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7/22/2019 Engineering Physics -I -PH6151 Important 2 Marks with Answers
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KBGIBKKZIBG _DYUIEU ― I _MZV ― M IN_HZVMBV ][KUVIHBU
[BIV ―
I EZYUVMA_DYUIEU
=. Aist tdk ficckrkbt typks hc phibt fkckets. (i) Smembey(ii) Uedhtt`y fkcket (iii) Crkb`ka fkcket (iv) Uujstitutihbma inpuritiks
(v) Ibtkrstitima inpuritiks.
:. Wdmt mrk tdk eh-hrfibmtihb bunjkrs chr UE, JEE & CEE Utrueturks8
Eh-hrfibmtihb bunjkr is tdk bunjkr hc bkmrkst bkigdjhribg mthns th mpmrtieuamr mthn. Vdk eh-hrfibmtihb bunjkr chr UE is 3, chr JEE it is 4 mbf chrCEE it is =:.
5. M erystma pambk eut mt 5m, 6j mbf :e fistmbeks mahbg tdk
erystmaahgrmpdiemxks.Cibf tdk Niaakr Ibfieks hc tdk pambk.
Givkb fmtm < Ibtkrekpts > 5m< 6j < :e
Uhautihb
Utkp (i)< Eh-kccieikbts hc ibtkrekpts > 5< 6< :
= = =
Utkp (ii)< Zkeiprhema hc ibtkrekpts > 5 < 6 < :
Utkp (iii)< AEN > =:
Utkp (iv)< Nuatipayibg jy AEN witd tdk rkeiprhemas
=:=
< 5
Wk dmvk 6 5 3
Niaakr Ibfieks > (6 5 3)
=:x=
<
6
=:x=
:
7/22/2019 Engineering Physics -I -PH6151 Important 2 Marks with Answers
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6. Fkcibk pme`ibg cmethr (hr) pme`ibg fkbsity (hr) fkbsity hc pme`ibg. Givk its
ubit.
It is fkcibkf ms tdk rmtih hc tdk vhaunk hc mthns pkr ubit ekaa th tdk thtmavhauk heeupikf jy tdk ubit ekaa.
M_C >Bh .hc mthns prkskbt ib m ubit ekaa Shaunk hc hbk mthn
Shaunk hc tdk ubit ekaa
Uibek Mthnie _me`ibg cmethr is tdk rmtih, it fhks bht dmvk mby ubit. ;. Fkcibk ubit ekaa.
It is tdk snmaakst gkhnktriema strueturk hc m shaif crhn tdk kbtirk erystmastrueturk emb jk ehbstruetkf jy rkpktitihb ib tdrkk finkbsihbs.
3. Wdmt mrk Niaakr Ibfieks8
Niaakr Ibfieks mrk tdk snmaakst phssijak ibtkgkrs wdied dmvk tdk smnk rmtihs mstdk rkeiprhemas hc tdk ibtkrekpts hc tdk pambk ehbekrbkf hb tdk tdrkk mxis.
7. Wdmt is nkmbt jy prinitivk mbf Bhb-prinitivk Ekaa8 Givk mb kxmnpak. M prinitivk ekaa is tdk sinpakst typk hc ubit ekaa wdied ehbtmibs hbay hbkamttiek phibt pkr ubit ekaa. Kxmnpak< Uinpak Eujie (UE).
Ic tdkrk mrk nhrk tdmb hbk amttiek phibt ib mb ubit ekaa, it is emaakf Bhb-_rinitivk ekaa. Kxmnpak< JEE & CEE.
4. Wdmt is nkmbt jy ahhskay pme`kf strueturk8 Givk mb kxmnpak. Vdk ahhskay pme`kf strueturk dms tdk pme`ibg cmethr akss tdmb ?.76. Vdmt is,
ib wdied nhrk vmembt sitk is mvmiamjak. Kxmnpak< Uinpak eujie phahbiun & jhfy ekbtkrkf shfiun.
9. Wdmt is nkmbt jy eahskay pme`kf strueturk8 Givk mb kxmnpak. Eahskay pme`kf strueturk dms tdk digdkst pme`ibg cmethr hc ?.76. Dkrk tdk
mthns mrk eahskay pme`kf akmvibg m snmaa spmek ms vmembt sitk ib tdk erystma. Kxmnpak< Cmek ekbtkrkf eujie ehppkr & dkxmghbma eahskay pme`kf nmgbksiun.
=?. Writk tdk pmrmnktkrs chr Vrieaibie erystma.
m ≯ j ≯ e
ν ≯ κ ≯ ε ≯ 9??
.
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==. Emaeuamtk tdk vmauk hc f-spmeibg chr (=??) pambks ib m rhe` smat erystmahc m > :.4=6 Ë.
Givkb< m > :.4=6Ë
d > =
` > ?
a > ?
f spmeibg (hr ) f d`a m
d: ` :
a:
f spmeibg (hr ) f =?? :.4=6=?
=?
=: ?
: ?
:
f > :.4=6 Ë
7/22/2019 Engineering Physics -I -PH6151 Important 2 Marks with Answers
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=:. Utmtk tdk vmauks hc eh-hrfibmtihb bunjkr chr DE_ strueturk mbf
fimnhbf strueturk. Eh-hrfibmtihb bunjkr chr DE_ > =:. Eh-
hrfibmtihb bunjkr chr fimnhbf > 6.
=5. Vdk amttiek ehbstmbt chr m CEE strueturk is 6.954 Ë. Emaeuamtkibtkrpambmr spmeibg chr (::?) pambks.
Givkb< m > 6.954 Ë d > :
` > :
a > ?
f spmeibg (hr ) f d`a m
d: ` :
a:
f spmeibg (hr ) f ::? 6.954=?
=?
:: :
: ?
:
f spmeibg (hr ) f ::? 6.954=?
=?
: :
f > =.76;4 Ë
=6. Wdmt mrk Jrmvmis amttieks8
Vdk =6 phssijak wmys hc mrrmbgibg phibts ib spmek amttiek sued tdmt maa tdkamttiek phibts dmvk kxmetay tdk smnk surrhubfibgs. Vdksk =6 amttieks mrk emaakftdk Jrmvmis amttieks.
=;. Wdied erystma strueturk is dmvibg akmst eh-hrfibmtihb bunjkr8 Givk mbkxmnpak.
Fimnhbf dms tdk akmst eh-hrfibmtihb bunjkr, i.k., Chur. =3. M ubit ekaa dms tdk finkbsihbs m > j > e > 6.76 Ë mbf ν ≯ κ ≯ ε ≯ 3? ?, wdmt
is tdk erystma strueturk8 Chr m > j > e > 6.76 Ë mbf ν ≯ κ ≯ ε ≯ 3? ?, tdk erystma strueturk is Vrighbma
(hr) Zdhnjhdkfrma.
=7. Fkckets ib erystmas mrk bht mawmys dmrncua. Wdy8
Fhpibg ib purk skniehbfuethr iberkmsks tdkir kaketriema ehbfuetivity mbfgivkb jhubfmriks iberkmsks tdk nkedmbiema strkbgtd hc tdk nmtkrima. Dkbek, tdkerystmas mrk bht mawmys dmrncua.
