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{1} IAYr Kc t Kc< {1.1} IAYr Kc t& Kis kr)n[ T*>ki giLimi> Kc k[ie f[rfir Yt[i nY) t[n[ (AYr Kc aiv[ C[. diKli tr)k[ {1} kirKini miT[ rKiy[l mkinn&> BiD&> {2} kiym) AYifn[ c&kvvimi> aivt&. v[tn. {3} m&D) prn&> Äyij. {4} prvini f) aikZ(_imi> ji[e Skiy C[ k[ uRpidn OD hi[y k[ OF hi[y t[m Cti> IAYr Kc j C[. uRpidn S*ºy hi[y Ryir[ pN IAYr Kc rh[ C[. uRpidnni a[kmi[ uRpidn Kc< X Y D F E C A O
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Kc< an[ aivk r[Kiai[n&> (vÅl[PNm&²y m&Ñiai[: 1. Kc< (vÅl[PNn&> mh_v2. Kc< a>g[ni (v(vF ²yili[3. (v(vF Kc< vµc[ni s>b>Fi[4. T*>kigiLi an[ li>bigiLimi> Kc< uRpidn
vµc[ni s>b>Fi[
1. Kc< (vÅl[PNn&> mh_v- Äyipir)k (nN<yi[ l[vi- nfini mh_im)krNni uÑ[Sn[ (s¹F krvi- m*D) ri[kiN pr a(Fktm vLtr m[Lvvi- vAt&n) (k>mt a>g[ni (nN<ymi> - Kc<ni s>dB[< uRpidn siFni[ni upyi[g
a>g[ni (nN<yi[ l[vi
2.Kc< a>g[ni (v(vF ²yili[:{1} IAYr Kc< an[ aIAYr Kc< {2} sr[riS Kc<
an[ s)mi>t Kc<{1.1} IAYr Kc<: uRpidn vF[ k[ GT[ pr>t& Kis kr)n[ T*>ki giLimi> Kc<mi> k[ie f[rfir Yt[i nY) t[n[ (AYr Kc< kh[vimi> aiv[ C[. diKli tr)k[
{1} kirKini miT[ rKiy[l mkinn&> BiD&> {2} kiym) AYifn[ c&kvvimi> aivt&. v[tn.{3} m&D) prn&> Äyij.{4} prvini f)
aikZ(_imi> ji[e Skiy C[ k[ uRpidn OD hi[y k[ OF hi[y t[m Cti> IAYr Kc< CD = FF j[Tl&> j C[. uRpidn S*ºy hi[y Ryir[ pN IAYr Kc< OA j[Tl&> rh[ C[.
uRpidnni a[kmi[
uRpidn Kc<
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Kc< a>g[ni (v(vF ²yili[:{1} IAYr Kc< an[ aIAYr Kc< {2} sr[riS Kc<
an[ s)mi>t Kc<{1.2} aIAYr Kc<: uRpidn vF[[ t[i Kc<mi> pN vwir[i Yiy, uRpidn GT[ t[i Kc<mi> pN GTiD[i Yiy an[ j[i uRpidn S*ºy Yiy t[i Kc< pN S*ºy Yiy t[n[ a(AYr Kc< kh[ C[. di.t.: kici miln[i Kc<
bLtNn[i Kc<d](nk mj*rn[ c&kvvimi>
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uRpidn Kc<
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aikZ(_imi> OE aIAYr Kc<n) r[Ki C[. uRpidnni p\miN siY[ aIAYr Kc<mi> f[rfir Yiy C[. S*ºy uRpidn[ ai K< pN S*ºy hi[y C[. uRpidn vFti t[ vF[ C[ an[ uRpidn Gtti t[ GT[ C[.
{1.3} k&l {IAYrKc< + aIAYr Kc<}: IAYr Kc< an[ aIAYr Kc<ni srviLin[ k&l Kc< kh[vimi> aiv[ C[.
uRpidnni a[kmi[
uRpidn Kc<
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-IAYr Kc< an[ aIAYr Kc< vµc[ni[ tfivt a[ mi#i p\miNni[ C[, p\kirni[ nY).- b>n[ kc< vµc[n) B[dr[Ki k[vL T>*ki giLimi> j mh_vn) C[. li>bi giLin) ØIOTa[ bFi[ j Kc< aIAYr Kc< hi[y C[.
aIAYr Kc<
{2} sr[riS Kc<: sr[riS Kc< a[Tl[ a[km d)q Kc<. K&l Kc<n[ k&l uRpidn vD[ BigviY) sr[riS Kc< mL[ C[.
