xf.kr
d{kk 4
DIKSHA ,i dSls MkmuyksM djsa\
fodYi 1 % vius eksckby czkmt+j ij diksha.gov.in/app Vkbi djsaA fodYi 2 % Google Play Store esaa DIKSHA NCTE <wa<+s ,oa MkmuyksM
cVu ij tap djsaA
DIKSHA App dks ykWp djs —> App dh leLr vuqefr dks Lohdkj djsa —> mi;ksxdrkZ Profile dk p;u djsaA
ikB~;iqLrd esa QR Code dks Scan djus ds fy, eksckby esa QR Code tap djsaA
eksckbZy dks QR Code ij dsfUnzr djsaA
lQy Scan ds i'pkr~ QR Code ls fyad dh xbZ lwph miyC/k gksxhA
MsLdVkWi ij QR Code dk mi;ksx dj fMftVy fo"k;&oLrq rd dSls igq¡ps \ eksckby ij QR dksM dk mi;ksx dj fMftVy fo"k; oLrq dSls çkIr djsa \
QR Code ds uhps 6 vad dk Alpha
Numeric Code fn;k x;k gSA czkmt+j esa diksha. gov.in/cg VkbZi djsaA
lpZ ckj ij 6 fMftV dk QR CODE VkbZi djsaA
izkIr fo"k;&oLrq dh lwph ls pkgh xbZ fo"k;&oLrq ij fDyd djsaA
jkT; 'kSf{kd vuqla/kku vkSj izf'k{k.k ifj"kn~ NÙkhlx<+] jk;iqj
l= 2021&22
,l-lh-bZ-vkj-Vh- & NÙkhlx<+
ekxZn'kZu ,oa lg;ksx
MkW- ân;dkUr nhoku ¼fo|k Hkou] mn;iqj½ la;kstd
MkW- fo|korh pUnzkdj leUo; ,oa lEiknu
MkW- lq/khj JhokLro ys[kd e.My
MkW- lq/khj JhokLro] vkj-ds- lsaxj] e/kq xqIrk] uUnyky 'kkg] gseUr ik.khxzkgh]
uhys'k oekZ] 'kadj flag jkBkSj] gfj'kadj iVsy] izeksn iVsy] v'kksd egk.kk] izseizdk'k 'kqDyk] lat; nsokaxu] jtuh f}osnh] xkSjh 'kekZ] vt; xqIrk] js.kq cksfnZ;k] lat; cksfy;k]
nhid ea=h] xksiky pkSchlk]
vkoj.k i`"B js[kjkt pkSjkxM+s
QksVksxzkQ
,l- vgen ¼vafre vkoj.k i`"B½ fp=kadu
,l- iz'kkUr
Vad.k ,oa ys vkmV fMtkbfuax ,l- ,e- bdjke] eqdqUn lkgw] lqjs'k lkgw
izdk’kd
NŸkhlx<+ ikB~;iqLrd fuxe] jk;iqj ¼N-x-½ eqnzd
eqfnzr iqLrdksa dh la[;k & ---
ikB~;p;kZ] ikB~;iqLrd] f'k{k.k izfØ;k vkfn lHkh vk;keksa dks lqn`<+ djuk jkT; 'kSf{kd vuqla/kku vkSj izf'k{k.k ifj"kn~
dk dk;Z gSA blh fn'kk esa vkjaHk ds dqN o"kksZa esa ikB~;Øe dks fu;ksftr djus ds lkFk&lkFk ikB~;iqLrd ys[ku dk dk;Z fd;k x;k gSA ikB~;iqLrdksa dh bl Ük`a[kyk esa geus xf.kr dks ,d O;kid {kerk ds :i esa fy;k gS ftldk ,d gh fgLlk la[;kvksa o ml ij lafØ;kvksa ls lEcfU/kr gSA blhfy, ikB~;Øe esa xf.kr ds vU; vk;keksa dks Hkh LFkku fn;k x;k gSA tSlk fd 2005 ds jk"Vªh; nLrkost esa Hkh dgk x;k gS] geus loky ds mRrj [kkstuk o dyu ¼algorithm½ ykxw djuk viuk mn~ns'; ugha ekuk gSA iqLrd esa geus cPpksa dks lkspus] vkil esa ckrphr djus] voèkkj.kk,¡ dks le>us ij tksj fn;k gSA geus ;g Hkh ekuk gS fd Hkk"kk ds ljy mi;ksx dks xf.kr ls tksM+us ls muds rkfdZd <k¡ps etcwr gksaxs o vo/kkj.kk,¡ Li"V gksxhA
xf.kr f'k{kd ;g dksf'k'k djrs gSa fd muds Nk=ksa dks v/;;u esa etk vk,] mudh d{kk thoUr cusA xf.kr D;ksa Mjkus yxrk gS vkSj blls yksx D;ksa nwj Hkkxrs gSa\ bu lokyksa dk iDdk mRrj fdlh ds ikl ugha gSA vyx&vyx rjg ls ge lc bl iz;kl esa tqVs gSaA ;g iqLrd Hkh ,sls gh iz;kl dks 'kq: djus dk ,d rjhdk gSA lh[kus dks ljy o ljl cukus ds lkFk&lkFk ,d vkSj egRoiw.kZ ckr ;g gS fd cPpksa ds fy, xf.kr flQZ iqLrd o d{kk rd gh lhfer u gks oju~ os mls vius vkl&ikl ls tksM+ ik,¡A os flQZ lafØ;k,¡ djus esa l{ke u gksa oju~ ;g Hkh tku ldsa fd fdl loky esa] dkSu lh ifjfLFkfr esa] D;k] dkSu lh lafØ;k bLrseky djuh gSA fofHkUu rjhdksa o tYnckth ls cprs gq, cPps ewy ckr dks le> ik,¡A
gekjk ekuuk gS fd fdlh fo"k; ds f'k{k.k esa Hkk"kk ds mi;ksx dk cM+k ;ksxnku gSA vr% iz;kl gS fd cPps fl)kUrksa o ifjHkk"kkvksas dks vius 'kCnksa esa O;Dr dj ik,¡ vkSj bu lc ij laokn dj ik,¡A dgha Hkh tfVy o cksf>y rduhdh 'kCnkoyh mi;ksx ugha dh xbZ gSA iqLrd cPpksa dks lEcksf/kr gS vkSj ;g vis{kk gS fd /khjs&/khjs os iqLrd dks Lo;a i<+ dj le> ik,¡xs o mlds vuqlkj fØ;k dj ik,¡xsA dksf'k'k ;g gS fd cPps xfrfof/k;ksa] fØ;kvksa o lokyksa dks Lo;a vFkok lewg esa djrs gq, vo/kkj.kkvksa dks vkRelkr djsa o vius fnekx esa fo"k; dh cqfu;knh vo/kkj.kkvksa dk etcwr <k¡pk cuk ldsaA geus dksf'k'k dh gS fp=ksa dk Hkjiwj mi;ksx gks vkSj cPps fp= cuk,¡] loky cuk,¡ o igsfy;k¡ jpsaA gesa vk'kk gS fd ;g iqLrd xf.kr dks o 'kkyk ds okrkoj.k dks vkuUniw.kZ o jksekapd cukus esa enn nsxhA
tc vki ;g iqLrd i<+ jgs gksa ;k i<+k jgs gksa rks gks ldrk gS dgha&dgha vkidks yxs fd ^^;g Bhd ugha gS**A ,sls fcUnqvksa ds ckjs esa gesa t:j crkb,A ;g Hkh crkb, fd ogk¡ D;k gksA dqN phtsa 'kk;n vkidks ,slh Hkh feyas ftUgsa ns[kdj yxs
^^;g vPNk gS** --- gesa bu phtksa ds ckjs esa Hkh crk,¡A vkids ;s vuqHko iqLrd dks csgrj cukus esa gekjh enn djsaxsA vki tkurs gSa fd nl vadksa ij vk/kkfjr vk/kqfud la[;k iz.kkyh Hkkjr esa gh tUeh vkSj iwjs fo'o us bls viuk;kA bl la[;k iz.kkyh esa ftu nl vad izrhdksa dk mi;ksx fd;k tk jgk gS muds ewy Lo:i Hkkjrh; nsoukxjh fyfi ds gSaA ns'k dh vkus okyh ihf<+;k¡ bUgsa igpkusa vkSj bu ij xoZ dj ldsa bl mn~ns'; ls mu ij vH;kl ds volj ikB~; iqLrd esa tksM+s tk jgs gSaA