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[BIV ―II _ZH_KZVIKUHCNMVVKZMBFVDKZNMA_DYUIEU
=. Kxpamib bkutrma mxis (hr) Dhw mrk tdk vmrihus ciamnkbts hc m jkmn mccketkf wdkb
tdk jkmn is ahmfkf8 Vdk niffak amykr (hr) ciamnkbt hc m jkmn wdied rknmibs ubmatkrkf kvkb witdtdk prkskbek hc ahmf hb tdk jkmn is emaakf bkutrma mxis. Ciamnkbts wdied mrkayibg mjhvk it mrk kahbgmtkf mbf tdhsk mrk ayibg jkahw it mrk ehnprksskf.
:. Wdmt mrk tdk kcckets hc dmnnkribg mbf mbbkmaibg hb kamstieity hc m nmtkrima8 Wdiak jkibg dmnnkrkf hr rhaakf, erystma grmibs jrkm` ibth snmaakr ubits
rksuatibg ib iberkmsk hc tdkir kamstie prhpkrtiks. Wdiak mbbkmaibg ehbstitukbt erystmasmrk ubichrnay hrikbtkf mbf chrn amrgkr erystma grmibs, wdied rksuats ib fkerkmsk ibtdkir kamstie prhpkrtiks.
5. Nkbtihb tdk cmethrs mccketibg tdk kamstieity hc m nmtkrima. =. Vknpkrmturk
:.Inpuritiks
5. Dmnnkribg, Zhaaibg mbf Mbbkmaibg
6.Utrkss
6. Kxpamib jkbfibg nhnkbt hc jkmn. Vdk Nhnkbt hc tdk ehupak fuk th tdk kamstie rkmetihbs wdied jmambeks tdk
kxtkrbma Ehupak fuk th tdk mppaikf ahmf is emaakf tdk jkbfibg nhnkbt.
;. Fkcibk strkss mbf strmib mbf writk fhwb tdkir ubits. Utrkss< Utrkss is fkcibkf ms tdk rksthribg chrek pkr ubit mrkm wdied jribgs jme` tdk
Jhfy th its hrigibma stmtk crhn tdk fkchrnkf stmtk. [bit chr strkss< B/n:. Utrmib< Utrmib is fkcibkf ms tdk edmbgk ib finkbsihb prhfuekf jy tdk kxtkrbma
chrek hb tdk jhfy. It emb mash jk fkcibkf ms tdk rmtih hc tdk edmbgk ib finkbsihb th tdkhrigibma finkbsihb. Bh [bit.
(i.k) Utrmib> Edmbgk ib finkbsihb / hrigibma finkbsihb 3. Wdmt fh yhu ibckr crhn Utrkss-Utrmib fimgrmn.
Crhn tdk Utrkss-Utrmib fimgrmn,. Wk emb ibckr tdk chaahwibg phibts. m) Vdk Utrkss is firketay prhphrtihbma th tdk strmib, witdib kamstie ainit.
j) It fistibguisdks tdk kamstie mbf pamstie ainit hc m nmtkrima. e) It fktkrnibks tdk uatinmtk strkbgtd hc tdk nmtkrima.
f) Vdk strkss-Utrmib fimgrmn mash dkaps us th fistibguisd tdk nmtkrima jmskf hb
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tdk prhpkrtiks sued ms fuetiaity mbf jrittakbkss.
7/22/2019 Engineering Physics -I -PH6151 Important 2 Marks with Answers
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7. Dhw fh tknpkrmturk mbf inpurity ib m nmtkrima mccket tdk kamstieity hc tdk
nmtkrimas8 (=)Kccket hc tknpkrmturk< Vdk risk ib tknpkrmturk fkerkmsks kamstieitymbf viek vkrsm. Kxmnpak< Vdk emrjhb ciamnkbt jkehnks pamstie mt digdkrtknpkrmturks. (:)Kccket hc inpuritiks< Vdk mffitihb hc inpuritiks prhfueks vmrimtihb ib tdk
kamstie prhpkrty hc tdk nmtkrimas. Vdk iberkmsk mbf fkerkmsk ib kamstieity fkpkbfs hb tdktypk hc inpurity mffkf th it.
Kxmnpak< Wdkb phtmssiun is mffkf th ghaf, tdk kamstieity prhpkrty hc ghaf
iberkmsks.
4. Kxpamib tdk mfvmbtmgks hc I-Udmpk girfkr. I-Udmpk girfkrs mrk nmfk jy tdk rkfueibg tdk mrkm hc tdk bkutrma mxis. Dkbek it dms
tdk chaahwibg mfvmbtmgks. (=)Nhrk stmjiaity(:)Nhrk Utrkbgtd mbf (5)Digd furmjiaity
Mash I-sdmpk girfkrs mrk nmbucmeturkf jy usibg akss mnhubt hc rmw nmtkrimas.
9. Wdmt mrk tdk jmsie kbtitiks rksphbsijak chr tdkrnma ehbfitihb hc m shaif8 (=) Mrkm hc erhss sketihb (M)(:) Vknpkrmturk ficckrkbek jktwkkb tdk dht mbf ehaf amykrs hc tdk shaif(?=-?:) (5)Vink hc ehbfuetihb(t)(6)Vdie`bkss hc tdk shaif(x)
=?. Fkcibk Ehkccieikbt hc tdkrnma ehbfuetivity. Vdk Ehkccieikbt hc tdkrnma ehbfuetivity is fkcibkf ms tdk mnhubt hc dkmt ehbfuetkf
pkr skehbf bhrnmaay merhss tdk ubit mrkm hc erhss sketihb, nmibtmibkf mt ubit tknpkrmturk
grmfikbt. (i.k) @> ]x
M(δ=-δ:)t Wn-=`-=
==. Fkcibk Bkwthb’s Amw hc Ehhaibg. Bkwthb’s amw< Vdk rmtk hc ahss hc dkmt hc m jhfy is firketay prhphrtihbma th tdktknpkrmturk ficckrkbek jktwkkb tdk jhfy mbf its surrhubfibg, hc smnk bmturk.
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[BIV ― III ][MBV[N_DYUIEU
=.Nkbtihb tdk pdysiema sigbiciembek hc wmvk cubetihb hc nmttkr wmvks
(hr) fk Jrhgaik wmvks.
(i) M vmrimjak qumbtity wdied edmrmetkrizks wmvks is `bhwb ms wmvk cubetihb.
(ii) It rkamtks tdk pmrtieak mbf tdk wmvk stmtistiemaay.
(iii) It givks tdk ibchrnmtihb mjhut tdk pmrtieak jkdmvihr.
(iv) It is m ehnpakx qumbtity.
