg;gpj;J ,Uf;Fk;.;; [hjfh;
gpwe;j Neuj;jpw;Fj; jf;fthW fPo;f;fz;l topKiwg;gb Mjpae;j guk ehopifiaf;
fzf;fpl Ntz;Lk;.
m) md;iwa el;rj;jpuk; Kbtjw;Fs; [hjfh;
[dpj;jpUe;jhy;>me;j el;rj;jpuj;jpNyNa mtu; [dpj;jjhff; nfhs;f.
[hjfh; gpwe;j ,e;j el;rj;jpuj;jpd; Mjpae;j
guk ehopifiaf; fz;Lgpbf;f> xU ehspd; msthd 60 ehopifapypUe;J>Kjy;ehs;
el;rj;jpu ,Ug;G ehopifiaf; fopf;f Ntz;Lk;. ,e;j tpilahdJ> [hjfh; gpwe;j
el;rj;jpuj;jpd; ;Kjy;ehs ,Ug;ghFk;.mjDld;; gpwe;jehspd; el;rj;jpu ,Ug;igf; $l;l
tUtNj Mjpae;j guk ehopifahFk;.
M). md;iwa el;rj;jpuj;jpd; ehopif Kbe;jgpd; cjahjpehopif ,Ue;jhy; mLj;j
el;rj;jpuj;jpy;>[hjfh; gpwe;jjhff; nfhs;sNtz;Lk;.
[hjfh; gpwe;j el;rj;jpuj;jpd; Mjpae;j guk
ehopif fzf;fpl> xU ehspd; nkhj;j ehopif msthd 60 ehopifapypUe;J>Kjy;ehs;
el;rj;jpu ,Ug;igf; fopf;f Ntz;Lk. mt;thW fopj;jhy; [hjfh; gpwe;j md;W cs;s>
gpwe;j el;rj;jpu ,Ug;G fpilf;Fk;. ,j;Jld; kWehs; el;rj;jpu ,Ug;igf; $l;l
Mjpae;j guk ehopif fpilf;Fk;.
khztu;fNs! Mjpae;j guk ehopif fz;Lgpbf;fj;
jahuhfptpl;Bh;fsh ? [hjfh; gpwe;j md;iwa el;rj;jpuf; Fwpg;Gfis
gQ;rhq;fj;jpypUe;J vLq;fs;. ekJ [hjfh; gpwe;j md;W> mjhtJ tp[a tUlk; Mb
khjk; 12 k; ehs; (28-7-2013) Qhapw;Wf;fpoik> ,Nutjp el;rj;jpuk; ,Ug;G 42 – 25 ehopif MFk;. Kjy;ehshd Mb 11 y; cj;jpul;lhjp el;rj;jpuk; 40 – 40 ehopifahFk;. cjahjpehopif 11 – 15> md;iwa ,Nutjp ehopiff;Fs; tUtjhy; [hjfh; gpwe;jJ ,Nutjp
el;rj;jpunkd KbT nra;fpNwhk;.
eh -- tp
xU ehspd; fhy msT ;; =
60 - 00
Mb 11 –cj;jpul;lhjp ,Ug;G = 40 - 40
Mb 11 – ,Nutjp ,Ug;G = 19 - 20
Mb 12 – ,Nutjp ,Ug;G = 42 - 25
,Nutjp Mjpae;j guk ehopif = 61 - 45
-----------------
cj;jpul;40-40
|
Nutjp
19 20
|
jp
42-25
|
Mjp 61-45
|
60
Mb12
cjahjp ehopif ------- 11 – 15 ehopif. [hjfh; gpwe;jJ Mb-12 Mk; Njjp.xU ehspd; msthd 60
ehopifapypUe;J Mb 11 Mk; Njjp cj;jpul;lhjp ,Ug;igf; fopj;J tUtJ Mb 12 k; Njjp
,Nutjp ,Ug;ghFk;. ,j;Jld; gpwe;j ehspd; ,Nutjp ,Ug;igf; $l;l Ntz;Lk;.