k&l Kc<k&l uRpidn
di.t. p[Q)n) am&k vAt&ni 1000 a[kmi[n&> uRpidn kr{ C[ an[ ji[ t[n&> k&l Kc< $i. 5000 hi[y ti[,
50001000
sr[riS Kc< $i. 5 YS[.
sr[riS Kc< =
sr[riS Kc< =
uRpidnni a[kmi[
a[km d)q sr[riS
IAYr Kc<
X
Y
DO Bsr[riS IAYr Kc< r[Ki
k&l IAYr Kc< k&l uRpidn
sr[riS IAYr Kc<n) r[Ki n)c[n) trf QLt) hi[y C[. J[ dSi<v[ C[ k[ sr[riS (AYr Kc< Sr&aitmi> vF& hi[y C[ j[m uRpidnmi> vFiri[ Yti> (AYr Kc< vF& a[kmi[ piCL vh[>cit& hi[viY) a[kmd)q (AYr Kc<mi> GTiDi[ Yiy C[.
sr[riS IAYr Kc< =
2.1 sr[riS IAYr Kc< : sr[riS IAYr Kc< a[ k&l IAYr Kc<n[ uRpidnni> a[kmi[n) s>²yi vD[ BigviY) p\i¼t Yiy C[.
uRpidnni a[kmi[
a[km d)q sr[riS
aIAYr Kc<
X
Y
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sr[riS aIAYr Kc< r[Ki
k&l aIAYr Kc< k&l uRpidn
sr[riS aIAYr Kc<n) r[Ki dSi<v[ C[ k[ sr[riS a(AYr Kc< am&k hd s&F) GT[ C[. Ryirbid t[mi> vFiri[ Yiy C[. aiY) sr[riS aIAYr Kc<n) r[Ki U aikirn) hi[y C[.
sr[riS IAYr Kc< =
2.2 sr[riS aIAYr Kc< : k&l aIAYr Kc<n[ k&l uRpidnni> a[km[i vD[ BigviY) j[ ai>k p\i¼t t[n[ sr[riS a(AYr Kc< kh[vimi> aiv[ C[. Sr&aitmi> t[ GT[ C[. am&k (b>d& pC) vF[ C[.
sr[riS k&l Kc<n) r[Ki sr[riS
aIAYr an[ sr[riS IAYr Kc<n) r[kin) upr hi[y C[, kirN k[ t[ b>n[ r[Kini[ srviLi[ dSi<v[ C[.
2.3 sr[riS k&l Kc< {sr[riS IAYr Kc< + sr[riS aIAYr Kc<} : sr[riS k&l Kc< S$aitmi> U>c&> hi[y C[, kirN k[ S$aitmi> uRpidn ai[C&> hi[y C[. an[ IAYr Kc< vFir[ hi[y C[. IAYr Kc< ai[Ci uRPidn vµc[ vh[>cie C[. J[m j[m uRpidn vF&jiy C[ t[m t[m IAYr Kc< vF& a[[kmi[ vµc[ vh[>cie C[ t[Y) sr[riS k&l Kc< GT[ C[. Am&k hd pC) sr[riS Kc< vF[ C[. kdni g[rliBi[ ai miT[ jvibdir C[.
uRpidnni a[kmi[
a[km d)q sr[riS
Kc<
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sr[riS aIAYr Kc< r[Ki
sr[riS IAYr Kc< r[Ki
sr[riS k&l Kc< r[Ki
uRpidnni a[kmi[
s)mi>
t Kc<
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{3} s)mi>t Kc<: vFirini> a[k a[kmn&> uRpidn krviY) k&l Kc<mi> Yti> f[rfirn[ s)mi>tKc< kh[vimi> aiv[ C[. T*ki>giLimi> IAYr Kc<mi> ki[e f[rfir Yti[ nY). miT[, s)mi>t Kc<a[ aIAYr Kc<mi> Yti[ f[rfir dSi<v[ C[.
s)mi>t Kc< r[Ki
k&l Kc<mi>
Yy[li[ frfiruRpidnni a[kmi[mi>
Yy[li[ f[rfir
s)mi>t Kc< =
s)mi>t Kc<ni[ ²yil s>cilk)y (nN<yi[ l[vimi> K*b j mh_vni[ C[. p[Q)ni[ mh_im nfia[ (b>d&a[ nkk) Yiy C[, jyi> s)mi>t Kc< an[ s)mi>t aivk srKi> Ye rh[.