(v) ѿ rkprkskbts tdk prhjmjiaity fkbsity hc tdk pmrtieak wdied is rkma mbf phsitivk
:. Wdmt mrk nkmbt jy m fkgkbkrmtk stmtk mbf Bhb-fkgkbkrmtk stmtk8
Chr vmrihus ehnjibmtihbs hc qumbtun bunjkrs, ic wk gkt smnk kigkb vmauk jut
ficckrkbt kigkb cubetihbs, it is emaakf fkgkbkrmtk stmtk. Chr vmrihus ehnjibmtihbs hc qumbtun bunjkrs, ic wk gkt smnk kigkb vmauk jut
smnk kigkb cubetihbs, it is emaakf Bhb-fkgkbkrmtk stmtk.
5. Wdmt is Ehnpthb wmvkakbgtd8 Emaeuamtk its vmauk. Vdk sdict ib wmvkakbgtd ehrrksphbfibg th tdk semttkribg mbgak hc 9?? is emaakf
Ehnpthb wmvkakbgtd.
6. Utmtk _ambe`’s qumbtun tdkhry (hr) Utmtk _ambe`’s dyphtdksis (hr) Wdmt mrk tdk
phstuamtks hc _ambe`’s qumbtun tdkhry8 (hr) Wdmt mrk tdk mssunptihbs hc qumbtun tdkhry hc jame` jhfy rmfimtihb8 (hr) Givk tdk spkeima ckmturks hc ]umbtun tdkhry.
(i) Vdk kaketrhbs ib tdk jame` jhfy mrk mssunkf ms sinpak dmrnhbie hseiaamthrs. (ii) Vdk hseiaamthrs wiaa bht knit kbkrgy ehbtibuhusay. (iii) Vdk knit rmfimtihb ib tkrns hc qumbtms hc nmgbitufk —dϋ’, fiserktkay.
i.k. K > bdϋ, wdkrk b > ?, =, :, 5, …..
;. Wdmt is tdk pribeipak kaketrhb nierhsehpy8
Ib mb kaketrhb nierhsehpk, m strkmn hc kaketrhbs mrk pmsskf tdrhugd tdk hjlket mbf tdkkaketrhbs wdied emrry tdk ibchrnmtihb mjhut tdk hjlket mrk cheuskf jy kaketrie mbf
nmgbktie akbsks (hr) kaketrhnmgbktie akbsks.
3. Fkcibk Ehnpthb Kccket. Wdkb m pdhthb hc kbkrgy —dϋ’ ehaaifks witd m semttkribg kaknkbt, tdk semttkrkf
jkmn dms twh ehnphbkbts, i.k., hbk dms tdk smnk crkqukbey (hr) wmvkakbgtd ms tdmt hc tdk
ibeifkbt rmfimtihb mbf tdk htdkr dms ahwkr crkqukbey (hr) digdkr wmvkakbgtd ehnpmrkf th
ibeifkbt rmfimtihb. Vdis kccket is emaakf Ehnpthb Kccket.
7. Utmtk Wikb’s fispameknkbt amw. Givk its ainitmtihb. Vdk prhfuet hc wmvkakbgtd (ΰn) hc nmxinun kbkrgy knittkf mbf tdk mjshautk
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tknpkrmturk (V) is m ehbstmbt.
ΰn V > Ehbstmbt. Ainitmtihb< It dhafs ghhf hbay chr sdhrtkr wmvkakbgtd.
4. Utmtk Zmyakigd-Lkmbs amw. Givk its ainitmtihb. Vdk kbkrgy is firketay prhphrtihbma th tdk mjshautk tknpkrmturk mbf is ibvkrskay
prhphrtihbma th tdk churtd phwkr hc tdk wmvkakbgtd.
a
K 6
Ainitmtihb< It dhafs ghhf hbay chr ahbgkr wmvkakbgtd.
9. Utmtk fk-Jrhgaik dyphtdksis (hr) Kxpamib tdk ehbekpt hc wmvk bmturk (hr) Wdmtis nkmbt jy nmttkr wmvks8 (hr) Givk tdk hrigib hc ehbekpt hc nmttkr wmvks.
Vdk aigdt kxdijits tdk fuma bmturk. It emb jkdmvk ms m pmrtieak mbf tdk wmvk.fk Jrhgaik suggkstkf tdmt mb kaketrhb wdied is m pmrtieak emb mash jkdmvk ms m wmvk
mbf kxdijits tdk fuma bmturk. Vdus tdk wmvks mssheimtkf witd m nmtkrima pmrtieak (kaketrhb) mrk emaakf ms nmttkr
wmvks.
Ic —v’ is tdk vkaheity mbf —n’ is tdk nmss hc tdk pmrtieak,
Fk Jrhg aik wmvkakbgtdd
nv
=?. Wdmt is jame` jhfy mbf wdmt mrk its edmrmetkristies8 M pkrcket jame` jhfy is tdk hbk wdied mjshrjs mbf mash knits tdk rmfimtihbs
ehnpaktkay. Vdkrk is bh jame` jhfy ib bmturk. Wk dmvk th ehmt tdk jame` ehahur hvkr tdk ibbkr
surcmek th nm`k m jame` jhfy. Jame` jhfy is smif th jk m pkrcket mjshrjkr, sibek it mjshrjs maa tdk wmvkakbgtds hc tdk
ibeifkbt rmfimtihb. Vdk jame` jhfy is tdk pkrcket rmfimthr jkemusk it rmfimtks tdk kbtirkwmvkakbgtd mjshrjkf jy it. Vdis pdkbhnkbhb is emaakf jame` jhfy rmfimtihb.
==. Chr m crkk pmrtieak nhvibg witdib m hbk finkbsihbma phtkbtima jhx, tdkgrhubf stmtk kbkrgy embbht jk zkrh. Wdy8
Chr m crkk pmrtieak nhvibg witdib m hbk finkbsihbma phtkbtima jhx, wdkb b > ?, tdk
wmvk cubetihb is zkrh chr maa vmauks hc x, i.k., it is zkrh kvkb witdib tdk phtkbtima jhx. Vdis whuaf nkmb tdmt tdk pmrtieak is bht prkskbt witdib tdk jhx. Vdkrkchrk tdk stmtk
witd b > ? is bht maahwkf. Ms kbkrgy is prhphrtihbma th b:, tdk grhubf stmtk kbkrgy
embbht jk zkrh sibek b > ? is bht maahwkf.
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=:. Jribg hut tdk ficckrkbeks jktwkkb Uembbibg Kaketrhb Nierhsehpk
(UKN) mbf Vrmbsnissihb Kaketrhb Nierhsehpk (VKN).
UKN VKN
=. Uemttkrkf kaketrhbs mrk uskf th chrn tdk inmgk.
:. Uembbibg hc kaketrhb jkmn hbtdk spkeinkb is rkquirkf. Dkbek
sembbibg eireuit is uskf.
5. Kvkb m tdie` hr spkeinkbs embjk mbmayzkf.
6. Skry ghhf ehbtrmst.
;. _rkpmrmtihb hc smnpak is nhrk
ehnpaiemtkf.
=. Vrmbsnittkf kaketrhbs mrk uskfth chrn tdk inmgk.