Ldwy f'k{kk foHkkx ,oa jkT; 'kSf{kd vuqla/kku vkSj çf'k{k.k ifj"kn~] N-x- }kjk f'k{kdksa ,oa fo|kfFkZ;ksa esas n{krk lao/kZu gsrq vfrfjDr ikB~; lalkèku miyCèk djkus dh n`f"V ls ETBs (Energized Text Books) ,d vfHkuo ç;kl gSA budk vkWu ykbu ,oa vkWQ ykbu ¼MkmuyksM djus ds mijkar½ mi;ksx fd;k tk ldrk gSA ETBs dk çeq[k mn~ns'; ikB~;oLrq ds vfrfjDr vkWfM;ks&ohfM;ks] ,uhes'ku QkWjesV esa vfèkxe lkexzh] vH;kl] ç'u ,oa f'k{kdksa ds fy, lanHkZ lkexzh çnku djuk gSA
xf.kr vkSj i;kZoj.k v/;;u dks loZtu ds fy, jkspd cukus dh bl ;k=k esa vki gekjs lkFk pysa rks ge feydj dqN dj ik,¡xsA
lapkyd
jkT; 'kSf{kd vuqla/kku vkSj izf'k{k.k ifj"kn~
NÙkhlx<+] jk;iqj
NRrhlx<+ jkT; 'kSf{kd vuqla/kku vkSj izf'k{k.k ifj"kn~ ds }kjk rS;kj dh xbZ d{kk&4 dh xf.kr dh ikB~;iqLrd vkids lkeus gSA iqLrd dk mn~ns'; d{kk&3 esa xf.kr lh[kus&fl[kkus ls lEcfU/kr tks dk;Z gqvk gS mldh le> dks lqn`<+ djuk rFkk blh Øe esa cPpksa ds xf.krh; dkS'kyksa o {kerkvksa dks c<+kuk gSA d{kk&3 dh iqLrd mi;ksx djrs le;
vkius ns[kk gh gksxk fd blesa ftl rjg dh xf.kr dh d{kk dh dYiuk gS mlesa fl[kkus o le>kus dh vis{kk lh[kus o le>us ij T;knk tksj gSA cPpksa dks fØ;k'khy gksuk gS vkSj lokyksa dk gy Lo;a lkspuk gSA
vkerkSj ij xf.kr i<+krs oDr cPpksa ls ;g vis{kk dh tkrh gS fd cPps lokyksa dks fl[kk, x, rjhdksa ;k fu;eksa ds vuqlkj gy dj ldsa] pkgs mUgksaus ml loky dks gy djus ds fy, t:jh vo/kkj.kkvksa ;k dkS'kyksa dks le>k gks ;k ughaA ifj.kkeLo:i cPps bu lh[ks x;s fu;eksa ;k rjhdksa dks ykxw djus esa xyfr;k¡ djrs gSaA blh le> dks izeq[k :i ls cnyus dk iz;kl gesa djuk gSA cPps ;fn loky ls lEcfU/kr cqfu;knh vo/kkj.kkvksa dks le> ysa rks fQj mUgsa vyx&vyx gy o rjhds ;kn djus dh vko';drk ugha gSA cPpksa dks cgqr ls vyx&vyx rjg ds lokyksa dks gy djus dk vH;kl djuk pkfg, vkSj gy djrs le; fdl rjhds ls gy djuk gS ;g lkspus dk ekSdk feyuk pkfg,A
'kq:vkr esa xf.krh; lafØ;kvksa dks le>us ds fy, Bksl oLrqvksa ds lkFk vuqHko t:jh gksrk gSA Bksl oLrqvksa ds lkFk T;knk ls T;knk dk;Z djuk vo/kkj.kkvksa dks le>us o mudks iq[rk djus esa enn djrk gSA ysfdu /khjs&/khjs cPpksa dks blds fy, rS;kj fd;k tkuk pkfg, fd os la[;kvksa o xf.krh; fpàksa dh vewrZrk dks le> ldsa rFkk Bksl oLrqvksa dh lgk;rk ds cxSj Hkh xf.kr dj ldsaA xf.kr dh vo/kkj.kk,¡ vewrZ gksrh gSaA mnkgj.k ds fy, ge la[;k dh ckr djrs gSaA 3 dks le>us ;k crkus ds fy, ge 3 dqlhZ] 3 Vscy] 3 cdfj;k¡ ,slk dg ldrs gSa] ij rhu fdlh Hkh lanHkZ ls ca/kk ugha gSA 3 dk LorU= vfLrRo gS tks dsoy mlds eku ij vk/kkfjr gSA gesa /khjs&/khjs 3 dks oLrqvksa ds lewg ls vyx ns[k ikus dh {kerk cPpksa esa ykuh gksrh gSA vewrZrk dh vksj c<+uk d{kk 3 o 4 esa vkSj T;knk gksrk gSA xf.kr f'k{k.k dk ,d mn~ns'; cPpksa esa vewrZ fparu dh {kerk c<+kuk Hkh gS vkSj vewrZrk ls bl izdkj tw>uk bl {kerk dks Hkh c<+krk gSA
cPpksa ds vuqHkoksa dks xgjk djus o fo'ys"k.k djus esa Hkk"kk dh Hkwfedk egRoiw.kZ gSA cPps i<+dj lkexzh dks le> ldsa rFkk mlls lEcfU/kr fopkj vU; yksxksa ds lkeus O;Dr dj ldsa o le>k ldsa blds fy, muds ikl f'k{kd ls laokn o vkilh ppkZ ds i;kZIr ekSds gksus pkfg,A mUgsa bl ckr dh Hkh LorU=rk gksuh pkfg, fd os viuh ifjHkk"kk,¡ o fl)kUr viuh
vr% d{kk esa lewgksa esa dk;Z djus] laokn o lkewfgd :i ls d{kk ds lkeus viuh ckr j[kus ds ekSds cukuk Hkh t:jh gSA
;g Hkh t:jh gS fd cPps ftl vo/kkj.kk dks lh[kus dh dksf'k'k dj jgs gSa ml vo/
kkj.kk ls lEcfU/kr <sj lkjs bckjrh loky djus o bckjrh lokyksa dks xf.krh; rF; esa cnyus dk dke Hkh os djsaA bl rjg ds cgqr ls loky gy djuk cPpksa dks xf.krh; lafØ;kvksa dks le>us o muds vFkZ nsus esa enn djrk gSA
tSlk fd igys Hkh dgk gS] fdlh Hkh vo/kkj.kk ls lEcfU/kr vyx&vyx rjg ds loky djus ls cPpksa dks viuh le> dks iDdk djus esa enn feyrh gSA fofHkUu rjg ds loky djrs gq, cPpksa dks viuh xyfr;k¡ idM+us o le> dks csgrj cukus dk ekSdk Hkh feyrk gSA vr%
vkils vis{kk gS fd vki iqLrd esa nh xbZ lkexzh ds vykok Hkh vU; u,&u, loky cuk;sa vkSj ubZ&ubZ xfrfof/k;k¡ [kkstsaA
xf.kr dh vo/kkj.kk,¡ ,d&nwljs ls tqM+h gqbZ gksrh gSaA mnkgj.k ds fy, ;fn cPps us tksM+ lh[k fy;k gS rks og xq.kk dh vo/kkj.kk dks lh[kus esa enn djrk gS vkSj lkFk gh xq.kk dh vo/kkj.kk] tksM+ dh le> dks csgrj cukus esa enn djrh gSA xf.kr flQZ d{kk rd gh lhfer u jgs oju~ cPps ds lkFk mlds ?kj Hkh tk,A blds fy, cPps ds vkl&ikl o nSfud thou esa xf.kr ls lEcfU/kr vuqHkoksa dks Hkh d{kk esa LFkku nsuk gksxkA ;g bl iqLrd dk igyk laLdj.k gSA bl iqLrd dks cPpksa ds lkFk mi;ksx esa ysrs gq, ;fn vkidks dgha leL;k vkrh gS rks vki gesa t:j fy[kdj crk,¡A bls vkSj csgrj dSls cuk;k tk ldrk gS blds fy, lq>ko Hkh ifj"kn~ dks vo'; HkstsaA
