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¥ÀæAiÀÄvÀß
§¸ÀªÀgÁd.n.JA
PÀ£ÀßqÀ ¨sÁµÁ ²PÀëPÀgÀÄ
¸ÀPÁðj ¥ËæqsÀ±Á¯É, gÀÆ¥À£ÀUÀÄr
§¼Áîj ¥ÀƪÀð ªÀ®AiÀÄ
Basava.vesha@gmail.com 1
GHS Roopanagudi ,ballari east TMBK
¸ÀA¢üUÀ¼ÀÄ
JgÀqÀÄ CPÀëgÀUÀ¼ÀÄ ¥ÀgÀ¸ÀàgÀ PÁ® «¼ÀA§«®èzÉ PÀÆrPÉƼÀÄîªÀÅzÀÄ ‘¸ÀA¢ü’JAzÀÄ CxÀð
JgÀqÀÄ ªÀtðUÀ¼ÀÄ (CPÀëgÀUÀ¼ÀÄ) PÁ®«¼ÀA§«®èzÀAvÉ ¸ÉÃgÀĪÀÅzÉà ¸ÀA¢ü0iÉĤ¸ÀĪÀÅzÀÄ.
* ¸ÀégÀzÀ ªÀÄÄAzÉ ¸ÀégÀ §AzÀÄ »ÃUÉ ¸ÀA¢ü0iÀiÁzÀgÉ ¸ÀégÀ¸ÀA¢ü J£ÀÄßvÉÛêÉ.
* ¸ÀégÀzÀ ªÀÄÄAzÉ ªÀåAd£À §AzÀÄ CxÀªÁ ªÀåAd£ÀzÀ ªÀÄÄAzÉ ªÀåAd£À §AzÀÄ
¸ÀA¢ü0iÀiÁzÀgÉ ªÀåAd£À¸ÀA¢ü J£ÀÄßvÉÛêÉ.
PÀ£ÀßqÀ ¸ÀA¢üUÀ¼ÀÄ
1. ¯ÉÆÃ¥À¸ÀA¢ü
JgÀqÀÄ ¥ÀzÀUÀ¼À£ÀÄß PÀÆr¸ÀĪÁUÀ ¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀzÀ°è£À ¸ÀégÀªÀÅ ¯ÉÆÃ¥ÀªÁUÀĪÀÅzÀÄ
¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀPÉÌ GvÀÛgÀ ¥ÀzÀzÀ D¢AiÀÄ°è£À ¸ÀégÀ ¸ÉÃjPÉƼÀÄîªÀÅzÀÄ
(¸ÀégÀzÀ ªÀÄÄAzÉ ¸ÀégÀªÀÅ §AzÀÄ ¸ÀA¢ü0iÀiÁUÀĪÁUÀ ¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀzÀ°è£À ¸ÀégÀªÀÅ
¯ÉÆÃ¥ÀªÁUÀĪÀÅzÀÄ ¯ÉÆÃ¥À¸ÀA¢ü (CxÀðªÀÅ PÉqÀ¢zÀÝ ¥ÀPÀëzÀ°è ªÀiÁvÀæ ¯ÉÆÃ¥ÀªÁUÀĪÀÅzÀÄ) )
GzÁºÀgÀuÉUÉ:-
HgÀÄ + C°è = HgÀ°è
(G + C) (GPÁgÀ ¯ÉÆÃ¥À)
¥ÀƪÀð¥ÀzÀzÀ CAvÀåzÀPÀëgÀ “gÀÄ” F CPÀëgÀzÀ CAvÀåzÀ°ègÀĪÀ “G” ¸ÀégÀ ¯ÉÆÃ¥À DV GvÀÛgÀ
¥ÀzÀzÀ D¢ ¸ÀégÀ “C” ¸ÉÃjPÉÆAqÀÄ “ gÀ ” DVzÉ
¯ÉÆÃ¥À ¸ÀA¢ü
HgÀÆgÀÄ ¸ÀA¥À£ÀßgÁzÀ ¥ÀƼÀÝqÉ
§¯Éè£ÉAzÀÄ DzÀ£ÉA§ vÉgÉ¢PÀÄ̪À
Basava.vesha@gmail.com 2
GHS Roopanagudi ,ballari east TMBK
ªÀiÁvÀAvÀÄ £ÉvÀÛgÉÆAzÉ ªÀÄ£ÀzÉƼÀUÉ
PÁt¯ÁUÀzÀÄ vÀ¥Àà°ÃAiÀÄzÉ EgÀļÀ½zÀÄ
ZÀj¸ÀÄvÀzÀégÀzÀ ¯ÉÃR£ÀªÀ£ÉÆâ vÉUÉzÀÄvÀÛjÃAiÀĪÀÄA
¨ÉÃqÀ¨ÉÃqÀgÀ¸ÀÄUÀ¼À ¤AwzÀð£ÀÄ fêÀvÉvÀÛªÀgÀÄ
HgÀÄ+HgÀÄ , ¸ÀA¥À£ÀßgÀÄ+DzÀ , ¥ÀƼÀÄÝ+JqÉ , §¯Éè£ÀÄ+JAzÀÄ ,DzÀ£ÀÄ+JA§
vÉgÉzÀÄ+EPÀÄ̪À , ªÀiÁvÀÄ+CAvÀÄ , £ÉvÀÛgÀÄ+ MAzÉ , ªÀÄ£ÀzÀ+ M¼ÀUÉ
PÁt®Ä+DUÀzÀÄ ,vÀ¥Àà®Ä+FAiÀÄzÉ ,EgÀļÀÄ+C½zÀÄ ,ZÀj¸ÀÄvÀ+CzÀégÀzÀ,
¯ÉÃR£ÀªÀ£ÀÄ+N¢ , vÉUÉzÀÄ+GvÀÛjÃAiÀĪÀÄA ,¨ÉÃqÀ¨ÉÃqÀ+CgÀ¸ÀÄUÀ¼À ,¤AvÀÄ+EzÀð£ÀÄ
fêÀvÉvÀÛ+CªÀgÀÄ
2. DUÀªÀÄ ¸ÀA¢ü
JgÀqÀÄ ¥ÀzÀUÀ¼À£ÀÄß PÀÆr¸ÀĪÁUÀ ¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀzÀ°è£À ¸ÀégÀªÀÅ ¯ÉÆÃ¥ÀªÁV
¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀPÉÌ GvÀÛgÀ ¥ÀzÀzÀ D¢AiÀÄ°è£À ¸ÀégÀ ¸ÉÃjPÉÆAqÁUÀ CxÀðªÀÅ PÉqÀĪÀAwzÀÝ°è
0iÀÄPÁgÀªÀ£ÉÆßà CxÀªÁ ªÀPÁgÀªÀ£ÉÆßà ºÉƸÀzÁV ¸ÉÃj¹PÉƼÀî¨ÉÃPÀÄ.