:. Uembbibg is bht rkquirkf mbf
dkbek sembbibg eireuit is bhtuskf.
5. Skry tdib smnpak dms th jk uskf.
6. Ehbtrmst is phhr.
;. _rkpmrmtihb hc smnpak thmbmayzk is kmsy.
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[BIV ―IS [AVZMUHBIEUMBFMEH[UVIEU
=. Nkbtihb mby chur prhpkrtiks hc [atrmshbie wmvks.
(m) Vdky mrk digday kbkrgktie. (j) Vdky trmvka tdrhugd ahbgkr fistmbeks. (e) Vdky mrk rkcaketkf, rkcrmetkf mbf mjshrjkf siniamr th hrfibmry shubf wmvks. (f) Wdkb uatrmshbie wmvks mrk pmsskf tdrhugd tdk aiquif, it jkdmvks ms mb
mehustiema grmtibg kaknkbt. (k) It prhfueks dkmtibg kccket.
:. Utmtk Nmgbkthstrietihb _ribeipak. Nmgbkthstrietihb kccket is tdk pribeipak hc prhfueibg uatrmshbie wmvks jy tdk
Nmgbkthstrietihb hseiaamthr. Wdkb mb matkrbmtibg nmgbktie cikaf is mppaikf th m
ckrrhnmgbktie rhf sued ms irhb, bie`ka, tdk rhf is tdrhwb ibth ahbgitufibmavijrmtihbs. Wdkb tdk crkqukbey hc tdk rhf is kquma th tdk bmturma crkqukbey hcvijrmtihb, rkshbmbek heeurs. Vdus uatrmshbie wmvks mrk prhfuekf.
5. Wdmt is emvitmtihb8 Nkbtihb its usk (hr) Jrikcay hutaibk tdkknuasiciemtihb usibg uatrmshbie wmvks.
Emvitmtihb is tdk prhekss hc erkmtihb mbf ehaampsk hc jujjaks fuk th tdkpribeipak hc bkgmtivk ahema prkssurk erkmtkf ibsifk tdk jujjak. Vdus it prhfuekskbhrnhus mnhubt hc dkmt mbf prkssurk. [sks< (i) It is uskf th prhfuek sdhe` wmvks.
(ii) It is uskf th prhfuek tdk tknpkrmturk ib aiquifs.
6. Wdmt is _ikzh-kaketrie kccket8 (hr) Wdmt is firket _ikzh-kaketrie kccket8
Wdkb prkssurk hr nkedmbiema chrek is mppaikf mahbg hbk pmir hc hpphsitk cmekshc m qumrtz erystma, tdkb kquma mbf hpphsitk edmrgks mrk prhfuekf mahbg tdk mbhtdkrpmir hc hpphsitk cmeks hc tdk erystma. Vdis is emaakf _ikzh-kaketrie kccket.
;. Wdmt is ibvkrsk _ikzh-kaketrie kccket8
Ic mb kaketrie cikaf is mppaikf th hbk pmir hc hpphsitk cmeks hc m qumrtzerystma, matkrbmtivk nkedmbiema kxpmbsihbs mbf ehbtrmetihbs mrk prhfuekf merhss tdkmbhtdkr pmir hc hpphsitk cmeks hc tdk erystma. Vdis is emaakf ibvkrsk _ikzh-kaketrie kccket.
3. Wdmt is shbhgrmn8 Nkbtihb its mppaiemtihb.
Uhbhgrmn is m tkedbiquk wdied is uskf th rkehrf tdk shubfs prhfuekf fuk th
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tdk punpibg metihb hc tdk dkmrt usibg uatrmshbies. It mash prhvifks tdk ibchrnmtihbhb dkmrt rmtih, rdytdnieity, jahhf punpibg, vmavk metihb kte.
7. Dhw mehustie grmtibg is is chrnkf8
Wdkb uatrmshbie wmvks mrk pmsskf tdrhugd tdk aiquif ai`k `krhskbk, fuk th
vmrimtihb ib prkssurk, tdk aiquif met ms mehustiema grmtibg. Bhw nhbhedrhnmtieaigdt is pmsskf tdrhugd tdis mehustiema grmtibg, it prhfueks ficckrkbt hrfkrs hcspketrun fuk th ficcrmetihb. [sibg ficcrmetihb ehbfitihb wk emb cibf tdk vkaheity hcuatrmshbies.
4. Wdmt is tdk pribeipak hc UHBMZ ib uatrmshbies8 Nkbtihb twh mppaiemtihbs hcit.
UHBMZ is m fkviek wdied stmbfs chr UHubf BM vigmtihb mbf Zmbgibg. It isjmskf hb tdk pribeipak hc KEDH-UH[BFIBG hc uatrmshbie wmvks. It ismehustiema tkedbiquk chr ahemtibg tdk hjlkets ai`k sujnmribk hr iekjkrgs ib skm jy
trmbsnittibg m digd crkqukbey shubf puask mbf rkekivibg it crhn tdk hjlket. Mppaiemtihbs< (i) It is uskf th ahemtk tdk hjlkets mt tdk jhtthn hc tdk skm.
(ii) It is uskf th cibf tdk fkptd hc tdk skm. (iii) It is uskf chr skisnie (kmrtd qum`k) survky.
9. Dhw mrk uatrmshbie wmvks uskf th nkmsurk tdk fkptd hc skm8
Kedh-shubfibg is tdk pribeipak uskf th cibf tdk fkptd hc tdk skm. M jkmn
hc uatrmshbie wmvks is trmbsnittkf thwmrfs tdk jhtthn hc tdk skm mbf tdk rkcaketkfsigbma is rkekivkf.
Vdk tink ibtkrvma jktwkkb trmbsnittkf mbf rkekivkf sigbma is bhtkf mbf akt itjk —t’. Ic —v’ is tdk vkaheity hc tdk uatrmshbies,
crhn
SkaheityFistmbek trmvkaakf
Vink tm`kb
v _Z Z]
t
v :ZH(mpprhx )
t
ZH Fkptd hc skm vt
:
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=?. Dhw mrk uatrmshbie wmvks fktketkf jy tdkrnma nktdhf8
Wdkb tdk uatrmshbie wmvks mrk pmsskf tdrhugd tdk pamtibun wirk ehbbketkf
th m Wdkmtsthbk’s jrifgk, tdk tknpkrmturk hc wirk edmbgks wdied ib turb edmbgkstdk rksistmbek hc tdk pamtibun wirk. Dkbek Wdkmtsthbk’s jrifgk ghks th ubjmambekfphsitihb. Witd rkspket th tdk jmambeibg phsitihb hc tdk Wdkmtsthbk’s jrifgk,uatrmshbie wmvks mrk fktketkf.