lapkyd
jkT; 'kSf{kd vuqla/kku vkSj izf'k{k.k ifj"kn~
NÙkhlx<+] jk;iqj
v/;k; ikB dk uke lh[kus ds vf/kxe i`"B Ø-
1- la[;k,¡ & 1&10
2- tksM+uk&?kVkuk M403 11&30
3- xq.kk&Hkkx M401, M402, M419 31&41
4- fHkUu M404, M405, M406 42&54
5- lefefr ,oa txg
dh le> M410, M420 55&58
6- ekiu M403, M413, M414, M415 59&74 7- le; M415, M416, M417, M418 75&83
8- T;kfefr M407, M409 84&97
9- ifjeki M412 98&102
10- {ks=Qy M408, M412 103&107
11- eqnzk M403 108&111
12- vk¡dM+ksa dk fu:i.k M421 112&118
13- phtsa dSlh fn[krh gSa \ M411 119&121
14- iSVuZ vkSj igsfy;k¡ M408, M420 122&129
15- gekjs nsoukxjh vad]
ifjp; vkSj vH;kl & 130&151
izLrkfor v/;kiu izfØ;k
f’k{kkFkhZ dks tksM+s@lewg@O;fDrxr rkSj ij volj miyC/k djkrs gq;s] fuEukafdr gsrq izksRlkfgr djuk pkfg,A
• fofHkUu rjhdksa tSls NksM+dj fxuuk] izfr:iksa dk foLrkj vkfn ds ek/;e ls xq.ku rF;ksa dks [kkstuk rFkk fy[kukA tSls 3 dk igkM+k cukus gsrq fo|kFkhZ NksM+dj fxuuk]
ckjckj ;ksx ;k fuEukafdr iSVuZ dk mi;ksx dj ldrk gSA
• nks vadksa dh la[;k dk foLrkj rFkk xq.ku tSls 23 dk 6 ls xq.kk fuEukuqlkj gy fd;k tk ldrk gSA
23 × 6 ¾ ¼20 $ 3½ × 6 ¾ 20 × 6 $ 3 × 6 ¾ 120 $ 18
¾ 138
• nSfud thou dh leL;kvksa ij xq.ku ds mi;ksx ls iz'u cukuk rFkk gy djukA tSls ;fn ,d isu dh dher 35 :- gS] rks 7 isu dh dher fdruh gksxh\
• xq.ku gsrq ekud dyu fof/k ij ppkZ ,oa fodkl djukA
• Hkkx fØ;k gsrq lewg cukuk tSls & 24 » 3 ¾
vFkkZr ;g Kkr djuk fd 24 esa 3 ds fdrus lewg gks ldrs gSa ;k fdrus 3 feydj 24 curs gSaA
• xf.krh; dFkuksa ij vk/kkfjr izklafxd iz’uksa dk fuekZ.k djukA tSls & dFku 25&10 ¾15] ij vyx&vyx fo|kFkhZ vyx&vyx izfrfØ;k ns ldrs gSa] ,d fo|kFkhZ ;g iz’u cuk ldrk gS ^^esjs ikl 25 lsc Fks] 10 lsc [kk fy;s rks fdrus lsc 'ks"k gSa\
• lewg dk;Z ds ek/;e ls izklafxd iz'u dk fuekZ.k djuk tSls iwjh d{kk dks nks lewg esa ckaVuk vkSj ,d lewg iz'u iwNs rFkk nwljk lewg fofHkUu lafØ;kvksa dk mi;ksx dj mUgsa gy djsa] blh izdkj nwljk lewg iz'u djs rks igyk mls gy djsA
• fHkUu la[;k,a tSls vk/kk] ,d pkSFkkbZ] rhu pkSFkkbZ ij ppkZ djuk rFkk mudk nSfud thou ls laca/k LFkkfir djukA
• fHkUukRed la[;kvksa dks fp=ksa@dkxt dks eksM+us dh xfrfof/k;kssa }kjk izLrqr djuk tSls &
¼1½ fp= ds vk/ks Hkkx esa jax Hkjsa
M401. la[;kvksa dh lafØ;kvksa dk mi;ksx nSfud thou esa dj ldrk gSA 2 rFkk 3 vadksa dh la[;kvksa dk xq.kk dj ldrk gSA
M402. ,d la[;k ls nwljh la[;k dks fofHkUu fof/k;ksa ls Hkkx ns ldrk gSA tSls fp=kys[k }kjk
¼fcUnqvksa dk vkys[ku dj½] cjkcj ckaVdj]
ckjackj ?kVkdj ]Hkkx rFkk xq.ku ds varZlaca/kksa dk mi;ksx djdsA
M403. nSfud thou ls lanfHkZr eqnzk] yEckbZZ] Hkkj]
vk;ru vkfn ls lacaf/kr la[;kvksa dh pkj lafØ;kvksa ij vk/kkfjr iz’uksa dh jpuk o gy dj ldrk gSA
M404. fHkUuksa ij dk;ZA ,d fn;s x;s fp= vFkok oLrqvksa ds lewg esa vk/kk] ,d pkSFkkbZ] rhu pkSFkkbZ Hkkx dks igpku ldrk gSA M405. la[;kvksa@la[;kadksa dh enn ls fHkUuksa dks
vk/kk] ,d pkSFkkbZ rFkk rhu pkSFkkbZ ds :i esa fUk:fir dj ldrk gSA
M406. fdlh fHkUUk dk vU; fHkUu ls rqY;rk fn[kk ikrk gSSA
M407. vius ifjos’k ls fofHkUu vkd`fr;ksa ds ckjs esa le> vftZr djrk gSA o`Rr ds dsUnz] f=T;k rFkk O;kl dks igpkurk gSA
M408. mu vkd`fr;ksa dks [kkstrk gS ftudk mi;ksx Vkby yxkus esa fd;k tk ldrk gSA M409. fn, x, tky ¼usV½ dh enn ls ?ku@?kukHk
cuk ldrk gSA
M410. dkxt eksM+dj@dkVdj] L;kgh ds /kCcksa }kjk]
ijkorZu leferrk iznf’kZr dj ldrk gSA vf/kxe ifj.kke (Learning Outcomes) f’k{kkFkhZ %
• vyXk&vyx f=T;k ds o`Ÿk cukukA
• ?kjksa@QqVikFk@fofHkUu bekjrksa ij yxh
• fofHkUu vkd`fr dh Vkby ds voyksdu ij ppkZA
• Lo;a dh Vkby dk fuekZ.k dj iqf"V djuk fd og VslysV (Tessellate) djrh gS ;k ughaA
• d{k ds d{kk ds fofHkUu oLrqvksa dks vyx&vyx n`f"Vdks.kksa ls ns[kuk rFkk bl n`f"Vdks.k ds vk/kkj ij mudk fp=
cukukA tSls&,d fxykl lkeus ls bl rjg ls fn[krk gS rks iz'u tSls & ^^ijUrq ;g Åij ls fdl rjg fn[ksxk** ;k
^^;g uhps ls fdl rjg dk fn[ksxk** iwNs tk ldrs gSaA
• :i;s dks iSls esa ifjofrZr djuk tSls & 20 :- esa 50 iSls ds fdrus flDds izkIr gks ldrs gSaA
• fcy cukuk rkfd fo|kFkhZ fcy cukrs le; pkjksa lafØ;k,a
;ksx@varj@xq.ku@Hkkx dk iz;ksx djsaA
• fdlh oLrq dh yackbZ@nwjh dk vuqeku yxkuk fQj okLrfod :i ls bls ukidj iqf"V djukA tSls&vius iyax dh yackbZ dk vuqeku yxkuk vFkok Ldwy ds xsV ls d{kk dh nwjh dk vuqeku yxkuk fQj okLrfod :i ls ukidj iqf"V djukA
• ,d rjktw cukdj ekud ckaVksa ls oLrqvksa dk otu djukA
;fn ekud ckV miyC/k u gksa rks ekud otu okys iSdsV dk mi;ksx fd;k tk ldrk gS] tSls fdyksxzke nky dk iSdsV] 200 xzke ued dk iSdsV] 100 xzke fcLdqV dk iSdsVA
