Page 9 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

bdkbZ iQyu

1-2 lEc¼ jkf'k;k¡

uksV

ge tkurs gSa fd o`Ùk dk {ks=kiQy mldh f=kT;k ij fuHkZj djrk gSA nwljs 'kCnksa esa] fHkUu&fHkUu f=kT;kvksa okys
o`Ùkksa dk {ks=kiQy fHkUu&fHkUu gksrk gSA blh izdkj fdlh /u la[;k osQ ?kVus ;k c<+us ij mldk oxZ Hkh ?kV ;k
c<+ tkrk gSA ;gk¡ o`Ùk dh f=kT;k vkSj mldk {ks=kiQy ;k la[;k rFkk mldk oxZ lEc¼ jkf'k;k¡ gSaA

uksV~l ,slh nks jkf'k;k¡ ftuesa ,d osQ cnyus ij nwljh Hkh cny tkrh gS] os lEc¼ jkf'k;k¡ dgykrh gSaA

;|fi ;g nksuksa lEc¼ jkf'k;k¡ pj gSa ijUrq buesa ls ,d gh dk eku LosPNk ls cnyk tk ldrk gS] nwljh jkf'k
dk eku LosPNk ls ugha oju~ fdlh fu;e osQ vuqlkj cnysxkA mnkgj.k osQ fy, o`Ùk dh f=kT;k ;fn ge LosPNk

ls 9 9 9 9 yas rks mldk {ks=kiQy 9 fu;e π osQ Øe'k% π9 π9 +π9 #π9 gksxkA
pj jkf'k;k¡ nks izdkj dh gksrh gSaµ
LorU=k pj
"

&
ijrU=k pj "

&

;fn nks pj jkf'k;k¡ vkSj ijLij bl izdkj lEc¼ gksa fd ,d pj jkf'k dks LosPNkiwoZd dksbZ Hkh eku
nsus ij nwljh pj jkf'k dk eku ml ij vkfJr gks rks dks LorU=k pj
"

& rFkk
dks ijrU=k pj "

& dgrs gSaA
mnkgj.kkFkZµeku yks : ;

vc pj dks LosPNkiwoZd fHkUu&fHkUu eku Øe'k% -9 9 9 nsus ij gesa osQ fHkUu&fHkUu eku Øe'k%
9 %9 +9 izkIr gksrs gSa] tks Li"Vr% ij vkfJr gSaA
vr% ;gk¡ LorU=k pj vkSj ijrU=k pj gSA

1-3 iQyu

iQyu dk fl¼kUr nks ijLij lEc¼ pj jkf'k;ksa

ij vk/kfjr gSA
eku yks f=kT;k osQ fdlh o`Ùk dk {ks=kiQy gS] rc
π
;gk¡ jkf'k LorU=k pj
"

& rFkk jkf'k ijrU=k pj "

&

gS] pw¡fd o`Ùk dk {ks=kiQy mldh f=kT;k ij vkfJr gSA
bl n'kk esa ge dgrs gSa fd pj ] nwljs pj dk ,d iQyu gS ftls xf.kr dh Hkk"kk esa bl izdkj fy[kdj
O;Dr djrs gSaµ
:
vFkkZr~ < iQyu gS] pj dk=

1-4 iQyu dh ifjHkk"kk

;gk¡ nks pj jkf'k;k¡ (LorU=k pj) rFkk (ijrU=k pj) fdlh fu;e > ? osQ }kjk bl izdkj lEc¼

gksa fd osQ izR;sd eku osQ fy, dk ,d fuf'pr ,oa vf}rh;
@ eku izkIr gks rks dks dk
iQyu dgrs gSa ftls : fy[kdj iznf'kZr djrs gSaA
osQ iQyuksa dks 9 9 φ 9 bR;kfn izrhdksa ls iznf'kZr fd;k tkrk gSA