3. (v(vF Kc< vµc[ni ai>tr s>b>Fi[: uRpidna[kmi[
IAYr Kc< {$}
aIAYr Kc< {$}
k&l Kc< {$.}
s)mi>t Kc< {$}
sr[. IAYr Kc< {$}
sr[. aIAYr Kc< {$}
sr[. k&l Kc< {$}
1 100 1100 1200 - 100 1100 12002 100 1200 1300 100 50 600 6503 100 1375 1475 175 33.3 458 4914 100 1400 1500 25 25 350 3755 100 1500 1600 100 20 300 3206 100 1700 1800 200 16.7 283.3 300
7 100 2000 2100 300 14.30 280.7 300
8 100 2400 2500 400 12.25 300 312
(v(vF Kc< vµc[ni ai>tr s>b>Fi[:
1. sr[riS Kc<a[ k&l Kc<n[ uRpidnni k&l a[kmi[ vD[ BigviY) p\i¼t Yiy C[
2. p[Q) gm[ t[Tl&> uRpidn kr[ Cti> T*>kigiLimi> IAYr Kc<mi> ki[e f[rfir Yti[ nY)
3. s)mi>t Kc< GTti[ hi[y C[ Ryir[ k&l Kc< Gtti jti dr[ vF[ C[ an[ jyir[ s)mi>t Kc< vFti[ hi[y C[, Ryir[ k&l Kc< vFti jti dr[ vFti[ hi[y C[.
4. s)mi>t Kc< jyir[ sr[riS Kc< krti vF& hi[y C[, Ryir[ sr[riS Kc< GT[ C[.
5. s)mi>t Kc< jyir[ sr[riS Kc< krti vF& hi[y C[, Ryir[ sr[riS Kc< vF[ C[.
uRpidnni a[kmi[
Kc<
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Y
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sr[riS aIAYr Kc< r[Ki
sr[riS IAYr Kc< r[Ki
sr[riS k&l Kc< r[Ki
s)mi>t Kc< r[Ki
6. sitmi> a[km sr[riS Kc< ºy*ntm hi[y, a[Tl[ ai[Cimi> ai[Ci[ hi[y, Ryir[ s)mi>t Kc< an[ sr[riS Kc< an[ sr[riS Kc< srKi Yiy C[.
7. s)mi>t Kc< ji[ sr[riS Kc< krti ai[Ci[ hi[y ti[ sr[riS aIAYr Kc< GT[ C[.
8.s)mi>t Kc< ji[ sr[riS aIAYr Kc< krti vFir[ hi[y ti[ sr[riS aIAYr Kc< GT[ C[.
9. sr[riS Kc< an[ s)mi>t Kc< jyir[ GT[ C[ Ryir[ s)mi>t Kc< K*b zDpY) vF[ C[ an[ jyir[ b>n[ Kc< vF[ C[ Ryir[ pN s)mi>t Kc< K*b zDpY) vF[ C[.
uRpidnni a[kmi[
Kc<
X
Y
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sr[riS aIAYr Kc< r[Ki
sr[riS IAYr Kc< r[Ki
sr[riS k&l Kc< r[Ki
s)mi>t Kc< r[Ki
4. T*>ki giLi an[ li>bi giLimi> Kc< - uRpidn s>b>Fi[: {4.1} T*>kigiLimi> Kc<-uRpidn vµc[ni
s>b>Fi[:T*>ki[giLi[ a[Tl[ smyni[ a[vi[ giLi[ k[ j[ dr(myin IAYr siFni[n&> p\miN bdl) Skit&> nY) mi#i aIAYr siFni[ j bdl) Skiy C[. miT[ kh) Skiy k[ p[Q)n&> uRpidn vF) Sk[ C[, pN t[n&> kd vFt& nY). T*kigiLimi> Kc<-uRpidnni s>b>Fi[n)c[ni #iN ²yili[ni aiFir[ krvimi> aiv[ C[.