• 500 xzke ds iSdsV ds LFkku ij 250 xzke ds nks iSdsV iz;ksx djuk ¼;k leku otu ds iRFkj dk mi;ksx½
• ik=ksa dk vk;ru ekius gsrq Lo;a dh ekiuh cukukA tSls&
200 fe-yh- dh cksry dk iz;ksx fdlh tx ;k crZu esa ikuh dh ek=k ekius gsrq ekiu bdkbZ ds :i esa djukA
• dSysaMj dk voyksdu rFkk v/;;u djuk rFkk ;g tkudkjh izkIr djuk fd ekg@o"kZ esa fdrus lIrkg gksrs gSaA fo|kFkhZ izR;sd ekg esa fnuksa dh la[;k rFkk fnu fdl izdkj rkjh[kksa ls lacaf/kr gksrs gSa vkfn iSVuZ ¼izfr:i½ dks [kkstsaA
• d{kk ds vanj@ckgj ?k.Vs vkSj feuV esa le; crkus@i<+us ds vuqHko dk mi;ksx djukA
• vkxs fxuuk ;k ;ksx@varj ds mi;ksx ls fdlh ?kVuk esa yxus okys le; dh x.kuk djuk A
• vius ifjos"k ls iSVuZ @fMtkbu [kkstuk ¼vkd`fr;ksa rFkk la[;kvksa dk iz;ksx dj½] vkSj ,sls iSVuZ dks cukuk vkSj foLrkj djukA
• nSfud thou dh xfrfof/k;ksa ls tkudkjh ,d= djuk rFkk muls vFkZiw.kZ fu"d"kZ fudkyukA bu vuqHkoksa dk iz;ksx dj fo|kfFkZ;ksa dks vkadM+ksa ds laxzg.k ¼MkVk gSaMfyax½ lacaf/kr xfrfof/k;ksa esa layXu djukA
• v[kckjksa@if=dkvksa ds vkadM+ksa@n.M vkjs[k dks i<+uk
lkbM n`’; (Side View) dk fp=kadu dj ldrk gSA
M412. ljy T;kferh; vkd`fr;ksa ¼f=Hkqt] vk;r]
oxZ½ dk {ks=Qy rFkk ifjeki ,d nh gqbZ vkd`fr dks bdkbZ ekudj Kkr dj ldrk gSA tSls & fdlh Vscy dh Åijh lrg dks Hkjus ds fy;s ,d tSlh fdruh fdrkcksa dh vko’;drk iM+sxhA
M413. ehVj dks lsaVhehVj o lsaVhehVj dks ehVj esa cny ldrk gSA
M414. fdlh oLrq dh yackbZ nks LFkkuksa ds chp dh nwjh] fofHkUu oLrqvksa ds Hkkj] nzo dk vk;ru vkfn dk vuqeku yxk ldrk gS rFkk okLrfod eki }kjk mldh iqf"V djrk gSA M415. nSfud thou esa yackbZ] nwjh] otu] vk;ru rFkk le; ls lacaf/kr iz’uksa dks pkj ewyHkwr xf.krh; lafØ;k dk mi;ksx dj gy dj ldrk gSA
M416. ?kM+h ds le; dks ?k.Vss rFkk feuV esa i<+
ldrk gS rFkk mUgsaa.m./p.m. ds :i esa O;Dr djrk gSA
M417. 24 ?k.Vs dh ?kM+h dks 12 ?k.Vs dh ?kM+h ls lacaf/kr dj ldrk gSA
M418. nSfud thou dh ?kVukvksa esa yxus okys le; varjky dh x.kuk] vkxs@ihNs fxurh tksM+us@?kVkus ds ek/;e ls dj ldrk gSA M419. xq.ku rFkk Hkkx esa iSVuZ dh igpku djrk
gSA ¼9 ds xq.kd rd½
M420. lefefr ij vk/kkfjr T;kferh iSVuZ dk voyksdu] igpku dj mudk foLrkj dj ldrk gSA
M421. bdV~Bk dh xbZ tkudkjh dks lkj.kh]
n.Mkjs[k ds ek/;e ls iznf’kZr dj muls fu"d"kZ fudky ldrk gSA
la[;k,¡
gtkj dk ifjp;
crkvks vkSj fxurkjs esa Hkh fn[kkvksA
lcls NksVh lcls cM+h
la[;k la[;k
1- ,d vad dh lcls NksVh vkSj lcls cM+h la[;kA
&&&&&&&&] &&&&&&&&
2- nks vadksa dh lcls NksVh vkSj lcls cM+h la[;kA
&&&&&&&&] &&&&&&&&
3- rhu vadksa dh lcls NksVh vkSj lcls cM+h la[;kA
&&&&&&&&] &&&&&&&&
vc crkvks&
9 $ 1 = &&&&] 9 ds ckn vkrk gS &&&&
99 $ 1 = &&&&] 99 ds ckn vkrk gS &&&&
blh izdkj&
999 $ 1 = \] 999 ds ckn D;k vk,xk\ &&&&
la[;k,¡
v/;k; 1
fQj rks] bdkbZ dh NM+ dks [kkyh djds] bu
nl eksfr;ksa ds cnys ngkbZ dh NM+ ij ,d
eksrh Mkyuk gksxkA
jktw vkSj pank Hkh ;g tkuus dh dksf'k'k dj jgs gSaA
crkvks] jktw vkSj pank D;k djsaxs\
crkvks] jktw vkSj pank D;k djsaxs\
crkvks] jktw vkSj pank D;k djsaxs\
crkvks] jktw vkSj pank D;k djsaxs\
crkvks] jktw vkSj pank D;k djsaxs\
bdkbZ dh NM+ ij ,d eksrh vkSj Mkyuk pkgas rks ml ij ugha
vk,xk] D;ksafd ,d NM+ ij ukS eksrh gh vk ldrs gSaA jktw bl fxurkjs
ij bdkbZ] ngkbZ vkSj lSdM+s dh NM+ksa ij ukS&ukS eksrh gSaA bl rjg ukS lkS fuU;kuos dh la[;k iznf'kZr gks
jgh gSA vxj blesa bdkbZZ ds LFkku ij ,d eksrh vkSj c<+k nsa]
rks D;k gksxk\
ysfdu] ngkbZ dh NM+ ij Hkh ukS eksrh igys ls gh gSa vr% ngkbZ dh NM+ dks [kkyh djds bu nl eksfr;ksa
ds cnys lSdM+s dh NM+ ij ,d eksrh Mkyuk gksxkA
vksg! ysfdu lSdM+s ij Hkh rks ukS&ukS eksrh igys ls gSaA
vc D;k djsa\
rc rks lSdM+s dh NM+ dks [kkyh djds bu nl eksfr;ksa ds cnys ,d eksrh vxys LFkku ij Mkyuk gksxkA vr% gesa ,d u;h NM+ dh vko';drk gksxh vFkkZr~ ,d u;k LFkku cukuk gksxkA bl vxys LFkku dks ge gtkj dgrs gSaA vr% lSdM+s ds nl eksfr;ksa ds cnys ,d eksrh gtkj dh NM+ esa MkysaxsA
vc crkvks&
999 esa 1 feykus ij dkSu&lh la[;k cusxh\ bls dSls fy[ksaxs\ ---
;g Hkh crkvks&
1 $ 1 $ 1 $ 1 $ 1 $ 1 $ 1 $ 1 $ 1 $ 1 = 10
;kuh nl bdkb;k¡ = --- ngkbZ
10 $ 10 $ 10 $ 10 $ 10 $ 10 $ 10 $ 10 $ 10 $ 10 = 100
;kuh nl ngkb;k¡ = --- lSdM+k
blh rjg&
100 $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 = 1000 nl lSdM+s = --- gtkj
jktw vkSj pank us fxurkjksa ij dqN la[;k,¡ iznf'kZr dh gSaA bUgsa i<+ks rFkk la[;kvksa dks vadksa vkSj 'kCnksa esa fy[kks&
lS-lS- n- b- lS- g-
lS- n- b- g-
3 1 4 2 rhu gtkj ,d lkS c;kyhl
lS-lS- n- b-
g- g- lS-lS- n- b-
ala[;k dks vadksa vkSj 'kCnksa esa fy[kksA
1- 4321 --- 2- 1234 --- 3- 2222 ---
4- --- N% gtkj ukS lkS ipkl
5- 7089 ---
6- --- vkB gtkj N% lkS nks