(¸ÀégÀzÀ ªÀÄÄAzÉ ¸ÀégÀªÀÅ §AzÁUÀ ¯ÉÆÃ¥À¸ÀA¢ü ªÀiÁrzÀgÉ CxÀðªÀÅ PÉqÀĪÀAwzÀÝ°è D JgÀqÀÄ
¸ÀégÀUÀ¼À ªÀÄzsÀåzÀ°è 0iÀÄPÁgÀªÀ£ÉÆßà CxÀªÁ ªÀPÁgÀªÀ£ÉÆßà ºÉƸÀzÁV ¸ÉÃj¹ ºÉüÀÄvÉÛêÉ. EzÀPÉÌ
‘DUÀªÀÄ ¸ÀA¢ü’ J£ÀÄߪÀgÀÄ)
DUÀªÀÄ ¸ÀA¢ü
PÉÊAiÀÄ£ÀÄß ªÀÄgÀªÀ£ÀÄß
ªÀļɬÄAzÀ ªÀÄUÀÄ«UÉ
±Á¯ÉAiÀÄ°è ªÀÄ£ÉAiÉƼÀUÉ
Basava.vesha@gmail.com 3
GHS Roopanagudi ,ballari east TMBK
¨sÉÃzÀ«®è PÉÊ«rzÀÄ
ªÀÈ¢ÞAiÀiÁV ¨sÉÃzÀªÁV
±ÀªÀªÁzÀªÀÅ
PÉÊ + C£ÀÄß , ªÀÄgÀ+ C£ÀÄß , ªÀļÉ+EAzÀ , ªÀÄUÀÄ+EUÉ , ±Á¯É+C°è ,
ªÀÄ£É+M¼ÀUÉ ,¨sÉÃzÀ+E®è ,PÉÊ+ErzÀÄ ,ªÀÈ¢Þ+DV ,¨sÉÃzÀ+DV ,±ÀªÀ+DzÀªÀÅ
PÉÊ + C£ÀÄß = PÉÊ + 0iÀiï + C£ÀÄß = PÉÊ0iÀÄ£ÀÄß ,
(PÉÊ+C£ÀÄß PÀÆr¹UÁUÀ PÉÊ£ÀÄß DUÀÄvÀÛzÉ. DzÀgÉ EzÀgÀ CxÀð PÉqÀÄvÀÛzÉ. ºÁUÉ ªÀiÁqÀzÉ “AiÀiï ”
CPÀëgÀªÀ£ÀÄß ºÉƸÀzÁV ¸ÉÃj¸À¨ÉÃPÀÄ.)
ªÀÄ¼É + EAzÀ = ªÀÄ¼É + 0iÀiï + EAzÀ = ªÀļɬÄAzÀ
ªÀÄUÀÄ + EUÉ = ªÀÄUÀÄ + ªï + EUÉ = ªÀÄUÀÄ«UÉ
3. DzÉñÀ ¸ÀA¢ü
¸ÀA¢ü0iÀiÁUÀĪÁUÀ MAzÀÄ CPÀëgÀzÀ ¸ÁÜ£ÀzÀ°è (¸ÀܼÀzÀ°è) ¨ÉÃgÉÆAzÀÄ CPÀëgÀªÀÅ §gÀĪÀÅzÉÃ
DzÉñÀ ¸ÀA¢ü0iÉĤ¸ÀĪÀÅzÀÄ.
(¸ÁªÀiÁ£ÀåªÁV GvÀÛgÀ¥ÀzÀzÀ D¢0iÀÄ°ègÀĪÀ PÀ vÀ ¥À ªÀåAd£ÀUÀ½UÉ PÀæªÀĪÁV UÀ zÀ §
ªÀåAd£ÀUÀ¼ÀÄ DzÉñÀªÁV §gÀÄvÀÛªÉ. PÉ®ªÉÇAzÀÄ ¸À® `¥À § ªÀÄ ’ UÀ½UÉ `ªÀ ’ PÁgÀ
DzÉñÀªÁUÀÄvÀÛzÉ. ¸À PÁgÀPÉÌ ZÀ d bÀ UÀ¼ÀÄ DzÉñÀªÁUÀÄvÀÛªÉ.)