==. Nkbtihb tdk usks hc uatrmshubf ib eaibiema nkfieibk (hr) Nkbtihb tdknkfiema mppaiemtihbs hc uatrmshbies. (i) [atrmshbie wmvks mrk uskf chr fktketibg tunhurs mbf htdkr fkckets ib dunmb
jhfy. (ii) [atrmshbie wmvks mrk uskf th rknhvk `ifbky sthbks mbf jrmib tunhurs witdhut
mby ahss hc jahhf. (iii) [atrmshbie tdkrmpy is uskf th trkmt fiskmsk ai`k bkurmagie mbf rdkunmtie pmibs
kte. =:. Wdy uatrmshbie crkqukbeiks grkmtkr tdmb 5 NDz embbht jk
prhfuekf jy nmgbkthstrietihb nktdhf8
Ib Nmgbkthstrietihb nktdhf, tdk crkqukbey is ibvkrskay prhphrtihbma th tdkakbgtd hc tdk rhf. Vdk crkqukbey emb jk iberkmskf hbay jy fkerkmsibg tdk akbgtd hc tdkrhf th m grkmtkr ibstmbt. It is prmetiemaay inphssijak. Mash, it dms th jk bhtkf tdmttdk mnjikbt tknpkrmturk matkrs tdk nmgbktizmtihb hc tdk rhf mbf ib turb wiaa mcckettdk kamstie prhpkrtiks. Dkbek uatrmshbie crkqukbeiks grkmtkr tdmb 5 NDz embbht jkprhfuekf jy nmgbkthstrietihb nktdhf.
=5. Fkcibk M-Uemb fispamy ib uatrmshbies. M semb is mb mnpaitufk nhfk fispamy. It givks hbk finkbsihbma ibchrnmtihb
mjhut tdk spkeinkb. It is uskf th fktket tdk phsitihb mbf sizk hc tdk camws witdtdk dkap hc edmbgk ib its mnpaitufk.
=6. Aist hut tdk mppaiemtihbs hc uatrmshbie wmvks. (i) Nkmsurknkbt hc fkptd hc tdk skm. (ii) Fktketihb hc camws ib nmtkrimas.
(iii) Euttibg, friaaibg, wkafibg mbf gribfibg. (iv) Upkkf up tdk edkniema rkmetihb (Ehmguamtihb) (v) Zkaikvibg tdk jhfy pmibs
(vi) Eakmbibg mbf fryibg tdk eahtdks.
=;. Aist hut tdk kbgibkkribg/ ibfustrima mppaiemtihbs hc uatrmshbies. (i) Jy hseiaamtibg tdk gamss rhf witd uatrmshbie crkqukbey, dhaks emb jk friaakf ib
tdk dmrf stkka pamtks. (ii) Vdky mrk uskf ib wkafibg mbf euttibg.
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(iii) Vdky mrk uskf ib eakmbibg eahtds mbf tiby pmrts hc wmted. (iv) Vdky mrk uskf th chrn maahys hc ubichrn ehnphsitihbs.
=3. Emb wk usk m ehppkr rhf ib m Nmgbkthstrietihb gkbkrmthr8 Wdy8
Bh, ehppkr rhf embbht uskf th prhfuek uatrmshbie wmvks ib Nmgbkthstrietihb gkbkrmthr. Jkemusk it is bht m Ckrrhnmgbktie nmtkrima.
=7. Givk tdk pribeipak uskf ib nkmsurknkbt hc vkaheity hc jahhf cahw. Wdkb uatrmshbie wmvk stri`ks tdk jahhf vksska, tdk jkmn is rkcaketkf jy
pmrtieaks hc jahhf. Fkpkbfibg uphb tdk vkaheity hc jahhf, tdk rkcaketkf jkmn isFhppakr sdict. Vdkrkchrk jy tdk pribeipak hc fhujak Fhppakr kccket, tdk vkaheity hc
jahhf cahw emb jk emaeuamtkf.
=4. Mb uatrmshubf puask skbt jy m shurek ib skm is rkcaketkf jy m sujnkrgkftmrgkt mt m fistmbek ;97.;? en mbf rkmedks tdk shurek mctkr ?.45 skehbfs.Cibf tdk vkaheity hc shubf ib skm wmtkr.
Givkb< Fistmbek (f) > ;97.;? en Vink tm`kb (t) > ?.45 ske.
Chrnuam<
Skaheity (v ) :f
t
Skaheity(v ):;97.;?
?.45
Skaheity (v ) ==9;.??
?.45
Skaheity (v ) =659.7; n / s
=9. M qumrtz erystma witd m tdie`bkss hc ?.; nn mbf m fkbsity hc :3;? `g/n 5
vijrmtks ahbgitufibmaay prhfueibg uatrmshbie wmvks. Cibf tdk cubfmnkbtma
crkqukbey hc vijrmtihb, ic tdk Yhubg’s nhfuaus hc qumrtz is 7.9 x =?=? Bn-:.
Givkb< Vdie`bkss (t) > ?.; x =?-5 n
Fkbsity ( ύ) > :3;? ̀ g/n5
Yhubg’s nhfuaus (K) > 7.9 x =?=? Bn-: Chrnuam<
Crkqukbey ( c ) _ K
:t
:?.;=?5
Crkqukbey ( c )=;6;9.97
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==?5
:3;?
Cubfmnkbtma crkqukbey ( c ) ;.6;997 NDz
[BIV ― S _DHVHBIEU MBF CIJZK H_VIEU
=. Utmtk tdk prhpkrtiks hc amskr jkmn (hr) cubfmnkbtma edmrmetkristies hc amskrs (hr)Bmnk tdk prhpkrtiks hc amskr wdied mrk nm`ibg it suitmjak chr ibfustrimamppaiemtihbs. (i) Vdk amskr jkmn is digday firketihbma. (ii) It dms digd ibtkbsity. (iii) It dms purkay nhbhedrhnmtie. (iv) It dms ehdkrkbek.
:. Wdmt fh yhu nkmb jy phpuamtihb ibvkrsihb8
Ib gkbkrma, tdk bunjkr hc mthns ib tdk grhubf stmtk wiaa jk nhrk tdmb tdmt hc tdkmthns ib tdk kxeitkf stmtk. Vdis is emaakf usuma phpuamtihb.
Vdk stmtk hc medikvibg nhrk bunjkr hc mthns ib tdk kxeitkf stmtk tdmb tdmt hc tdkmthns ib tdk grhubf stmtk is emaakf phpuamtihb ibvkrsihb.
5. Fkcibk nktmstmjak stmtk. It is tdk stmtk chr wdied tdk aick tink is nhrk tdmb tdk kxeitkf stmtk, i.k., it is tdk
nhrk stmjak stmtk wdied aiks jktwkkb tdk kxeitkf stmtk mbf tdk ahwkr stmtk.
6. Wdy is phpuamtihb ibvkrsihb bkekssmry chr amskr metihb8 (hr) Kxpamib tdk bkkf hcphpuamtihb ibvkrsihb ib tdk prhfuetihb hc amskrs.
Wdkb phpuamtihb ibvkrsihb is medikvkf, tdk nmlhrity hc mthns mrk ib tdk kxeitkfstmtk. Uh tdk mjshrptihb ehkccieikbt wiaa jk bkgmtivk. Vdk bkgmtivk mjshrptihb ehkccieikbtemusks tdk mnpaiciemtihb hc tdk ibeifkbt jkmn jy stinuamtkf knissihb. Vdus tdk amskrjkmn is prhfuekf. Dkbek, phpuamtihb ibvkrsihb is m nust chr tdk prhfuetihb hc amskr jkmn.