1. sr[riS IAYr Kc< an[ uRpidn2. sr[riS aIAYr Kc< an[ uRpidn3. sr[riS k&l Kc< an[ uRpidn4. s)mi>t Kc< an[ uRpidn
uRpidnni a[kmi[
a[km d)q sr[riS
IAYr Kc<
X
Y
DO Bsr[riS IAYr Kc< r[Ki
k&l IAYr Kc<n[ k&l uRpidnni> a[km[i vD[ BigviY) j[ ai>k p\i¼t t[n[ sr[riS (AYr Kc< kh[vimi> aiv[ C[. sr[riS (AYr Kc< Sr&aitmi> vF& hi[y C[. uRpidnmi> vFiri[ Yti> (AYr Kc< vF& a[kmi[ piCL vh[>cit& hi[viY) a[kmd)q (AYr Kc<mi> GTiDi[ Yiy C[.a[Tl[ k[ a[km d)q IAYr Kc< GT[ C[. miT[ IAYr Kc< r[Ki n)c[ trf QLt) hi[y C[, t[ (x(tj r[Kin[ ApS<vin&> vlN Friv[ C[ pr>t& ApS<t) nY), kirN k[ sr[riS IAYr Kc< kyir[y S*ºy bnti[ nY). ai r[Kini[ aikir T[k`(nkl BiPimi> kh)a[ ti[ “rectangular hyperbola” hi[y C[.
1. sr[riS IAYr Kc< an[ uRpidn: sr[riS IAYr Kc< a[ k&l IAYr
Kc<n[ uRpidnni> a[kmi[n) s>²yi vD[ BigviY) p\i¼t Yiy C[.
sr[riS aIAYr Kc<n) r[Ki
dSi<v[ C[ k[ uRpidnmi> vFiri siY[ sr[riS a(AYr Kc< am&k hd s&F) GT[ C[. Ryirbid t[mi> vFiri[ Yiy C[. aiY) sr[riS aIAYr Kc<n) r[Ki U aikirn) hi[y C[. ain&> kirN p[Q)ni IAYr siFnni[ mh_im upyi[g Ye gyi> bid, a(AYr siFni[mi> vFiri[ krti uRpidnmi> Gtti dr[ vFiri[ Yvi pim[ C[, miT[ a[km (dq aIAYr siFni[n) uRPidkti Gtvi pim[ C[.
2. sr[riS aIAYr Kc< an[ uRpidn : k&l aIAYr Kc<n[ k&l uRpidnni> a[km[i vD[
BigviY) j[ ai>k p\i¼t t[n[ sr[riS a(AYr Kc< kh[vimi> aiv[ C[.
uRpidnni a[kmi[
a[km d)q sr[riS
aIAYr Kc<
X
Y
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sr[riS aIAYr Kc< r[Ki
sr[riS k&l Kc<n) r[Ki sr[riS
aIAYr an[ sr[riS IAYr Kc<n) r[Kin) upr hi[y C[, kirN k[ t[ b>n[ r[Kini[ srviLi[ dSi<v[ C[.
3. sr[riS k&l Kc< an[ uRpidn : sr[riS k&l Kc< a[ sr[riS aIAYr Kc< an[ sr[riS
(AYr Kc<ni[ srviLi[ C[. sr[riS k&l Kc< S$aitmi> U>c&> hi[y C[, kirN k[ S$aitmi> uRpidn ai[C&> hi[y C[. an[ IAYr Kc< vFir[ hi[y C[. IAYr Kc< ai[Ci uRpidn vµc[ vh[>cie C[. j[m j[m uRpidn vF&jiy C[ t[m t[m IAYr Kc< vF& a[[kmi[ vµc[ vh[>cie C[ t[Y) sr[riS k&l Kc< GT[ C[. am&k hd pC) sr[riS Kc< vF[ C[. kdni g[rliBi[ an[ GTt) p[diSni[ (nym ai miT[ jvibdir C[.
uRpidnni a[kmi[
a[km d)q sr[riS
Kc<
X
Y
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sr[riS aIAYr Kc< r[Ki
sr[riS IAYr Kc< r[Ki
sr[riS k&l Kc< r[Ki
uRpidnni a[kmi[
s)mi>
t Kc<
X
Y
O
4. s)mi>t Kc< an[ uRpidn: vFirini> a[k a[kmn&> uRpidn krviY) k&l
Kc<mi> Yti> f[rfirn[ s)mi>tKc< kh[vimi> aiv[ C[. T*ki>giLimi> IAYr Kc<mi> ki[e f[rfir Yti[ nY). miT[, s)mi>t Kc<a[ aIAYr Kc<mi> Yti[ f[rfir dSi<v[ C[.
s)mi>t Kc< r[Ki
s)mi>t Kc< S$aitmi> GT[ C[ a[n&> kirN vFt) s)mi>t p[diS k[ vFti mLtrni[ (nym C[ Ryir pC) s)mi>t Kc< vF[ C[ t[n&> kirN GTt) s)mi>t p[diSni[ (nym C[.