DzÉñÀ ¸ÀA¢ü
ªÀļÉUÁ® PÀqÀĪɼÀÄÛ zsÀÈwUÉlÄÖ
ªÉÄÊzÉÆÃgÀÄ ªÉįÁévÀÄ ¥ÉÆÃUÀ¯ÉéüÀÄÌA
Basava.vesha@gmail.com 4
GHS Roopanagudi ,ballari east TMBK
¨ÉA§vÀÄÛ ºÉƸÀUÁ® PÉÊ«rzÀÄ
PÀAUÉlÄÖ PÀA§¤ ªÉÄÊzÉƼÉ
EAZÀgÀ ¨ÉªÀĪÀ𤠨ÉlÖzÁªÀgÉ
ªÀÄ¼É + PÁ® , PÀqÀÄ+¥É¼ÀÄÛ , zsÀÈw+PÉlÄÖ , ªÉÄÊ+vÉÆÃgÀÄ , ªÉÄïï+ªÀiÁvÀÄ ,
¥ÉÆÃUÀ¯ï+¥ÉüÀÄÌA , ¨É£ï+¥ÀvÀÄÛ .ºÉƸÀ+PÁ® PÉÊ+»rzÀÄ , PÀuï + PÉlÄÖ , PÀuï + ¥À¤
ªÉÄÊ+vÉÆ¼É ,E£ï+¸ÀgÀ , ¨ÉªÀÄgï + ¥À¤ , ¨ÉlÖzÀ+vÁªÀgÉ
¸ÀA¸ÀÌöÈvÀ ¸ÀA¢üUÀ¼ÀÄ
¸ÀA¸ÀÌöÈvÀ ¸ÀégÀ ¸ÀA¢üUÀ¼ÀÄ
JgÀqÀÄ ¸ÀA¸ÀÌöÈvÀ ±À§ÝUÀ¼ÀÄ ¸ÉÃj ¸ÀA¢ü0iÀiÁzÀgÉ ¸ÀA¸ÀÌöÈvÀ ¸ÀA¢ü DUÀÄvÀÛzÉ.
MAzÀÄ ¸ÀA¸ÀÌöÈvÀ ±À§ÝªÀÅ PÀ£ÀßqÀ ±À§ÝzÉÆqÀ£É ¸ÉÃj ¸ÀA¢ü0iÀiÁzÀgÉ PÀ£ÀßqÀ ¸ÀA¢ DUÀÄvÀÛzÉ.
¸ÀA¸ÀÌöÈvÀzÀ°è ¸ÀégÀPÉÌ ¸ÀégÀ ¥ÀgÀªÁzÁUÀ ¸ÀégÀ¸ÀA¢üUÀ¼ÁUÀÄvÀÛªÉ.
ªÀåAd£ÀPÉÌ ªÀåAd£À ¥ÀgÀªÁzÁUÀ ªÀåAd£À ¸ÀA¢üUÀ¼ÁUÀÄvÀÛªÉ.
1. ¸ÀªÀtð ¢ÃWÀð ¸ÀA¢ü
¸ÀªÀtð¸ÀégÀUÀ¼ÀÄ(CD,EF,GHIÄIÄ)MAzÀgÀªÀÄÄAzɪÀÄvÉÆÛAzÀÄ(C+C,C+D,C+C..E+E)
§AzÁUÀ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è MAzÉà ¢ÃWÀð¸ÀégÀªÀÅ(D,F,H) DzÉñÀªÁV §gÀĪÀÅzÀÄ ¸ÀªÀtð
¢ÃWÀð¸ÀA¢ü.
«zÁå + C¨sÁå¸À = «zÁå¨sÁå¸À
(D + C) = D
E°è ‘D’ JA§ ¸ÀégÀzÀ ªÀÄÄAzÉ ‘C’ JA§ ¸ÀégÀ §A¢zÉ. F JgÀqÀÆ ¸ÀégÀUÀ¼ÀÄ
¸ÀªÀtð¸ÀégÀUÀ¼ÀÄ EªÀÅ »ÃUÉ MAzÀgÀ ªÀÄÄAzÉ MAzÀÄ §A¢ªÉ. CªÉgÀqÀÆ ºÉÆÃV CªÀÅUÀ¼À
¸ÁÜ£ÀzÀ°è CzÉà ¸ÀªÀtðUÀ¼À MAzÀÄ ¢ÃWÀð¸ÀégÀªÀÅ §A¢zÉ.
GzÁºÀgÀuÉUÉ:-
Basava.vesha@gmail.com 5
GHS Roopanagudi ,ballari east TMBK
¸ÀªÀtð ¢ÃWÀð ¸ÀA¢ü
ªÀĺÁvÀä ªÀzsÀÆ¥ÉÃvÀ ¸ÀPÀ¼ÁZÁAiÀÄð
VjñÀ ¤eÁ±ÀæªÀÄ ZÀAzÁæPÀð
¸ÀÄgÁ¸ÀÄgÀ f£Á®AiÀÄ ®QëñÀ
PÁzÁlzÁl
ªÀĺÁ + DvÁä , ªÀzsÀÆ+G¥ÉÃvÀ , ¸ÀPÀ¼À+DZÁAiÀÄð ,Vj+F±À ,¤d+D±ÀæªÀÄ
ZÀAzÀæ+CPÀð ,¸ÀÄgÀ + C¸ÀÄgÀ ,f£À+D®AiÀÄ ,®Qëöä+F±À , PÁzÁlzÀ+Dl
(2) UÀÄt¸ÀA¢ü
C D PÁgÀUÀ½UÉ E F PÁgÀUÀ¼ÀÄ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘K’ PÁgÀªÀÇ, G H
PÁgÀUÀ¼ÀÄ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘N’ PÁgÀªÀÇ, IÄ PÁgÀ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è
‘Cgï’ PÁgÀªÀÇ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. EzÀPÉÌ ‘UÀÄt¸ÀA¢ü’ JAzÀÄ ºÉ¸ÀgÀÄ.
UÀÄt ¸ÀA¢ü
zÉêÉÃAzÀæ ªÀĺÀ¶ð ªÀÄAqÀ¼ÉñÀégÀ
eÁÕ£ÉñÀégÀ ªÀĺÉñÀ ¸ÀÆgÉÆåÃzÀAiÀÄ
PÀ¯ÉÆÃ¥Á¸ÀPÀ
zÉêÀ + EAzÀæ , ªÀĺÁ + IĶ , ªÀÄAqÀ¼À + F±ÀégÀ ,eÁÕ£À+F±ÀégÀ, ªÀĺÁ + F±À
¸ÀÆgÀå + GzÀ0iÀÄ , PÀ¯Á+G¥Á¸ÀPÀ
Basava.vesha@gmail.com 6
GHS Roopanagudi ,ballari east TMBK
(3) ªÀÈ¢Þ ¸ÀA¢ü
C D PÁgÀUÀ½UÉ K L PÁgÀUÀ¼ÀÄ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘L’ PÁgÀªÀÇ, N O
PÁgÀUÀ¼ÀÄ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘O’ PÁgÀªÀÇ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. EzÀPÉÌ ‘ªÀÈ¢Þ¸ÀA¢ü’
J£ÀÄߪÀgÀÄ.