re;jpud; epd;w el;rj;jpu ghjk; fhzy;:-
xU el;rj;jpuj;jpw;F ehd;F
ghjq;fs; vd;gJ ePq;fs; mwpe;j xd;Nw. ekf;F te;j tpilahd 61 – 45 ehopif vd;gJ ehd;F ghjj;jpd; msT vd;gjhy;> ,Nutjpapd; xU
ghjj;jpw;fhd msitf; fhz>,ij 4 My; tFf;f Ntz;Le;jhNd ? ehd;F ghj msT = 61 – 45 ÷ 4
= 15 kPjp 1 – 45 ,ij tpdhbahf;fp 4 My; tFf;f 1× 60 +45
= 105 ÷ 4 = 26 ¼ tp. MFk;. vdNt xUghjj;jpd; msT 15
ehopif 26¼ tpdhb MFk;.
m) [hjfh; gpwe;j ehSf;F Kjy; ehs; el;rj;jpu ,Ug;igAk;> cjahjp ehopifAk;
$l;l Ntz;Lk;.;
M) cjahjp ehopifapy; ,Ue;J [hjfh; gpwe;j el;rj;jpuj;jpd; Ke;ija
el;rj;jpu
,Ug;igf; fopf;f Ntz;Lk;.
m.tpd; gb cjahjp ehopif = 11--15
Kjy;ehs; ,Nutjp ,Ug;G = 19--20 ;
,Nutjpel;rj;jpuj;jpd;;nry;;ehopif=
|
30-35
,Nutjp el;rj;jpuj;jpd; Mjpae;j guk ehopif 61 – 45 >4 ghjnkdpy; 1 ghjk; 15–26 ¼ vd Kd;dNu fz;Nlhk;.
,Nutjp el;rj;jpu nry; -- 30 -35.,jpy; 15 .26 If; fopj;Jtu kPjp 15 – 09 MFk;.,jpy; mLj;j ghj msthd
15.26 If; fopf;f KbahJ>vdNt> ,Nutjp – 2 ,y; re;jpud; ,Uf;fpwhu;. ,Nutjp el;rj;jpuk; kPdj;jpy; ,Ug;gjhy;>
mJNt [hjfupd; n[d;k ,uhrpahFk;. ,Nutjp el;rj;jpuk; GjDf;FupaJ. Gjdpd; jprh Mz;L
17 MFk;.
,dp jrh ,Ug;G fhzNtz;Lk; :- jrh tUlq;fs; vd;gJ> ehk; fz;Lgpbj;j
Mjpme;j guk ehopiff;Fr; rkkhdJ. mjhtJ 61 – 45 M.m.g ehopif = 17 jrh tUlq;fs;.
Mjp me;j guk ehopifapypUe;J>el;rj;jpu ,Ug;G ehopiff;Fj; jrh ,Ug;G fzf;fpl
Ntz;Lk;.
jrh ,Ug;Gf; fhz :
el;rj;jpu ,Ug;G × jrh tUlk;
-------------------------------------------------------;
= jrh ,Ug;G
Mjp me;j guk ehopif
Mb khjk; 12 Mk; Njjp gpwe;j
[hjfUf;Fj; jrh ,Ug;Gf; fzf;fpLNthk;.
n[d;k el;rj;jpuk; Nutjp – Gjd; jpir 17 tUlk;.
Mjpae;j guk ehopif = 61 – 45
,Nutjp el;rj;jpu nry;
(--) = 30 – 35
--------------------
,Nutjp el;rj;jpu ,Ug;G = 31 – 10
,f; fzpjk; nra;Ak; NghJ
ehopifia tpdhbahf khw;wpf;nfhs;s Ntz;Lk;.
/ jrh tUlk; =
---------- = 8 . 5803. ( 8 vd;gJ jrh tUlk;)
3705
,jpy; fhy;FNyl;lupy; 8. If; fopj;jhy; .5803 I 12 My; ngUf;f 6.9636
tUk;.,jpy; 6 vd;gJ khjj;ijf;Fwpf;Fk;. ,e;j tpilapy; 6 If; fopj;Jtpl;L 30 My;
ngUf;f 28.908 tUk;. ,ij 28 ehl;fshf vLj;jf; nfhs;syhk;. vdNt
Gjd; kfh jrh ,Ug;G -- 8 tUlk; 6 khjk; 28 ehl;fshFk;.