T*>kigiLimi> Kc< an[ uRpidnni s>b>Fi[n) r[Ki ¹viri smj*t)1. uRpidn vFti> sr[riS IAYr
Kc< GTt&> jiy C[ an[ t[Y) r[Kini[ QiL äN hi[y C[.
2. sr[riS aIAYr Kc< S$aitmi> GT[ C[ an[ am&k (b>d& bid t[ vFvi mi>D[ C[.
3. sr[riS k&l Kc< pN S$aitmi> GT[ C[ an[ Ryir pC) t[ vF[ C[. aiY) t[n) r[Kini[ U aikir hi[y C[.
4. s)mi>t Kc< pN S$aitmi> GT[ C[ an[ pC) vFvi mi>D[ C[.
5. s)mi>t Kc< r[Ki a[ sr[riS aIAYr Kc<n) r[Ki tYi sr[riS k&l Kc<n) r[Kin[ ºy&ntm (b>d&a[ C[d[ C[.
6. s)mi>t Kc< jyir[ sr[riS Kc< krti ai[C&> hi[y C[, Ryir[ sr[riS Kc< GT[ C[, an[ s)mi>t Kc< jyir[ sr[riS Kc< krti vF& hi[y Ryir[ s)mi>t Kc< vF[ C[.
7. s)mi>t Kc< ji[ sr[riS Kc< krti ai[C&> hi[y ti[ sr[riS aIAYr Kc< GT[ C[. s)mi>t Kc< ji[ sr[riS aIAYr Kc< krti> vFir[ hi[y ti[ sr[riS aIAYr Kc< vF[ C[.
uRpidnni a[kmi[
Kc<
X
Y
O
sr[riS aIAYr Kc< r[Ki
sr[riS IAYr Kc< r[Ki
sr[riS k&l Kc< r[Ki
s)mi>t Kc< r[Ki
4.2 li>bi giLimi> Kc< an[ uRpidn vµc[ni s>b>Fi[libi>giL[ aIAYr siFni[ upri>t IAYr siFni[ni p\miNmi> pN vFiri[ GTiDi[ kr)n[ p[Q)n&> kd bdl) Skiy C[. aim li>b[ giL[ bFi[ j Kc< aIAYr bn[ C[. li>bigiLin) sr[riS Kc<n) r[Ki pN T*>kigiLin) sr[riSn) sr[riS aIAYr Kc<n) r[Kin) j[m U aikirn) hi[y C[. Tfivt mi#i a[Tli[ j hi[y C[ k[ t[ vFir[ C)Cr) k[ spiT hi[y C[. j[ miT[ni kirNi[ -
XB C D E FuRpidnni a[kmi[
s)mi>
t Kc<
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R S T V
libi>giLin) sr[riS Kc<n) r[Ki
1. li>b[giL[ IAYr Kc< pN aIAYr Kc< bn[ C[.
2. li>b[ giL[ siFni[n&> (vBijn Sky bn[ C[.
3. j$)yiti[n[ an&lx)n[ siFni[ni upyi[gmi> f[rfir Sky bn[ C[.
bij&n) aikZ(_imi> HH’ r[Ki libi>giLin) sr[riS Kc< r[Ki dSi<v[ C[. j[ ¼liºTni pi>c j&di j&di kd p\miN[ bdlit) uRpidnn) T*kigiLin) sr[riS Kc<n) r[Kiai[ C[.
- k[Tli>k aY<SiA#i)ai[ ai r[Kin[ “aiyi[jn r[Ki” tr)k[ pN ai[LKiv[ C[.
H’H
li>bi giLin) sr[riS Kc<n) r[Kini lxNi[1. U aikirn) hi[y C[. tfivt mi#i a[Tli[ j hi[y C[ k[ t[ vFir[ C)Cr) k[ spiT hi[y C[.
2. j[m j[m vF& mi[Ti kdni[ ¼liºT upyi[g l[t) jiy t[m t[m S$aitmi> sr[riS Kc< GTt&> jiy C[, pr>t& pC) vF[ C[.
3. li>bigiLin) Kc< r[Ki pr ºy*ntm Kc< dSi<vti[ ¼liºT a[ eOT kdni ¼liºT t[mj t[n) jmN) an[ Dib& bij&ni ¼liºT eOT kdni kh) Skiy nh)> kirN k[ li>bi giLin) Kc< r[Kin[ t[ni ºy*ntm (b>d& pr ApS<ti nY).
XB C D E FuRpidnni a[kmi[
s)mi>
t Kc<
Q
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R S T V
libi>giLin) sr[riS Kc<n) r[Ki H’H