ªÀÈ¢Þ ¸ÀA¢ü
KPÉÊPÀ
d£ÉÊPÀå
ªÀ£ËµÀ¢ü
CµÉÖöʱÀégÀå
KPÀ + KPÀ ,CµÀÖ + L±ÀégÀå ,ªÀ£À + OµÀzsÀ , d£À + LPÀå
(4) 0iÀÄuï ¸ÀA¢ü
E, F, G, H, IÄ PÁgÀUÀ½UÉ ¸ÀªÀtðªÀ®èzÀ ¸ÀégÀ ¥ÀgÀªÁzÀgÉ E F PÁgÀUÀ½UÉ ‘0iÀiï’
PÁgÀªÀÇ, G H PÁgÀUÀ½UÉ ‘ªï’ PÁgÀªÀÇ, IÄ PÁgÀPÉÌ ‘gï’ (gÉÃ¥sÀ)ªÀÇ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ.
EzÀPÉÌ 0iÀÄuï ¸ÀA¢ü0iÉÄAzÀÄ ºÉ¸ÀgÀÄ.
AiÀÄuï ¸ÀA¢ü
CvÀåªÀ¸ÀgÀ
eÁvÀåwÃvÀ
Basava.vesha@gmail.com 7
GHS Roopanagudi ,ballari east TMBK
PÉÆÃmÁå¢üñÀégÀ
PÉÆÃmÁå£ÀÄPÉÆÃn
Cw + CªÀ¸ÀgÀ ,eÁw + CwÃvÀ, PÉÆÃn + C¢üñÀégÀ ,PÉÆÃn+ C£ÀÄPÉÆÃn
¸ÀA¸ÀÌöÈvÀ ªÀåAd£À ¸ÀA¢üUÀ¼ÀÄ
(1) d±ÀÛ÷é¸ÀA¢ü
¥ÀǪÀð±À§ÝzÀ PÉÆ£É0iÀÄ°ègÀĪÀ PÀZÀlvÀ¥À ªÀåAd£ÀUÀ½UÉ 0iÀiÁªÀ ªÀtð ¥ÀgÀªÁzÀgÀÆ ¥Áæ0iÀıÀB
CzÉà ªÀUÀðzÀ ªÀÄÆgÀ£É0iÀÄ ªÀåAd£ÁPÀëgÀUÀ¼ÀÄ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. EzÀPÉÌ d±ÀÛ÷é¸ÀA¢ü0iÉÄ£ÀÄߪÀgÀÄ.
d±ÀÛ÷é ¸ÀA¢ü
ªÁUÉÝë
CdAvÀ
µÀqÁ£À£À
¢UÀAvÀ
C©Þ
ªÁPï+zÉë, CZï + CAvÀ , µÀmï+ D£À£À¢Pï + CAvÀ , C¥ï + ¢ü
Basava.vesha@gmail.com 8
GHS Roopanagudi ,ballari east TMBK
(2) ±ÀÄÑvÀé ¸ÀA¢ü
¸ÀPÁgÀ,vÀªÀUÁðPÀëgÀUÀ½UÉ ±ÀPÁgÀ ZÀªÀUÁðPÀëgÀUÀ¼ÀÄ ¥ÀgÀªÁzÁUÀ ¸ÀPÁgÀPÉÌ ±ÀPÁgÀªÀÇ, vÀªÀUÀðPÉÌ
ZÀªÀUÀðªÀÇ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ.
‘±ÀÄÑ’ JAzÀgÉ ±ÀPÁgÀ ZÀªÀUÁðPÀëgÀUÀ¼ÀÄ. (±ï=±ÀPÁgÀ, ZÀÄ=ZÀ bÀ d gÀhÄ k) EªÀÅUÀ¼ÀÄ DzÉñÀªÁV
§gÀĪÀÅzÉà ±ÀÄÑvÀé¸ÀA¢ü J¤¸ÀĪÀÅzÀÄ.
±ÀÄÑvÀé ¸ÀA¢ü
±ÀgÀZÀÑAzÀæ
dUÀeÉÆåÃw
¥ÀAiÀıÀåAiÀÄ£À
±ÀgÀvï + ZÀAzÀæ dUÀvï + eÉÆåÃw ¥À0iÀĸï + ±À0iÀÄ£À
(3) C£ÀÄ£Á¹PÀ ¸ÀA¢ü
ªÀUÀð ¥ÀæxÀªÀÄ ªÀtðUÀ½UÉ 0iÀiÁªÀ C£ÀÄ£Á¹PÁPÀëgÀ ¥ÀgÀªÁzÀgÀÆ, CªÀÅUÀ½UÉ CAzÀgÉ PÀ ZÀ l vÀ
¥À ªÀåAd£ÀUÀ½UÉ PÀæªÀĪÁV Y k t £À ªÀÄ ªÀåAd£ÀUÀ¼ÀÄ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ.