7- --- ukS gtkj uCcs
8- 3007 --- 9- 5671 ---
10- --- N% gtkj lkr lkS bdlB
lgh la[;k ij yxkvksA
rhu gtkj lkr lkS mulB 769 3759 3957 3579
ik¡p gtkj rhu lkS chl 5302 5203 5320 5023
,d gtkj nks 1002 1020 1200 1000
N% gtkj nl 60010 6010 6100 6001
nks gtkj rhu lkS mugÙkj 2369 2963 2379 230069
pkj gtkj nks lkS nl 40210 4210 4012 40120
iwjk djksA
1- 1234 = 1 g- $ 2lS- $ 3n- $ 4b- = 1000 $ 200 $ 30 $ 4
2- 2430 = $ $ $ = $ $ $
3- --- = $ $ $ = 3000 $ 100 $ 0 $ 5
4- --- = 6 g- $ 0lS- $ 8n- $ 8b- = $ $ $
5- --- = $ $ $ = 5000 $ 400 $ 0 $ 0
6- --- = 9 g- $ 0lS- $ 0n- $ 1b- = $ $ $
lgh tksM+h cukvksA
1- 4306 5000 $ 0 $ 60 $ 1
2- 1534 1000 $ 300 $ 50 $ 4
3- 4603 4000 $ 300 $ 0 $ 6
4- 1354 1000 $ 500 $ 30 $ 4
5- 5601 4000 $ 600 $ 0 $ 3
6- 5061 5000 $ 600 $ 0 $ 1
Øe iwjk djksA
1- 1207] ---] 1209] ---] 1211] ---
2- 203] 303] 403] ---] ---] ---] --- 3- 2399] ---] 2401] ---] ---] --- 4- 755] 745] 735] ---] ---] ---] --- 5- 999] 888] 777] ---] ---] ---] ---
cM+h la[;k crkvksA
cM+h la[;k dSls irk yxk\
1- 5336 vkSj 2336 esa
2- 2135 vkSj 2155 esa
3- 1523 vkSj 1323 esa
4- 3427 vkSj 3347 esa
7 6 5 4 3 2 1
1 2 3 4 5 6 7
lgh vkSj xyr dFku igpkuksA xyr dFku dks lgh djksA
t Sl s& 5356 > 4213> 3915 > 2999 ¼lgh ½
1. 1515 < 5151 < 6345 < 7135 ¼ ½ ---
2. 1239 < 1042 < 1043 > 1051 ¼ ½ ---
3. 8976 < 8796 > 7321 > 5432 ¼ ½ ---
4. 5601 < 6510 < 7345 < 8342 ¼ ½ ---
5. 4259 < 5942 > 6724 > 9243 ¼ ½ --- dksbZ Hkh ik¡p la[;k,¡ yksA mUgsa NksVs&cM+s fpg~u dk mi;ksx djrs gq, igys ?kVrs Øe esa o fQj c<+rs Øe esa tekvksA
fcuk dksbZ vad nksgjk,] ftruh la[;k,¡ cuk ldrs gks cukvks vkSj i<+ks &
1- 3 vkSj 8 ls nks vadksa dh la[;k,¡
--- 2- 2 vkSj 4 ls nks vadksa dh la[;k,¡
--- 3- 1] 2 vkSj 4 ls rhu vadksa dh la[;k,¡
--- 4- 5] 6 vkSj 0 ls rhu vadksa dh la[;k,¡
--- 5- 3] 4] 7 vkSj 9 ls pkj vadksa dh la[;k,¡
---] ---] ---] ---] ---]
---] ---] ---] ---] ---]
---] ---] ---] ---] ---]
---] ---] ---] ---] ---
6- 1] 2] 5 vkSj 0 ls pkj vadksa dh la[;k,¡
---] ---] ---] ---] ---]
---] ---] ---] ---] ---]
---] ---] ---] ---] ---]
---] ---] ---] ---] --- fdruh la[;k,¡ cuh\
uhps fn;s x;s vadksa dk mi;ksx djds pkj vadksa okyh lcls NksVh vkSj lcls cM+h la[;k cukvksA ;kn jgs dksbZ vad nksgjkuk ugha gSA
lcls NksVh la[;k lcls cM+h la[;k 1- 1] 2] 3] 4 ls
2- 3] 0] 2] 5 ls 3- 8] 7] 6] 9 ls 4- 4] 2] 8] 1 ls 5- 5] 9] 0] 2 ls
rqeus vc rd 9999 rd dh la[;kvksa dks i<+uk&fy[kuk lh[kk gSA bu la[;kvksa dks cukus esa nl vadksa dk mi;ksx gksrk gSA
crkvks dkSuls
D;k bu nl vadksa dk mi;ksx fd, fcuk dksbZ la[;k fy[kh tk ldrh gS\ &&&&&&&&
D;k rqe tkurs gks la[;kvksa dks fy[kus ds vkSj Hkh rjhds gksrs gSa\
?kM+h dk fp= cuk gS] bls ns[kks&
,sls fpg~u rqeus Hkh ?kfM+;ksa esa ns[ks gksaxsA ;s fpg~u jkseu la[;kvksa ds gSaA rqeus ,sls fpg~u vkSj dgk¡ ns[ksa gSa\
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
?kM+h ds fp= dks ns[kdj crkvks] izFke nl jkseu la[;kad dkSuls gSa\
1 2 3 4 5 6 7 8 9 10
I IX
jkseu la[;kad esa 'kwU; ds fy, dksbZ fpg~u ugha gksrkA
jkseu la[;kad iz.kkyh esa dsoy lkr izrhdksa dk mi;ksx gksrk gS&
I V X L C D M
1 5 10 50 100 500 1000
dkSu&lh la[;k fdlds ikl
57] 50 vkSj 60 ds chp dh la[;k gSA
57 fdlds T;knk ikl gS\ 50 ds ;k 60 ds ikl --- vr% 57 dk fudVu 60 gSA tks ngkbZ dk fudVre eku gS
72] 70 vkSj 80 ds chp dh la[;k gSA
72 fdlds T;knk ikl gS\ ---A vr% 72 dk fudVu gS --- -
108 fdlds T;knk ikl gS\---A vr% 108 dk fudVu gS ---A
580] 500 o 600 ds chp dh la[;k gSA
580 fdlds T;knk ikl gS\--- vr% 580 dk fudVu gSA ---
820 fdlds T;knk ikl gS\--- vr% 820 dk fudVu gS ---
122 fdlds T;knk ikl gS\ ---A 122 dk fudVu gSA --- fo'ks"k fLFkfr % ;fn dksbZ la[;k fdUgha nks la[;kvksa ds chp gks rks mldk fudVu dSls djsaxs\
250 fdlds T;knk ikl gS\
250] 200 vkSj 300 ds chpks&chp gSA ,slh fLFkfr esa 250 dk fudVu 300 ekuk tk;sxkA vr% 250 dk fudVu 300 gSA
1- nh xbZ la[;kvksa dk ngkbZ ds fudVre eku irk djksA
24] 65] 92] 148
2- nh xbZ la[;kvksa dk lSdM+s ds fudVre eku irk djksA 235] 709] 676] 550
3- nh xbZ la[;kvksa dk ngkbZ o lSdM+s nksuksa ds fudVre eku irk djksA 138] 559] 427
funsZ'kkuqlkj fMCcksa esa la[;k fy[kksA
1 8
2 2 2 8
2 1 5 tksM
+ks 8
?kVkvks
s
3 tksM+ks 17
4 ?kVkvks 8 ?kV
kvkss
12 tksM+ks
18 tksM+ks 6 ?kV
kvkss
12 ?kVkvks 25
42
10 ?kVkvks
8 ?kVkvks
6 TkksM+ks
12 TkksM+ks 35
& 70
$ 50
& 40
$ 60 180
tksM+uk&?kVkuk
v/;k; 2
28 20 12 32 48
iSVuZ dks le>ks vkSj vkxs c<+kvksA
1. 1+2+3 = 6 2. 1+2+3 = 6
2+3+4 = 9 4+5+6 = 15
3+4+5 = 12 7+8+9 = 24
--- ---
--- ---
--- ---
3. 2+4+6 = 12 4. 1+3+5 = 9
8+10+12 = 30 7+9+--- =
--- ---
--- ---
--- ---
5. 6.