;. Wdmt mrk Kibstkib’s ehkccieikbts8
Vdk Kibstkib’s ehkccieikbts M mbf J meehubts chr sphbtmbkhus mbf stinuamtkfknissihb / mjshrptihb prhjmjiaitiks hc aigdt jy m systkn hc pmrtieaks. It mash kxpamibs tdkinphrtmbek hc nktmsmtjak stmtks.
3. Fkcibk Metivk nkfiun mbf Metivk ekbtkr. Vdk nkfiun ib wdied tdk phpuamtihb ibvkrsihb tm`ks pamek is emaakf ms metivk nkfiun. Vdk nmtkrima ib wdied tdk mthns mrk rmiskf th kxeitkf stmtk th medikvk
phpuamtihb ibvkrsihb is emaakf ms metivk ekbtkr.
7. Wdmt is nkmbt jy hptiema rkshbmthr8 (hr) rkshbmbek emvity8
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Mb hptiema rkshbmthr is m ckkfjme` systkn wdied ehbsists hc mb metivk nkfiun `kpt ib
jktwkkb m =??% nirrhr mbf m pmrtima nirrhr. Dkrk tdk ibtkbsity hc aigdt prhfuekf ib tdkmetivk nkfiun is iberkmskf jy nm`ibg tdk aigdt th jhubek jme` mbf chrtd jktwkkb tdknirrhrs. Cibmaay tdk amskr jkmn ehnks tdrhugd tdk pmrtima nirrhr.
4. Emb m twh akvka systkn jk uskf chr tdk prhfuetihb hc amskr8 Wdy8
Bh, twh akvka systkn embbht jk uskf chr tdk prhfuetihb hc amskr. Jkemusk chr phpuamtihb ibvkrsihb th jk medikvkf mt akmst tdrkk akvkas mrk rkquirkf.
9. Aist hut tdk ficckrkbeks jktwkkb m dhahgrmn mbf m pdhthgrmpd (hr) Dhw fhks Dhahgrmpdy ficckrcrhn _dhthgrmpdy8
_dhthgrmpd Dhahgrmn =. Hrfibmry aigdt is uskf.
:. Vdk vmrimtihb hcmnpaitufk mahbk isrkehrfkf.
5. It givks :F pieturk.
6. Akbs is uskf.
=. Amskr aigdt is uskf.
:. Vdk fistrijutihb hcmnpaitufk mbf pdmsk isrkehrfkf.
5. It givks 5F pieturk.
6. Bh akbs is uskf. =?. Wdmt mrk tdk twh typks hc trmbsitihbs tdmt mrk phssijak ib m EH: gms amskr8
(i) Vrmbsitihb crhn msynnktrie nhfk P??=^ th jkbfibg nhfk P?:?^ wiaa knit amskr hcwmvkakbgtd 9.3 αn.
(ii) Vrmbsitihb crhn msynnktrie nhfk P??=^ th synnktrie nhfk P=??^ wiaa knitamskr hc wmvkakbgtd =?.3 αn.
==. Wdmt mrk tdk rhaks pamykf jy B: mbf Dk ib EH: amskr8 (hr) Wdmt mrk tdk cubetihbshc B: mbf Dk ib EH: amskr8
Ib EH: amskr, tdk bitrhgkb (B:) dkaps th iberkmsk tdk phpuamtihb hc mthns ib tdk
uppkr akvka hc EH:. Dkaiun (Dk) dkaps th fkphpuamtk tdk mthns ib tdk ahwkr akvka hc EH: mbf th ehha
tdk fisedmrgk tujk.
=:. Wdmt is tdk rhak pamykf jy Dk ib Dk-Bk amskr8 (hr) Wdmt is tdk cubetihb hc Dk ibDk- Bk amskr8
Ib Dk-Bk amskr, Dkaiun dkaps th iberkmsk tdk phpuamtihb hc mthns crhn ahwkr akvka th uppkr akvka, tdkrkjy prhfueks phpuamtihb ibvkrsihb.
=5. Wdmt is stinuamtkf knissihb hc rmfimtihb8
Mb mthn ib tdk kxeitkf stmtk is ibfuekf th rkturb th grhubf stmtk tdkrkjy rksuatibg ib
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twh ib pdhthbs hc smnk crkqukbey mbf kbkrgy is emaakf ms stinuamtkf knissihb.
=6. Aist hut tdk ehbfitihbs th medikvk amskr metihb. (i) _hpuamtihb ibvkrsihb sdhuaf jk medikvkf. (ii) Utinuamtkf knissihb sdhuaf jk prkfhnibmbt hvkr sphbtmbkhus knissihb.
=;. Nkbtihb tdk ficckrkbt typks hc punpibg nktdhfs ib Amskrs (hr) wdmt mrktdk ficckrkbt nktdhfs hc medikvibg phpuamtihb ibvkrsihb8
(i) Hptiema punpibg (ii) Firket kaketrhb kxeitmtihb
(iii) Ibkamstie mthn-mthn ehaaisihb
(iv) Firket ehbvkrsihb
(v) Edkniema prhekss
=3. Fkcibk dhahgrmpdy.
Dhahgrmpdy fkmas witd inmgk ehbstruetihb jy nkmbs hc ibtkrckrkbek
tkedbiquks witdhut usibg akbsks. Dkrk tdk fistrijutihb hc mnpaitufk mbf pdmsk isrkehrfkf ib 5F nmbbkr sh ms th gkt ehnpaktk ibchrnmtihb hc tdk hjlket th jkpdhthgrmpdkf.
=7. Fistibguisd jktwkkb sphbtmbkhus knissihb mbf stinuamtkf knissihb.
Uphbtmbkhus knissihb Utinuamtkf knissihb
=. Vdk mthn ib tdk kxeitkf stmtk
rkturbs th grhubf stmtk witdhutmby kxtkrbma triggkribg.
:. Knittkf pdhthb trmvkas ibrmbfhn firketihb.
5. Vdk rmfimtihb is akss ibtkbskmbf ibehdkrkbt.
6. Vdk pdhthbs mrk bht ib pdmsk.
;. Vdis prhekss is m `ky cmethrchr hrfibmry aigdt knissihb.
=. Vdk mthn ib tdk kxeitkf stmtkrkturbs th grhubf stmtk jy kxtkrbma triggkribg.
:. Knittkf pdhthb trmvkas ibm pmrtieuamr firketihb.
5. Vdk rmfimtihb is digdayibtkbsk, nhbhedrhnmtie mbfehdkrkbt.
6. Vdk pdhthbs mrk ib pdmsk.
;. Vdis prhekss is m `ky cmethr chramskr hpkrmtihb.
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=4. Aist hut tdk mppaiemtihbs hc amskrs ib Kbgibkkribg.