C£ÀÄ£Á¹PÀ
µÀtÄäR
¸À£ÁߣÀ
Basava.vesha@gmail.com 9
GHS Roopanagudi ,ballari east TMBK
ªÁYäAiÀÄ
G£ÁäzÀ
vˣˊAiˀ
²æêÀÄ£ÀäºÁ
µÀmï+ ªÀÄÄR , ¸Àvï + ªÀiÁ£À ªÁPï + ªÀÄ0iÀÄ , Gvï+ªÀiÁzÀ, vÀvï+ªÀÄAiÀÄ ,
²æêÀÄvï+ªÀĺÁ
±ÀĨsÀªÁUÀ°
Basava.vesha@gmail.com 10
GHS Roopanagudi ,ballari east TMBK

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Sandhigalu

  • 2. ¸ÀA¢üUÀ¼ÀÄ JgÀqÀÄ CPÀëgÀUÀ¼ÀÄ ¥ÀgÀ¸ÀàgÀ PÁ® «¼ÀA§«®èzÉ PÀÆrPÉƼÀÄîªÀÅzÀÄ ‘¸ÀA¢ü’JAzÀÄ CxÀð JgÀqÀÄ ªÀtðUÀ¼ÀÄ (CPÀëgÀUÀ¼ÀÄ) PÁ®«¼ÀA§«®èzÀAvÉ ¸ÉÃgÀĪÀÅzÉà ¸ÀA¢ü0iÉĤ¸ÀĪÀÅzÀÄ. * ¸ÀégÀzÀ ªÀÄÄAzÉ ¸ÀégÀ §AzÀÄ »ÃUÉ ¸ÀA¢ü0iÀiÁzÀgÉ ¸ÀégÀ¸ÀA¢ü J£ÀÄßvÉÛêÉ. * ¸ÀégÀzÀ ªÀÄÄAzÉ ªÀåAd£À §AzÀÄ CxÀªÁ ªÀåAd£ÀzÀ ªÀÄÄAzÉ ªÀåAd£À §AzÀÄ ¸ÀA¢ü0iÀiÁzÀgÉ ªÀåAd£À¸ÀA¢ü J£ÀÄßvÉÛêÉ. PÀ£ÀßqÀ ¸ÀA¢üUÀ¼ÀÄ 1. ¯ÉÆÃ¥À¸ÀA¢ü JgÀqÀÄ ¥ÀzÀUÀ¼À£ÀÄß PÀÆr¸ÀĪÁUÀ ¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀzÀ°è£À ¸ÀégÀªÀÅ ¯ÉÆÃ¥ÀªÁUÀĪÀÅzÀÄ ¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀPÉÌ GvÀÛgÀ ¥ÀzÀzÀ D¢AiÀÄ°è£À ¸ÀégÀ ¸ÉÃjPÉƼÀÄîªÀÅzÀÄ (¸ÀégÀzÀ ªÀÄÄAzÉ ¸ÀégÀªÀÅ §AzÀÄ ¸ÀA¢ü0iÀiÁUÀĪÁUÀ ¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀzÀ°è£À ¸ÀégÀªÀÅ ¯ÉÆÃ¥ÀªÁUÀĪÀÅzÀÄ ¯ÉÆÃ¥À¸ÀA¢ü (CxÀðªÀÅ PÉqÀ¢zÀÝ ¥ÀPÀëzÀ°è ªÀiÁvÀæ ¯ÉÆÃ¥ÀªÁUÀĪÀÅzÀÄ) ) GzÁºÀgÀuÉUÉ:- HgÀÄ + C°è = HgÀ°è (G + C) (GPÁgÀ ¯ÉÆÃ¥À) ¥ÀƪÀð¥ÀzÀzÀ CAvÀåzÀPÀëgÀ “gÀÄ” F CPÀëgÀzÀ CAvÀåzÀ°ègÀĪÀ “G” ¸ÀégÀ ¯ÉÆÃ¥À DV GvÀÛgÀ ¥ÀzÀzÀ D¢ ¸ÀégÀ “C” ¸ÉÃjPÉÆAqÀÄ “ gÀ ” DVzÉ ¯ÉÆÃ¥À ¸ÀA¢ü HgÀÆgÀÄ ¸ÀA¥À£ÀßgÁzÀ ¥ÀƼÀÝqÉ §¯Éè£ÉAzÀÄ DzÀ£ÉA§ vÉgÉ¢PÀÄ̪À Basava.vesha@gmail.com 2 GHS Roopanagudi ,ballari east TMBK
  • 3. ªÀiÁvÀAvÀÄ £ÉvÀÛgÉÆAzÉ ªÀÄ£ÀzÉƼÀUÉ PÁt¯ÁUÀzÀÄ vÀ¥Àà°ÃAiÀÄzÉ EgÀļÀ½zÀÄ ZÀj¸ÀÄvÀzÀégÀzÀ ¯ÉÃR£ÀªÀ£ÉÆâ vÉUÉzÀÄvÀÛjÃAiÀĪÀÄA ¨ÉÃqÀ¨ÉÃqÀgÀ¸ÀÄUÀ¼À ¤AwzÀð£ÀÄ fêÀvÉvÀÛªÀgÀÄ HgÀÄ+HgÀÄ , ¸ÀA¥À£ÀßgÀÄ+DzÀ , ¥ÀƼÀÄÝ+JqÉ , §¯Éè£ÀÄ+JAzÀÄ ,DzÀ£ÀÄ+JA§ vÉgÉzÀÄ+EPÀÄ̪À , ªÀiÁvÀÄ+CAvÀÄ , £ÉvÀÛgÀÄ+ MAzÉ , ªÀÄ£ÀzÀ+ M¼ÀUÉ PÁt®Ä+DUÀzÀÄ ,vÀ¥Àà®Ä+FAiÀÄzÉ ,EgÀļÀÄ+C½zÀÄ ,ZÀj¸ÀÄvÀ+CzÀégÀzÀ, ¯ÉÃR£ÀªÀ£ÀÄ+N¢ , vÉUÉzÀÄ+GvÀÛjÃAiÀĪÀÄA ,¨ÉÃqÀ¨ÉÃqÀ+CgÀ¸ÀÄUÀ¼À ,¤AvÀÄ+EzÀð£ÀÄ fêÀvÉvÀÛ+CªÀgÀÄ 2. DUÀªÀÄ ¸ÀA¢ü JgÀqÀÄ ¥ÀzÀUÀ¼À£ÀÄß PÀÆr¸ÀĪÁUÀ ¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀzÀ°è£À ¸ÀégÀªÀÅ ¯ÉÆÃ¥ÀªÁV ¥ÀǪÀð ¥ÀzÀzÀ CAvÀåPÀëgÀPÉÌ GvÀÛgÀ ¥ÀzÀzÀ D¢AiÀÄ°è£À ¸ÀégÀ ¸ÉÃjPÉÆAqÁUÀ CxÀðªÀÅ PÉqÀĪÀAwzÀÝ°è 0iÀÄPÁgÀªÀ£ÉÆßà CxÀªÁ ªÀPÁgÀªÀ£ÉÆßà ºÉƸÀzÁV ¸ÉÃj¹PÉƼÀî¨ÉÃPÀÄ. (¸ÀégÀzÀ ªÀÄÄAzÉ ¸ÀégÀªÀÅ §AzÁUÀ ¯ÉÆÃ¥À¸ÀA¢ü ªÀiÁrzÀgÉ CxÀðªÀÅ PÉqÀĪÀAwzÀÝ°è D JgÀqÀÄ ¸ÀégÀUÀ¼À ªÀÄzsÀåzÀ°è 0iÀÄPÁgÀªÀ£ÉÆßà CxÀªÁ ªÀPÁgÀªÀ£ÉÆßà ºÉƸÀzÁV ¸ÉÃj¹ ºÉüÀÄvÉÛêÉ. EzÀPÉÌ ‘DUÀªÀÄ ¸ÀA¢ü’ J£ÀÄߪÀgÀÄ) DUÀªÀÄ ¸ÀA¢ü PÉÊAiÀÄ£ÀÄß ªÀÄgÀªÀ£ÀÄß ªÀļɬÄAzÀ ªÀÄUÀÄ«UÉ ±Á¯ÉAiÀÄ°è ªÀÄ£ÉAiÉƼÀUÉ Basava.vesha@gmail.com 3 GHS Roopanagudi ,ballari east TMBK
  • 4. ¨sÉÃzÀ«®è PÉÊ«rzÀÄ ªÀÈ¢ÞAiÀiÁV ¨sÉÃzÀªÁV ±ÀªÀªÁzÀªÀÅ PÉÊ + C£ÀÄß , ªÀÄgÀ+ C£ÀÄß , ªÀļÉ+EAzÀ , ªÀÄUÀÄ+EUÉ , ±Á¯É+C°è , ªÀÄ£É+M¼ÀUÉ ,¨sÉÃzÀ+E®è ,PÉÊ+ErzÀÄ ,ªÀÈ¢Þ+DV ,¨sÉÃzÀ+DV ,±ÀªÀ+DzÀªÀÅ PÉÊ + C£ÀÄß = PÉÊ + 0iÀiï + C£ÀÄß = PÉÊ0iÀÄ£ÀÄß , (PÉÊ+C£ÀÄß PÀÆr¹UÁUÀ PÉÊ£ÀÄß DUÀÄvÀÛzÉ. DzÀgÉ EzÀgÀ CxÀð PÉqÀÄvÀÛzÉ. ºÁUÉ ªÀiÁqÀzÉ “AiÀiï ” CPÀëgÀªÀ£ÀÄß ºÉƸÀzÁV ¸ÉÃj¸À¨ÉÃPÀÄ.) ªÀÄ¼É + EAzÀ = ªÀÄ¼É + 0iÀiï + EAzÀ = ªÀļɬÄAzÀ ªÀÄUÀÄ + EUÉ = ªÀÄUÀÄ + ªï + EUÉ = ªÀÄUÀÄ«UÉ 3. DzÉñÀ ¸ÀA¢ü ¸ÀA¢ü0iÀiÁUÀĪÁUÀ MAzÀÄ CPÀëgÀzÀ ¸ÁÜ£ÀzÀ°è (¸ÀܼÀzÀ°è) ¨ÉÃgÉÆAzÀÄ CPÀëgÀªÀÅ §gÀĪÀÅzÉà DzÉñÀ ¸ÀA¢ü0iÉĤ¸ÀĪÀÅzÀÄ. (¸ÁªÀiÁ£ÀåªÁV GvÀÛgÀ¥ÀzÀzÀ D¢0iÀÄ°ègÀĪÀ PÀ vÀ ¥À ªÀåAd£ÀUÀ½UÉ PÀæªÀĪÁV UÀ zÀ § ªÀåAd£ÀUÀ¼ÀÄ DzÉñÀªÁV §gÀÄvÀÛªÉ. PÉ®ªÉÇAzÀÄ ¸À® `¥À § ªÀÄ ’ UÀ½UÉ `ªÀ ’ PÁgÀ DzÉñÀªÁUÀÄvÀÛzÉ. ¸À PÁgÀPÉÌ ZÀ d bÀ UÀ¼ÀÄ DzÉñÀªÁUÀÄvÀÛªÉ.) DzÉñÀ ¸ÀA¢ü ªÀļÉUÁ® PÀqÀĪɼÀÄÛ zsÀÈwUÉlÄÖ ªÉÄÊzÉÆÃgÀÄ ªÉįÁévÀÄ ¥ÉÆÃUÀ¯ÉéüÀÄÌA Basava.vesha@gmail.com 4 GHS Roopanagudi ,ballari east TMBK
  • 5. ¨ÉA§vÀÄÛ ºÉƸÀUÁ® PÉÊ«rzÀÄ PÀAUÉlÄÖ PÀA§¤ ªÉÄÊzÉÆ¼É EAZÀgÀ ¨ÉªÀĪÀ𤠨ÉlÖzÁªÀgÉ ªÀÄ¼É + PÁ® , PÀqÀÄ+¥É¼ÀÄÛ , zsÀÈw+PÉlÄÖ , ªÉÄÊ+vÉÆÃgÀÄ , ªÉÄïï+ªÀiÁvÀÄ , ¥ÉÆÃUÀ¯ï+¥ÉüÀÄÌA , ¨É£ï+¥ÀvÀÄÛ .