blh rjg ds nks iSVuZ rqe Hkh cukvksA
6 7 8 36 15 13
5 11
dksbZ la[;k 64 yh mls vU;
la[;kvksa ls bl izdkj ik;k 60 $ 4 ¾ 64]
73 & 9 ¾ 64]
69 & 5 ¾ 64
tSls ;fn mRrj 18 gks rks & blls lEcfU/kr loky gks ldrs gSa &
Û 9 esa 9 tksM+us ij D;k feysxk\
Û ,d Vksdjh esa 9 vke rks nks Vksdjh esa fdrus gksaxs\
Û 25&7 D;k gksrk gS\
Û 9 dk nqxuk D;k gksxk\
Û 9 × 2 ¾ ---
la[;k [ksy
rkfydk esa ls dksbZ ,d la[;k yksA rkfydk dh gh vU; la[;kvksa esa lafØ;kvksa dk mi;ksx djrs gq, tks la[;k rqeus yh gS og la[;k cukvksA
43 12 69 5 51 85
24 45 64 49 36 59
16 15 10 19 73 34
14 6 7 28 52 31
38 13 21 43 4 60
79 90 32 17 9 40
Û tksM+ ds ,sls vkSj loky cukvks ftudk mRrj 34 gksA Û vc ?kVko ds ,sls vkSj loky cukvks ftudk mRrj 34 gksA
uhps dqN mRrj fn, x, gSa] muls lEcfU/kr bckjrh loky cukvksA
Û mRrj gS 35
Û mRrj gS 44
Û mRrj gS 21
Û mRrj gS 12
fxzM ij tksM+&?kVko djksA
$ 731 605 615 & 881 7005 6382
210 941 613 6392
318 780
605 103
<
<
>
=
>
loky cukvks
mnkgj.k& 5 0 2 5
& 2 5 $ 1 0
2 5 3 5
1 4
& $ & $
4 8 3 8
9
& $ & $
7 8 9 2 7 3
,slk D;ksa\
221 222 223 224 225 226 227 228 229 230
231 232 233 234 235 236 237 238 239 240
241 242 243 244 245 246 247 248 249 250
251 252 253 254 255 256 257 258 259 260
rkfydk ns[kks vkSj crkvks&
231] 221 ls fdruh vf/kd gS\ &&&&&&&&&
241] 231 ls fdruh vf/kd gS\ &&&&&&&&&
251] 241 ls fdruh vf/kd gS\ &&&&&&&&&
243] 242 ls fdruh vf/kd gS\ &&&&&&&&&
244] 243 ls fdruh vf/kd gS\ &&&&&&&&&
245] 244 ls fdruh vf/kd gS\ &&&&&&&&&
,sls vkSj Øe cukvks vkSj muds vUrj Lo;a <w¡<+ksA
bl rkfydk esa ls dksbZ ,d la[;k pquksA mlds uhps dh nks la[;kvksa dks tksM+ksA vc mlh la[;k ds ck;ha vksj dh nks la[;kvksa dks tksM+ksA vUr esa nksuksa ;ksxQyksa dk vUrj fudkyksA
mnkgj.k&
;fn la[;k 237 pqurs gSaA rc uhps fy[kh nks la[;kvksa dk tksM+ 247 $ 257 ¾ 504 rFkk ck;ha vksj dh la[;kvksa dk tksM+ 236 $ 235 ¾ 471
504 o 471 dk vUrj] 504 & 471 ¾ 33
,slk rhu vkSj la[;kvksa ds lkFk djksA D;k lHkh mÙkjksa esa dksbZ [kkl ckr gS\
++++++++++++
uhps fn, x, lokyksa dks jkgqy vkSj fj;k us gy fd;kA crkvks fdlus loky lgh gy fd;k\ ckWDl esa mldk uke fy[kksA
712$18] 216 $ 17] 762&176] 800&191
jkgqy }kjk fd, x, loky fj;k }kjk fd, x, loky
1
7 1 2 7 1 2
$ 1 8 $ 1 8
7 2 10 7 3 0
1
2 1 6 2 1 6
$ 1 7 $ 1 7
2 3 3 3 8 6
7 6 2 7 6 2
& 1 7 6 & 1 7 6
5 8 6 6 1 4
8 0 0 8 0 0
& 1 9 1 & 1 9 1
6 0 9 7 9 1
vius lkfFk;ksa ls ppkZ djks fdlus dgk¡ xyrh dh \
dher fdruh
,d HkSal dh dher 5000 #-] xk; dh dher 3000 #- rFkk cdjh dh dher 1000 #- gSA fp= ns[kks vkSj crkvksA
1- izR;sd iafDr esa cus tkuojksa dh dher tksM+ dj [kkyh fMCcksas esa fy[kksA
2- izR;sd LrEHk ds uhps tkuojksa dh dqy dher fy[kksA
3- nks xk; vkSj nks cdjh dh dqy dher crkvksA
4- ,d HkSal] ,d xk; vkSj rhu cdfj;ksa dh dqy dher crkvksA
5- ,d HkSal dh dher ls fdruh cdfj;k¡ [kjhnh tk ldrh gSa\
6- 'kSyw us ,d xk;] ,d HkSal rFkk ,d
cdjh [kjhnhA blds ckn Hkh mlds ikl brus #i;s Fks fd og ,d cdjh vkSj [kjhn ldrk gSA crkvks mlds ikl dqy fdrus #i;s Fks\
foLrkfjr :i esa tksM+uk
mnkgj.k& 3453 dks 5286 esa tksM+ksA
3453 ¾ 3 g- $ 4 lS- $ 5 n- $ 3 b- 3453 ¾ 3000 $ 400 $ 50 $ 3 blh izdkj
5286 ¾ 5 g- $ 2 lS- $ 8 n- $ 6 b-
¾ 5000 $ 200 $ 80 $ 6 vr%
3453 ¾ 3000 $ 400 $ 50 $ 3 $ 5286 ¾ 5000 $ 200 $ 80 $ 6 8000 $ 600 $ 130 $ 9
;kuh 8 g- $ 6 lS- $ 13 n- $ 9 b-
;k 8 g- $ ¼6$1½ lS- $ 3 n- $ 9 b-
;k 8 g- $ 7 lS- $ 3 n- $ 9 b-
mnkgj.k& 6875 dks 2749 esa tksM+ksA 6875 ¾ 6000 $ 800 $ 70 $ 5 2749 ¾ 2000 $ 700 $ 40 $ 9 8000 $ 1500 $ 110 $ 14
8 g- $ 15 lS- $ 11 n- $ 14 b-
;k 8 g- $ 15 lS- $ 12 n- $ 4 b-
;k 8 g- $ 16 lS- $ 2 n- $ 4 b-
;k 9 g- $ 6 lS- $ 2 n- $ 4 b- vr% ;ksxQy 9624
laf{kIr :i&
6 8 7 5 $ 2 7 4 9
9 6 2 4
5000 700
80 10
1 1 1
foLrkfjr :i ls ;ksxQy Kkr djksA
1- 2721 vkSj 2620 dk 2- 3510 vkSj 2410 dk 3- 4618 vkSj 3206 dk 4- 7390 vkSj 2000 dk 5- 5881 vkSj 2830 dk 6- 8215 vkSj 1037 dk
foLrkfjr :i esa ?kVkuk
mnkgj.k& 8657 esa ls 6523 ?kVkvks 8657 ¾ 8000 $ 600 $ 50 $ 7 & 6523 ¾ 6000 $ 500 $ 20 $ 3 2000 $ 100 $ 30 $ 4 2 g- $ 1 lS- $ 3 n- $ 4 b- vr%
8657 & 6523 2134
mnkgj.k& 6324 esa ls 4875 ?kVkvks 5000 200 10
6324 ¾ 6000 $ 300 $ 20 $ 4 & 4875 ¾ 4000 $ 800 $ 70 $ 5 1000 $ 400 $ 40 $ 9 1 g- $ 4 lS- $ 4 n- $ 9 b- ¾ 1449 vr%
6324 & 4875 1449
foLrkfjr :i ls ?kVkvksA
1- 6301 esa ls 2100 2- 5810 esa ls 3000 3- 5380 esa ls 4210 4- 5000 esa ls 4000 5- 6000 esa ls 6000 6- 8215 esa ls 1037