(i) Digd phwkr amskrs mrk uskcua th jamst dhaks ib fimnhbfs mbf dmrf stkka.
(ii) Vdky mrk uskf th tkst tdk prkskbek hc phrks, erme`s, jahw dhaks kte. ib tdk nmtkrimas
(iii) Vdky mrk uskf chr wkafibg mbf euttibg.
=9. Wdmt is tdk pribeipak hc skniehbfuethr amskr8
Vdk kaketrhbs ib tdk ehbfuetihb jmbf ehnjibks witd m dhak ib tdk vmakbekjmbf mbf dkbek tdk rkehnjibmtihb hc kaketrhb mbf dhak prhfueks kbkrgy ib tdk chrnhc aigdt. Vdis pdhthb, ib turb nmy ibfuek mbhtdkr kaketrhb ib tdk ehbfuetihb jmbf th
vmakbek jmbf mbf tdkrkjy stinuamtk tdk knissihb hc mbhtdkr pdhthb.
:?. Fistibguisd jktwkkb dhnhlubetihb mbf dktkrhlubetihb skniehbfuethramskrs (hr) Wdmt mrk tdk mfvmbtmgks hc dktkrhlubetihb skniehbfuethr amskrth dhnhlubetihb skniehbfuethr amskr8
Dhnhlubetihb amskr Dktkrhlubetihb amskr
=. Dhnhlubetihb amskr is nmfk jym sibgak erystmaaibk nmtkrima.
:. _hwkr hutput is ahw. 5. _uaskf hutput (Uhnktinks
ehbtibuhus) 6. It dms digd tdrksdhaf eurrkbt
fkbsity. ;. Ehst is akss. 3. Aick tink is akss.
=. Dktkrhlubetihb amskr is nmfk jy ficckrkbt
erystmaaibk nmtkrima. :. _hwkr hutput is digd. 5. Ehbtibuhus hutput.
6. It dms ahw tdrksdhaf eurrkbt fkbsity.
;. Ehst is nhrk.
3. Aick tink is nhrk.
:=. Wdmt mrk tdk mfvmbtmgks hc Bf-YMG amskr8
(i) It dms ahwkr kxeitmtihb tdrksdhaf. (ii) Uibek it dms m digdkr tdkrnma ehbfuetivity tdmb Zujy mbf htdkr shaif stmtk
amskrs, it akbfs itskac chr gkbkrmtihb hc amskr puasks mt m digdkr puaskrkpktitihb rmtk hr m qumsi-ehbtibuhus wmvk hpkrmtihb.
(iii) Its kccieikbey is rkamtivkay digdkr.
::. Wdmt is nkmbt jy punpibg8
Bmturmaay, tdk phpuamtihb ibvkrsihb is medikvkf hbay mt bkgmtivktknpkrmturk wdied is inphssijak. Dkbek tdk prhekss jy wdied phpuamtihb
ibvkrsihb is medikvkf jy mrticieima nkmbs is emaakf punpibg.
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:5. Wdmt is spaieibg8 Nkbtihb twh typks hc spaieibg.
Upaieibg is tdk tkedbiquk uskf th ehbbket tdk cijkrs pkrnmbkbtay. Ib tdistkedbiquk, twh cijkrs emb jk lhibkf witd tdk dkap hc kamsthnkr hr chur rhf spaieks usibg
mb mfdksivk hr nmtedibg gka. Vypks< (i) Nkedmbiema Upaieks
(ii) Cusihb Upaieks
:6. Wdmt is tdk jmsie pribeipak hc cijkr hptie ehnnubiemtihb8
Vhtma ibtkrbma rkcaketihb is tdk jmsie pribeipak hc cijkr hptie ehnnubiemtihb systkn. _ribeipak< Wdkb aigdt trmvkas crhn m fkbskr th m rmrkr nkfiun, mt m pmrtieuamr
mbgak hc ibeifkbek emaakf eritiema mbgak, tdk rmy knkrgks mahbg tdk surcmek hc
skpmrmtihb. Wdkb mbgak hc ibeifkbek kxekkfs tdk eritiema mbgak, tdk ibeifkbt rmy isrkcaketkf ib tdk smnk nkfiun mbf tdis pdkbhnkbhb is emaakf thtma ibtkrbma
rkcaketihb.
:;. Fistibguisd jktwkkb stkp ibfkx cijkr mbf grmfkf ibfkx cijkr.
Utkp Ibfkx Cijkr Grmfkf Ibfkx cijkr
=. Vdk ficckrkbek ib rkcrmetivkibfieks jktwkkb tdk ehrk mbfeamffibg is hjtmibkf ib m sibgak stkpmbf dkbek emaakf ms stkp ibfkxcijkr.
:. Vdk aigdt prhpmgmtihb ib tdk chrnhc nkrifihbma rmys. 5. Vdk aigdt rmys pmss tdrhugd tdk
cijkr mxis. 6. It chaahws m zig-zmg pmtd hc
aigdt prhpmgmtihb. ;. It dms ahw jmbfwiftd. 3. Fisthrtihb is nhrk.
=. Vdk ficckrkbek ib rkcrmetivkibfieks jktwkkb tdk ehrk mbfeamffibg grmfumaay iberkmsks crhnekbtrk th ibtkrcmek mbf dkbek emaakfgrmfkf ibfkx cijkr.
:. Vdk aigdt prhpmgmtihb ib tdk chrnhc s`kw rmys.
5. Vdk aigdt rmys fh bht erhss tdk cijkrmxis.
6. It chaahws m dkaiema pmtd hcaigdt prhpmgmtihb.
;. It dms digd jmbfwiftd. 3. Fisthrtihb is vkry akss.
:3. Wdmt mrk metivk mbf pmssivk skbshrs8
Ib metivk skbshrs (hr) ibtribsie skbshrs, tdk pdysiema pmrmnktkr th jk skbskf
firketay mets hb tdk cijkr itskac th prhfuek tdk edmbgks ib tdk trmbsnissihbedmrmetkristies.
Ib pmssivk skbshrs (hr) kxtribsie skbshrs, skpmrmtk skbsibg kaknkbt wiaa jk
uskf mbf tdk cijkr wiaa met ms m guifibg nkfim th tdk skbshrs.
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:7. Wdmt is emaakf nhfk hc prhpmgmtihb ib hptiema cijkrs8
Nhfk hc prhpmgmtihb rkprkskbts tdk bunjkr hc phssijak firketihbs hrpmtd hc prhpmgmtihb hc aigdt tdrhugd tdk hptiema cijkrs. Wdkb sibgak rmy hc aigdtprhpmgmtk tdrhugd m pmtd, tdkb it is emaakf sibgak nhfk mbf wdkb nmby rmysprhpmgmtk tdrhugd ficckrkbt firketihbs, it is emaakf nuatinhfk.