ºÉƸÀ+PÁ® PÉÊ+»rzÀÄ , PÀuï + PÉlÄÖ , PÀuï + ¥À¤ ªÉÄÊ+vÉÆ¼É ,E£ï+¸ÀgÀ , ¨ÉªÀÄgï + ¥À¤ , ¨ÉlÖzÀ+vÁªÀgÉ ¸ÀA¸ÀÌöÈvÀ ¸ÀA¢üUÀ¼ÀÄ ¸ÀA¸ÀÌöÈvÀ ¸ÀégÀ ¸ÀA¢üUÀ¼ÀÄ JgÀqÀÄ ¸ÀA¸ÀÌöÈvÀ ±À§ÝUÀ¼ÀÄ ¸ÉÃj ¸ÀA¢ü0iÀiÁzÀgÉ ¸ÀA¸ÀÌöÈvÀ ¸ÀA¢ü DUÀÄvÀÛzÉ. MAzÀÄ ¸ÀA¸ÀÌöÈvÀ ±À§ÝªÀÅ PÀ£ÀßqÀ ±À§ÝzÉÆqÀ£É ¸ÉÃj ¸ÀA¢ü0iÀiÁzÀgÉ PÀ£ÀßqÀ ¸ÀA¢ DUÀÄvÀÛzÉ. ¸ÀA¸ÀÌöÈvÀzÀ°è ¸ÀégÀPÉÌ ¸ÀégÀ ¥ÀgÀªÁzÁUÀ ¸ÀégÀ¸ÀA¢üUÀ¼ÁUÀÄvÀÛªÉ. ªÀåAd£ÀPÉÌ ªÀåAd£À ¥ÀgÀªÁzÁUÀ ªÀåAd£À ¸ÀA¢üUÀ¼ÁUÀÄvÀÛªÉ. 1. ¸ÀªÀtð ¢ÃWÀð ¸ÀA¢ü ¸ÀªÀtð¸ÀégÀUÀ¼ÀÄ(CD,EF,GHIÄIÄ)MAzÀgÀªÀÄÄAzɪÀÄvÉÆÛAzÀÄ(C+C,C+D,C+C..E+E) §AzÁUÀ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è MAzÉà ¢ÃWÀð¸ÀégÀªÀÅ(D,F,H) DzÉñÀªÁV §gÀĪÀÅzÀÄ ¸ÀªÀtð ¢ÃWÀð¸ÀA¢ü. «zÁå + C¨sÁå¸À = «zÁå¨sÁå¸À (D + C) = D E°è ‘D’ JA§ ¸ÀégÀzÀ ªÀÄÄAzÉ ‘C’ JA§ ¸ÀégÀ §A¢zÉ. F JgÀqÀÆ ¸ÀégÀUÀ¼ÀÄ ¸ÀªÀtð¸ÀégÀUÀ¼ÀÄ EªÀÅ »ÃUÉ MAzÀgÀ ªÀÄÄAzÉ MAzÀÄ §A¢ªÉ. CªÉgÀqÀÆ ºÉÆÃV CªÀÅUÀ¼À ¸ÁÜ£ÀzÀ°è CzÉà ¸ÀªÀtðUÀ¼À MAzÀÄ ¢ÃWÀð¸ÀégÀªÀÅ §A¢zÉ. GzÁºÀgÀuÉUÉ:- Basava.vesha@gmail.com 5 GHS Roopanagudi ,ballari east TMBK
  • 6. ¸ÀªÀtð ¢ÃWÀð ¸ÀA¢ü ªÀĺÁvÀä ªÀzsÀÆ¥ÉÃvÀ ¸ÀPÀ¼ÁZÁAiÀÄð VjñÀ ¤eÁ±ÀæªÀÄ ZÀAzÁæPÀð ¸ÀÄgÁ¸ÀÄgÀ f£Á®AiÀÄ ®QëñÀ PÁzÁlzÁl ªÀĺÁ + DvÁä , ªÀzsÀÆ+G¥ÉÃvÀ , ¸ÀPÀ¼À+DZÁAiÀÄð ,Vj+F±À ,¤d+D±ÀæªÀÄ ZÀAzÀæ+CPÀð ,¸ÀÄgÀ + C¸ÀÄgÀ ,f£À+D®AiÀÄ ,®Qëöä+F±À , PÁzÁlzÀ+Dl (2) UÀÄt¸ÀA¢ü C D PÁgÀUÀ½UÉ E F PÁgÀUÀ¼ÀÄ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘K’ PÁgÀªÀÇ, G H PÁgÀUÀ¼ÀÄ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘N’ PÁgÀªÀÇ, IÄ PÁgÀ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘Cgï’ PÁgÀªÀÇ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. EzÀPÉÌ ‘UÀÄt¸ÀA¢ü’ JAzÀÄ ºÉ¸ÀgÀÄ. UÀÄt ¸ÀA¢ü zÉêÉÃAzÀæ ªÀĺÀ¶ð ªÀÄAqÀ¼ÉñÀégÀ eÁÕ£ÉñÀégÀ ªÀĺÉñÀ ¸ÀÆgÉÆåÃzÀAiÀÄ PÀ¯ÉÆÃ¥Á¸ÀPÀ zÉêÀ + EAzÀæ , ªÀĺÁ + IĶ , ªÀÄAqÀ¼À + F±ÀégÀ ,eÁÕ£À+F±ÀégÀ, ªÀĺÁ + F±À ¸ÀÆgÀå + GzÀ0iÀÄ , PÀ¯Á+G¥Á¸ÀPÀ Basava.vesha@gmail.com 6 GHS Roopanagudi ,ballari east TMBK