1000 100 10
rhu vadksa dh nks ls vf/kd la[;kvksa dk tksM+
mnkgj.k
&147] 253 rFkk 268 dks tksM+ks bUgsa gy djks
lS- n- b- 1-
1
1 4 7 1 2 7
$ 2 5 3 $ 2 1 0
$ 2 6 8 $ 2 4 2
8
lS- n- b- 2-
1 1
1 4 7 1 2 4
$ 2 5 3 $ 2 6 7
$ 2 6 8 $ 7 1 3
6 8
lS- n- b- 3-
1 1
1 4 7 1 4 5
$ 2 5 3 $ 2 4 6
$ 2 6 8 $ 1 3 2
6 6 8
laf{kIr :i
1 1 4-
1 4 7 1 1 5
$ 2 5 3 $ 1 0 6
$ 2 6 8 $ 7 0 3
6 6 8
bl oxZ esa 1 ls 100 rd dh la[;k,¡ fy[kh gSaA
;gk¡a la[;k 13 esa nksuksa vadksa dk tksM+ 1$3 ¾ 4 gSA ,sls gh la[;k 57 esa vadksa dk tksM+ 5$7 ¾ 12 vFkkZr 1$2 ¾ 3 gSA
vc bl fn, x, oxZ esa la[;k ds vadksa dk tksM+ fy[kks rFkk iwjs oxZ dks HkjksA
D;k bl oxZ esa fy[kh la[;kvksa esa dksbZ Øe fn[kkbZ nsrk gS \
njtvcvxcvl;drltlvlvxflxvlxc njtvcvxcv
l;drltlvlvxflxvlxc njtvcvxcvl;drltlvlvxflxvlxc njtvcvxcv
l;drltlvlvxflxvlxc njtvcvxcvnjtvcvxcvl;drltl;drltlvlvxflxlvlvxflxvlxcvlxc njtvcvxcv
l;drltlvlvxflxvlxc njtvcvxcv
l;drltlvlvxflxvlxc
,slh rhu la[;k,¡a fy[kks ftudk ;ksxQy+ 125 gksA
27 $ 50 $ 48 ¾ 125
$ $ ¾ 125
$ $ ¾ 125
$ $ ¾ 125
$ $ ¾ 125
bUgsa gy djks
1- iVsy ikjk Ldwy esa dqy 438 cPps gSa] muesa 198 yM+fd;k¡ gSaA Ldwy esa yM+dksa dh la[;k fdruh gSa\
2- ,d cxhps esa vke ds 245] ve:n ds 368 rFkk iihrs ds 154 isM+ gSaA cxhps esa dqy fdrus isM+ gaS\
3- ,d fo|ky; esa fgUnh dh 435 iqLrdsa] xf.kr dh 412 iqLrdsa rFkk vaxzsth dh 138 iqLrdsa izkIr gqbZaA crkvks dqy fdruh iqLrdsa izkIr gqbZa\
4- ,d cPps us 360 i`"B dh dkWih [kjhnh mlus dqN fnuksa esa 272 i`"B fy[k fy,A crkvks fdrus i`"B [kkyh jg x,\
5- fgUnh] xf.kr vkSj vaxzsth dh iqLrdksa esa Øe'k% 368] 370 rFkk 205 i`"B gSaA crkvks iqLrdksa esa dqy fdrus i`"B gSa\
6- ,d xzke iapk;r ds pquko esa igys mEehnokj us 638 er izkIr fd, nwljk mEehnokj 758 er izkIr dj fot;h ?kksf"kr gqvk rks crkvks igyk mEehnokj fdrus erksa ls gkj x;k\
7- ve:n ds nks cxhpksa ls Øe'k% 352 rFkk 256 ve:n rksM+s x,A crkvks igys cxhps ls fdrus ve:n vf/kd rksM+s x,\
pkj vadksa dh la[;kvksa dk tksM+
mnkgj.k& 4538 vkSj 3485 dks tksM+ksA g - lS- n- b-
1 1 1
4 5 3 8
$ 3 4 8 5
8 0 2 3
30$ 9 ¾ 39 13$13$13 ¾ 39 10$10$19 ¾ 39
gy djks&
1- 4 3 8 5 2- 5 7 3 8 3- 3 4 7 5
$ 2 8 7 6 $ 2 5 7 5 $ 3 6 8 7
4- 6 3 4 6 5- 3 4 3 6 6- 5 7 8 5
$ 2 8 2 $ 2 0 8 $ 3 5 1 2
7- 7213 $ 2587 8- 1111 $ 1199 9- 5789 $ 3122
10- 4747 $ 4363 11- 689 $ 4678 12- 7172 $ 938
pkj vadksa dh la[;kvksa ij ?kVko
mnkgj.k& 8327 esa ls 6853 ?kVkvksA g - lS- n- b-
8 3 2 7
& 6 8 5 3
1 4 7 4
gy djks&
1- 5 0 7 8 2- 7 9 8 1 3- 5 6 7 2
& 2 7 8 4 & 2 5 0 3 & 3 2 4 0
4- 3 5 6 3 5- 6 2 3 0 6- 2 5 0 8
& 2 7 0 6 & 2 4 5 1 & 1 3 9 2
7- 5643 & 2154 8- 9634 & 5071 9- 5000 & 2550
10- 7111 & 5222 11- 4444 & 2165 12- 8100 & 7899
7 1 2 1 2
eSnk pkoy 'kDdj xsgwa /kku lwth eVj ued
uhps rhu xk¡oksa dh tula[;k ds ckjs esa dqN vkadM+s fy[ks gq, gSa&
efgyk,¡ iq#"k yM+ds yM+fd;k¡
Hkkuqizrkiiqj 4134 3975 1152 987
vkluk 3412 3116 1017 1075
vHkuiqj 3532 3580 875 915
lkj.kh ns[kdj bu iz'uksa ds mÙkj nksA 1- Hkkuqizrkiiqj esa dqy fdrus yksx jgrs gSa\
2- vkluk esa efgykvksa ls iq#"k fdrus de gSa\
3- Hkkuqizrkiiqj vkSj vkluk esa dqy fdrus yM+ds gSa\
4- vHkuiqj esa yM+dksa vkSj yM+fd;ksa dh dqy la[;k fdruh gS\
fp= ns[kks vkSj crkvks
[kk| inkFkZ xsgw¡ pkoy eSnk 'kDdj ued lwth eVj /kku
,d cksjs esa 75 fdyks 50 fdyks 50 fdyks 50 fdyks 40 fdyks 40 fdyks 75fdyks 75 fdyks
Û•lwth dk dqy otu fdrus fdyksxzke gS\
Û•pkj cksjs pkoy vkSj rhu cksjs ued dk dqy otu fdrus fdyksxzke gS\
Û•lwth ds cksjksa dk otu eSnk ds cksjksa ds otu ls fdrus fdyksxzke de gS\
Û•Åij fn, x, [kk| inkFkksZa esa fdu&fdu dk otu leku gS\
Û•,d cksjk eSnk] nks cksjs pkoy dk dqy otu fdrus fdyksxzke gS\
Û•Åij fn, x, [kk| inkFkksZa esa fdldk otu lcls de vkSj fdldk otu lcls vfèkd gS\ ---
Û•lHkh [kk| inkFkksZa ds cksjksa dh dqy la[;k gS\
fp= ns[kdj crkvks fdlus fdrus #i, dk lkeku [kjhnkA
gjiky us lkbZfdy] Vh-oh- [kjhnkA ¼ ½
nkfu'k us cSV&ckWy] jsfM;ks] eksckby [kjhnkA ¼ ½
jktw us ckYVh&ex] vkyekjh] VsyhQksu [kjhnkA ¼ ½
lyek us gkWdh&fLVd] jsfM;ks] eksckby [kjhnkA ¼ ½
jhfr us ckYVh&ex] jsfM;ks] vkyekjh [kjhnkA ¼ ½
vxj gj O;fDr ds ikl 9]500 #- gksa rks izR;sd ds ikl fdrus&fdrus #i;s cps\
vc crkvks&
1- gjiky vkSj nkfu'k esa ls fdlus T;knk #i, dk lkeku [kjhnk\
2- nkfu'k us jhfr ls fdrus vf/kd #i, dk lkeku [kjhnk\
3- jktw vkSj lyek us feydj dqy fdrus #i, dk lkeku [kjhnk\
4- lyek us gjiky ls fdrus de #i, dk lkeku [kjhnk\