:4. Wdmt is tdk rhak hc eamffibg ib hptiema cijkr8
Mb hptiema cijkr ehbsists hc ehrk wdied is surrhubfkf jy eamffibg. Dkrk tdkrhak hc eamffibg is th nm`k tdk aigdt th succkr thtma ibtkrbma rkcaketihb ibsifk tdkcijkr, smtiscyibg tdk ehbfitihb tdmt tdk aigdt sdhuaf trmvka crhn fkbskr nkfiun thrmrkr nkfiun.
:9. Nkbtihb tdk prhpkrtiks hc fktkethrs uskf ib tdk cijkr hptie ehnnubiemtihb. (i) Mjiaity th ehbvkrt hptiema sigbma ibth kaketriema sigbma (ii) Cmst rksphbsk tink
(iii) \krh fmr` eurrkbt (iv) Ehst kccketivk
5?. Wdmt mrk tdk wmys ib wdied mb hptiema cijkr is emtkghrizkf8 (hr) Dhwmrk cijkrs eamssicikf8
Hptiema cijkrs mrk emtkghrizkf jmskf hb (i) nmtkrima (ii) Bunjkr hc Nhfks
(iii) Zkcrmetivk ibfkx prhciak
Jmskf hb nmtkrima (m) Gamss Cijkr(j) _amstie Cijkr
Jmskf hb Bunjkr hc Nhfks (m) Uibgak nhfk cijkr(j) Nuati nhfk cijkr
Jmskf hb Zkcrmetivk ibfkx prhciak (m) Utkp ibfkx cijkr
(j) Grmfkf ibfkx cijkr5=. Fkcibk Bunkriema Mpkrturk.
Bunkriema Mpkrturk (BM) is fkcibkf ms tdk sibk hc tdk meekptmbek mbgak. Icb= mbf b: mrk tdk rkcrmetivk ibfkx hc tdk ehrk mbf eamffibg rkspketivkay,
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It is m nkmsurk hc tdk mnhubt hc aigdt tdmt emb jk meekptkf jy m cijkr.
5:. Writk mby twh nmlhr mfvmbtmgks hc hptiema cijkr ehnnubiemtihbhvkr htdkr ehbvkbtihbma ehnnubiemtihb systkns. (i) Hptiema ehnnubiemtihb emb jk nmfk kvkb ib tdk mjskbek hc kaketrieity. (ii) Vdk hptiema sigbmas mrk bht mccketkf jy mby kaketriema sigbmas hr aigdtbibg. (iii) Hptiema cijkr ehnnubiemtihb is crkk crhn Kaketrhnmgbktie ibtkrckrkbek
(KNI). (iv) Vdis is suitmjak th mby kbvirhbnkbtma ehbfitihbs. (v) Kmsy nmibtkbmbek, ahbgkr aick, kehbhniema mbf digd qumaity hptiema
sigbma trmbsnissihb. 55. Nkbtihb mby chur mfvmbtmgks hc hptiema cijkr (hr) ckmturks hc hptiema cijkr.
(i) It is aigdt ib wkigdt. (ii) It is snmaakr ib sizk. (iii) It is cakxijak mbf it emb jkbf th mby phsitihb. (iv) It is bhb-ehbfuetivk, bhb-rmfimtivk mbf bhb-ibfuetivk.
(v) Vdkrk is bh sdhrt eireuitibg. (vi) Vdkrk is bh ibtkrbma bhisk / erhss tma`s. (vii) It emb witdstmbf mby rmbgk hc tknpkrmturk. (viii) Bh bkkf th grhubf mbf bh vhatmgk prhjakn heeur.
56. Wdmt is stkp ibfkx cijkr8
Vdk ficckrkbek ib rkcrmetivk ibfieks jktwkkb tdk ehrk mbf eamffibg ishjtmibkf ib m sibgak stkp mbf dkbek emaakf ms stkp ibfkx cijkr.
5;. Wdmt is grmfkf ibfkx cijkr8
Vdk ficckrkbek ib rkcrmetivk ibfieks jktwkkb tdk ehrk mbf eamffibggrmfumaay iberkmsks crhn ekbtrk th ibtkrcmek mbf dkbek emaakf grmfkf ibfkx cijkr.
53. Aist tdk ehbfitihbs th jk smtiscikf chr thtma ibtkrbma rkcaketihb. (i) Aigdt sdhuaf trmvka crhn fkbskr nkfiun th rmrkr nkfiun. (ii) Vdk mbgak hc ibeifkbek (ϛ) hb ehrk sdhuaf jk grkmtkr tdmb tdk eritiema mbgak
(ϛe). i.k. ϛ 2ϛe.
(iii) Vdk rkcrmetivk ibfkx hc tdk ehrk (b=) sdhuaf jk grkmtkr tdmb tdk rkcrmetivkibfkx hc tdk eamffibg (b:).
i.k. b= 2 b:
57. Givk mppaiemtihb hc cijkr kbfhsehpk.
(i) Cijkr hptie kbfhsehpks mrk uskf ib nkfiema fimgbhsis.
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(ii) It is uskf th visumaizk tdk ibbkr hrgmbs hc tdk jhfy. (iii) Cijkr hptie kbfhsehpks mrk uskf ib vmrihus nkfiema cikafs sued msemrfihsehpy,
Ampmrhsehpy, Eysthsehpy kte.
54. Aist hut tdk cmethrs tdmt emusk ahss ib hptiema cijkr. (i) Furibg tdk trmbsnissihb hc aigdt tdrhugd hptiema cijkr, tdrkk nmlhr ahssks
wiaa heeur, viz., mttkbumtihb, fisthrtihb mbf fispkrsihb. (ii) Mttkbumtihb is nmibay emuskf fuk th tdk mjshrptihb, semttkribg mbf rmfimtihb
hc aigdt ibsifk tdk cijkrs. (iii) Fisthrtihb mbf fispkrsihb heeurs fuk th sprkmfibg hc aigdt mbf fuk th
nmbucmeturibg fkckets.
59. Nkbtihb mby chur mfvmbtmgks hc cijkr hptie skbshrs. (i) It dms bh kxtkrbma ibtkrckrkbek
(ii) It is uskf ib rknhtk skbsibg. (iii) Umckty hc fmtm trmbsckr. (iv) It is snmaa ib sizk.
6?. Wdmt mrk tdk rkquirknkbts hc aigdt shureks uskf ib cijkr hptieehnnubiemtihb8
(i) Vdk aigdt prhfuekf nust jk ms bkmray nhbhedrhnmtie ms phssijak. (ii) It nust nhfuamtk tdk shurek mt digd spkkfs. (iii) Vdk aigdt shurek sdhuaf dmvk ehnpmet sizk mbf digd kccieikbey. (iv) It sdhuaf jk rkaimjak, furmjak mbf ibkxpkbsivk. (v) It nust rkquirk vkry snmaa phwkr chr its hpkrmtihb.
(vi) Upketrma aibk wiftd hc tdk shurek sdhuaf jk ms snmaa ms phssijak. (vii) Emb hpkrmtk ehbtibuhusay mt rhhn tknpkrmturk chr nmby ykmrs. (viii) It sdhuaf jk nhfuamtkf hvkr m wifk rmbgk hc crkqukbeiks.