gQ;rhq;fj;jpypUe;J fpuf
epiyfisg; ghu;j;J fpuf ghjrhuq;fisg; ghu;j;J>ml;ltiz mikf;fTk;. mij
itj;Jj;jhd; [hjfupd; ,uhrpf;fl;lk;>ethk;rk; kw;Wk; jpNufhzk; Mfpa fl;lq;fis
mikf;f Ntz;Lk;.
tp[a tUlk; Mb khjk; 12 k; ehSf;fhd fpuf ghjrhu ml;ltiz:
fpufq;fs;
|
el;rj;jpuk;
|
ghjk;
|
#hpad;
|
G+rk;
|
3
|
re;jpud;
|
,Nutjp
|
2
|
nrt;tha;
|
jpUthjpiu
|
3
|
Gjd;
|
Gdu;G+rk;
|
1
|
FU
|
jpUthjpiu;
|
2
|
Rf;fpud;
|
kfk;
|
4
|
rdp
|
Rthjp
|
2
|
,uhF
|
Rthjp
|
4
|
NfJ
|
guzp
|
3
|
,uhrpr; rf;fuk; mikj;jy;:
NkNy cs;s fpuf ghjrhu ml;ltizglgb xU
Fwpg;gpl;l el;rj;jpughjk; ve;j uhrpapy;
,lk;ngWfpwNjh;>me;j ,uhrpapy fpufq;fis ,lNtz;Lk;.;
NfJ
|
nrt;
;FU
Gjd;
|
||
,uhrp
|
#hp
|
||
Rf;
|
|||
rdp
,uhF
|
,yf;
|
||
Gjd; jrh ,Ug;G : 8 tUlk; 6 khjk; 28 ehs;.
ethk;r rf;fuk; mikj;jy; :
md;G khztu;fNs! ,uhrpf;fl;lk;
mikg;gJ gw;wp mwpe;J nfhz;Nlhk;. ,e;j ,uhrpf;fl;lj;ij kl;Lk; itj;Jf; nfhz;L
njspthd gyd; ciug;gJ fbdk;. vdNt> ethk;rf;fl;l mikg;igAk;> el;rj;jpu
ghjhrhuq;fis etk;rf;fl;lj;ijg; ghu;j;jTld; nrhy;Yk; msTf;Fg; gapw;rp
ngw;why;jhd;; mJ rhj;jpakhFk;.. vdNt> khztu;fs;> mjpf ftdKld;>
jpUg;gj; jpUk;gg; gapw;rp vLj;Jf; nfhs;s Ntz;Lk;.; ,J Xh; ,uhrpia xd;gJ
ghfq;fshfg; gpupj;J mikf;Fk; fl;lk; vd;gijg; Gupe;J nfhs;s Ntz;Lk;.
Nk\k; Kjy; flfk; tiu – Nk\ kz;lyk;
(NfJ>re;jpud;>FUtpd; el;rj;jpuq;fs;); -- rpk;kk; Kjy; tpUr;rpfk; tiu --
rpk;k kz;lyk; (Rf;>nrt;tha;>rdpapd; el;rj;jpuq;fs;)> jDR Kjy; kPdk;
tiu – jDR kz;lyk;. (#hpad;>,uhF>Gjdpd; el;rj;jpuq;fs;)
|
|
,uhF
|
Gjd;
|
,yf;;
|
|
nrt;
;
|
ethk;rk;
|
Rf;
|
|
re;;>rdp
FU
|
|||
#hp
|
NfJ
|
||
jpNufhzr; rf;fuk; mikj;jy;:
,uhrpia %d;W rk ghfkhfg;
gphpj;J> mjd;;gb miktJ jpNufhzr; rf;ukhFk;. Xh; ,uhrpapd; 30 ghifia gj;J
ghif nfhz;l %d;W gphpthf;fp> Kjy; gj;Jg; ghifia> mNj ,uhrpapYk;> 2 tJ
gpupit 5 tJ ,uhrpapYk;> 3 tJ gpupit 9 tJ ,uhrpapYkhf ,l Ntz;Lk;.
;;
|
|||
Gjd;
;rdp
,uhF
|
jpNufhzk;
|
||
,yf;
;
|
NfJ
|
||
Rf;
|
#hp>re;
|
nrt;;
FU
|
|
khzt ez;gh;fNs! thf;fpa Kiwg;gb vt;thW [hjfk; fzpg;gJ vd;W ghh;j;Njhk;.