  • 7. (3) ªÀÈ¢Þ ¸ÀA¢ü C D PÁgÀUÀ½UÉ K L PÁgÀUÀ¼ÀÄ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘L’ PÁgÀªÀÇ, N O PÁgÀUÀ¼ÀÄ ¥ÀgÀªÁzÀgÉ CªÉgÀqÀgÀ ¸ÁÜ£ÀzÀ°è ‘O’ PÁgÀªÀÇ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. EzÀPÉÌ ‘ªÀÈ¢Þ¸ÀA¢ü’ J£ÀÄߪÀgÀÄ. ªÀÈ¢Þ ¸ÀA¢ü KPÉÊPÀ d£ÉÊPÀå ªÀ£ËµÀ¢ü CµÉÖöʱÀégÀå KPÀ + KPÀ ,CµÀÖ + L±ÀégÀå ,ªÀ£À + OµÀzsÀ , d£À + LPÀå (4) 0iÀÄuï ¸ÀA¢ü E, F, G, H, IÄ PÁgÀUÀ½UÉ ¸ÀªÀtðªÀ®èzÀ ¸ÀégÀ ¥ÀgÀªÁzÀgÉ E F PÁgÀUÀ½UÉ ‘0iÀiï’ PÁgÀªÀÇ, G H PÁgÀUÀ½UÉ ‘ªï’ PÁgÀªÀÇ, IÄ PÁgÀPÉÌ ‘gï’ (gÉÃ¥sÀ)ªÀÇ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. EzÀPÉÌ 0iÀÄuï ¸ÀA¢ü0iÉÄAzÀÄ ºÉ¸ÀgÀÄ. AiÀÄuï ¸ÀA¢ü CvÀåªÀ¸ÀgÀ eÁvÀåwÃvÀ Basava.vesha@gmail.com 7 GHS Roopanagudi ,ballari east TMBK
  • 8. PÉÆÃmÁå¢üñÀégÀ PÉÆÃmÁå£ÀÄPÉÆÃn Cw + CªÀ¸ÀgÀ ,eÁw + CwÃvÀ, PÉÆÃn + C¢üñÀégÀ ,PÉÆÃn+ C£ÀÄPÉÆÃn ¸ÀA¸ÀÌöÈvÀ ªÀåAd£À ¸ÀA¢üUÀ¼ÀÄ (1) d±ÀÛ÷é¸ÀA¢ü ¥ÀǪÀð±À§ÝzÀ PÉÆ£É0iÀÄ°ègÀĪÀ PÀZÀlvÀ¥À ªÀåAd£ÀUÀ½UÉ 0iÀiÁªÀ ªÀtð ¥ÀgÀªÁzÀgÀÆ ¥Áæ0iÀıÀB CzÉà ªÀUÀðzÀ ªÀÄÆgÀ£É0iÀÄ ªÀåAd£ÁPÀëgÀUÀ¼ÀÄ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. EzÀPÉÌ d±ÀÛ÷é¸ÀA¢ü0iÉÄ£ÀÄߪÀgÀÄ. d±ÀÛ÷é ¸ÀA¢ü ªÁUÉÝë CdAvÀ µÀqÁ£À£À ¢UÀAvÀ C©Þ ªÁPï+zÉë, CZï + CAvÀ , µÀmï+ D£À£À¢Pï + CAvÀ , C¥ï + ¢ü Basava.vesha@gmail.com 8 GHS Roopanagudi ,ballari east TMBK
  • 9. (2) ±ÀÄÑvÀé ¸ÀA¢ü ¸ÀPÁgÀ,vÀªÀUÁðPÀëgÀUÀ½UÉ ±ÀPÁgÀ ZÀªÀUÁðPÀëgÀUÀ¼ÀÄ ¥ÀgÀªÁzÁUÀ ¸ÀPÁgÀPÉÌ ±ÀPÁgÀªÀÇ, vÀªÀUÀðPÉÌ ZÀªÀUÀðªÀÇ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. ‘±ÀÄÑ’ JAzÀgÉ ±ÀPÁgÀ ZÀªÀUÁðPÀëgÀUÀ¼ÀÄ. (±ï=±ÀPÁgÀ, ZÀÄ=ZÀ bÀ d gÀhÄ k) EªÀÅUÀ¼ÀÄ DzÉñÀªÁV §gÀĪÀÅzÉà ±ÀÄÑvÀé¸ÀA¢ü J¤¸ÀĪÀÅzÀÄ. ±ÀÄÑvÀé ¸ÀA¢ü ±ÀgÀZÀÑAzÀæ dUÀeÉÆåÃw ¥ÀAiÀıÀåAiÀÄ£À ±ÀgÀvï + ZÀAzÀæ dUÀvï + eÉÆåÃw ¥À0iÀĸï + ±À0iÀÄ£À (3) C£ÀÄ£Á¹PÀ ¸ÀA¢ü ªÀUÀð ¥ÀæxÀªÀÄ ªÀtðUÀ½UÉ 0iÀiÁªÀ C£ÀÄ£Á¹PÁPÀëgÀ ¥ÀgÀªÁzÀgÀÆ, CªÀÅUÀ½UÉ CAzÀgÉ PÀ ZÀ l vÀ ¥À ªÀåAd£ÀUÀ½UÉ PÀæªÀĪÁV Y k t £À ªÀÄ ªÀåAd£ÀUÀ¼ÀÄ DzÉñÀUÀ¼ÁV §gÀÄvÀÛªÉ. C£ÀÄ£Á¹PÀ µÀtÄäR ¸À£ÁߣÀ Basava.vesha@gmail.com 9 GHS Roopanagudi ,ballari east TMBK
  • 10. ªÁYäAiÀÄ G£ÁäzÀ vÀ£ÀäAiÀÄ ²æêÀÄ£ÀäºÁ µÀmï+ ªÀÄÄR , ¸Àvï + ªÀiÁ£À ªÁPï + ªÀÄ0iÀÄ , Gvï+ªÀiÁzÀ, vÀvï+ªÀÄAiÀÄ , ²æêÀÄvï+ªÀĺÁ ±ÀĨsÀªÁUÀ° Basava.vesha@gmail.com 10 GHS Roopanagudi ,ballari east TMBK