,f; fzpj Kiwfis KOtJkhfg; Ghpe;J nfhs;s>gyKiw jpUk;gj; jpUk;g nra;J ghh;j;J
gapw;rp vLj;Jf; nfhs;tJ kpf mtrpakhd xd;whFk;. rpj;jpuKk; ifg; gof;fk; vd;gJ
Nghy;> vjw;FNk gapw;rp kpf mtrpakhfpwJ. mlj;J> jpUf;fzpj Kiwg;gb vq;qdk; [hjf
fzpjk; nra;tJ vd;W ghh;g;Nghk;. ;
fzpj;j [hjfk; rhpjhனா vd rhp ghh;f;Fk; topfs; ahit ?
1. #hpad;>rhpahd jkpo; khjj;jpw;Fhpa ,uhrpapy;; cs;shuh vd;gijg;
ghh;f;fTk;.
2. Rf;fpud;>Gjd; Mfpa fpufq;fs; #hpaDf;F Kd;gpd; %d;W fl;lq;fSf;Fs;
,Uf;Fk;.
3. ,uhF NfJ rkrg;jkkhfNt ,Uf;Fk;.
4. ,uhrpf;fl;lj;jpy; #hpaDld;>xNu ,uhrpapy; ,ize;Js;s fpufq;fs;
ethkrj;jpy; #hpaDf;F Kd;gpd; ,uhrpfspNyh my;yJ #hpaDld; ,ize;jpUe;jhNyh>
m];jkdkhfpa epiyapypUf;Fk;.;
5. ;; [hjfh; gfypy; gpwe;jpUe;jhy;>#hpad; epd;w ,uhrpf;F 7 ,uhrpf;Fs;
,yf;fk; mikAk;. ,uT vdpy; 7 ,y; ,Ue;J 12 tJ uhrpf;Fs; ,yf;dk; mikAk;.
6. #hpaDf;F 6>7>8 tJ ,uhrpfspy; FU>rdp> nrt;tha;
,Ue;jhy;>tf;u epiy milAk;.
7. tsh;gpiw fhy;jpy;>#hpaDf;F>7 ,uhrpf;Fs;Sk;>Njagpiwf; fhyj;jpy;7
– 12 f;Fs;s ,uhrpfspy; re;jpud; epiy ngWthh;.
Asdfghjkl;’asdfghjkl;qasdfghjklkjhgfdsa ;;
|
fbfhu epkplj;jpw;F chpa>
fhy;FNyl;lh; epkplk;;
|
|||||||||||
|
fep
|
fhep
|
fep
|
fhep
|
fep
|
fhep
|
fep
|
fhep
|
fep
|
fhep
|
fep
|
fhep
|
|
1
|
02
|
11
|
18
|
21
|
35
|
31
|
52
|
41
|
68
|
51
|
85
|
|
2
|
03
|
12
|
20
|
22
|
37
|
32
|
53
|
42
|
70
|
52
|
87
|
|
3
|
05
|
13
|
22
|
23
|
38
|
33
|
55
|
43
|
72
|
53
|
88
|
|
4
|
07
|
14
|
23
|
24
|
40
|
34
|
57
|
44
|
73
|
54
|
90
|
|
5
|
08
|
15
|
25
|
25
|
42
|
35
|
58
|
45
|
75
|
55
|
92
|
|
6
|
10
|
16
|
27
|
26
|
43
|
36
|
60
|
46
|
77
|
56
|
93
|
|
7
|
12
|
17
|
28
|
27
|
45
|
37
|
62
|
47
|
78
|
57
|
95
|
|
8
|
13
|
18
|
30
|
28
|
47
|
38
|
63
|
48
|
80
|
58
|
97
|
|
9
|
15
|
19
|
32
|
29
|
48
|
39
|
65
|
49
|
82
|
59
|
98
|
|
10
|
17
|
20
|
33
|
30
|
50
|
40
|
67
|
50
|
83
|
60
|
100
|
f.ep. fbfhu epkplk;.
---------------------- fh.ep. fhy;FNyl;lu; epkplk;.
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