vc rqe vius lkfFk;ksa ls mudh ilan dk lkeku iwNks vkSj mldh dher irk djksA
2500 #- 275 #-
950 #- 1250#-
430 #-
3250 #- 1860 #-
5200 #-
1105 #-
;ksxQyksa dk vkdyu
mnkgj.k& ,d FkSyh esa 78 daps vkSj nwljh FkSyh esa 23 daps gSaA nksuksa FkSfy;ksa ds dapksa dks ,d lkFk feyk fn;k tk, rks dqy dapksa dh la[;k dk vkdyu djksA 78 $ 23 dk vkdyu djus ds igys 78 vkSj 23 dk ngkbZ ds fudVre eku Kkr djrs gSa rFkk mUgsa tksM+rs gSaA
la[;k ngkbZ dk fudVu
78 80
23 20
vkdfyr ;ksxQy 80
$ 20 100 okLrfod ;ksxQy 78
$ 23 101
vr% nksuksa FkSfy;ksa ds dapksa dks ,d lkFk feykus ij yxHkx 100 daps izkIr gksus pkfg,A bl izdkj vkdfyr la[;k ¼100½] okLrfod la[;k ¼101½ esa dsoy 1 dk vUrj gSA
mnkgj.k& ,d izkFkfed fo|ky; esa 172 Nk= rFkk 121 Nk=k,¡ ntZ gSaA vc fo|ky; ds dqy fo|kfFkZ;ksa dh la[;k dk vkdyu djksA
vkdyu esa igys la[;kvksa ds fudVu dk mi;ksx djsaxsA
172 vkSj 121 dk vkdyu djus ij igys la[;kvksa 172 vkSj 121 dk fudVu lSdM+s ds fudVre djds tksM+us ij
la[;k lSdM+s dk fudVu
172 200
121 100
vkdfyr ;ksxQy& 200
$100 300
78 ;kuh 80 ds ikl 23 ;kuh 20 ds ikl
okLrfod ;ksxQy& 172
$121 293
vr% fo|ky; esa fo|kfFkZ;ksa dh vkdfyr la[;k 300 gS tks fo|kfFkZ;ksa dh okLrfod la[;k 293 ds cgqr djhc gSA
mnkgj.k& jkt vius ?kj ls cktkj Vh-oh-] ia[kk ysus ds fy, fudykA mudh dher Øe'k%
3725 :-] 1650 :- Fkh] rks crkvks jkt dks yxHkx fdrus :i;s ysdj pyuk pkfg,A
3725 vkSj 1650 ds gtkj ds fudVre eku Kkr djsaxsA la[;k gtkj dk fudVu
3725 4000
1650 2000
vkdfyr ;ksxQy 4000
$ 2000 6000 okLrfod ;ksxQy 3725
$ 1650 5375
vr% jkt dks nksuksa lkeku [kjhnus ds fy, yxHkx 6000 #- ysdj cktkj tkuk pkfg,A
vkdfyr rFkk okLrfod ;ksxQy crkvksA
ladsr& Û ;fn la[;k nks vad dh gS rks fudVu ngkbZ dk
•Û ;fn rhu vad dh gS rks fudVu lSdM+s dk
•Û ;fn pkj vad dh gS rks fudVu gtkj dk
1- 47] 81 2- 67] 32 3- 97] 15 4- 72] 138
5- 8251] 1310 6- 5371] 3800 7- 7214] 1818 8- 632] 225
9- 5990] 4137 10- 265] 381 11- 703] 581 12- 6410] 3817
oSfnd xf.kr dh fof/k;k¡
vHkh rd rqeus tksM+uk] ?kVkuk] xq.kk ,oa Hkkx djuk lh[k fy;k gSA bu lafØ;kvksa dks djus dh dqN ljy vkSj etsnkj fofèk;k¡ oSfnd xf.kr esa Hkh gSaA ;gk¡ ge mu fof/k;ksa ls rqEgkjk ifjp; djk,¡xsA bu fofèk;ksa ds ckjs esa tkuus ds igys vkvks vadksa ls ifjp; dj ysa &
vad %& 0] 1] 2] 3] 4] 5] 6] 7] 8] 9 ;s nl vad gSaA bUgha vadksa dk ç;ksx dj lHkh la[;k,¡
fy[kh tkrh gSaA
chtkad %& oSfnd xf.kr esa 1 ls 9 rd ds vadksa dks chtkad dgrs gSaA fdlh la[;k dk chtkad Kkr djus ds fy, la[;k ds vadksa dk ;ksx rc rd djrs gSa] tc rd ,d vad dh la[;k çkIr u gks tk,A
mnkgj.k ds fy, &
35 dk chtkad Kkr djus ds fy, blds vadksa dks tksM+saxsA 3 $ 5 ¾ 8
vr% 35 dk chtkad 8 gSA bl çdkj &
97 dk chtkad &
9 $ 7 ¾ 16 ysfdu 16 esa 2 vad gSaA
vr% blds vadksa dks Hkh tksM+saxs 1 $ 6 ¾ 7
vr% 97 dks chtkad 7 gSA
ije fe= vad%& ftu 2 vadksa dk ;ksx 10 gksrk gS] os vkil esa ¼,d nwljs ds½ ije fe=
dgykrs gSaA
tSls %& 1 $ 9 ¾ 10
vr% % 1 dk ije fe= 9 gS
vkSj 9 dk ije fe= 1 gS
vkvks] vc FkksM+k vH;kl djsaA vH;kl
ç'u 1 %& la[;k,¡ fy[kus ds fy, dkSu&dkSu ls vadksa dk ç;ksx gksrk gS\
ç'u 2 %& uhps fy[kh la[;kvksa ds chtkad crkvks &
(i) 12 (ii) 15 (iii) 17 (iv) 19
(v) 37 (vi) 44 (vii) 56 (viii) 67
(ix) 96 (x) 183
ç'u 3 %& bu vadksa ds ije fe= vad crkvks &
(i) 2 (ii) 3 (iii) 4 (iv) 5
,dkfèkdsu iwosZ.k
,dkfèkdsu iwosZ.k dk eryc gS igys dh la[;k ls ,d vfèkd tSls %& 2dk ,dkfèkd gS 3] blh çdkj 3 dk ,dkfèkd gS 4
D;k rqe 1 ls 9 rd çR;sd vad dk ,dkfèkd crk ldrs gks\
,d U;wusu iwosZ.k ,d U;wusu iwosZ.k dk vFkZ gS igys dh la[;k ls ,d deA
tSls %& 8 dk ,d U;wusu 7 gSA blh çdkj 5 dk ,d U;wusu 4 gSA vc rqe 9 ls 1 rd çR;sd la[;k dk ,d U;wusu crkvksA
oSfnd xf.kr dh fofèk;ksa eas vusd LFkkuksa ij ,dkf/kdsu iwosZ.k vkSj ,d U;wusu iwosZ.k dk mi;ksx gksrk gSA
vc crkvks &
bu la[;kvksa dks nks ckj ,dkf/kd djus ij dkSu lh la[;k,¡ çkIr gksaxh\
(i) 22 (ii) 43 (iii) 30 (iv) 58
dHkh&dHkh la[;k dk ,d ls vf/kd ckj ,dkf/kd vFkok ,d U;wu djus dh Hkh vko';drk gksrh gSA
tSls %& 12 dk ,d ckj ,dkf/kd djus ij 13] 13 ls iqu% ,dkfèkd djus ij 14 vFkkZr~ 12 ls nks ckj ,dkf/kd djus ij la[;k 14 çkIr gksrh gSA
vkvks] vc 12 ls gh nks ckj ,d U;wu djrs gSaA
12 ls ,d ckj ,d U;wu djus ls 11 feyk] 11 ls ,d ckj ,d U;wu djus ij 10 feyk]
vFkkZr 12 ls nks ckj ,d U;wu djus ij la[;k 10 çkIr gksrh gSA
bu la[;kvksa dks rhu ckj ,dkf/kd djus ij dkSu lh la[;k,¡ çkIr gksaxh\
(i) 23 (ii) 15 (iii) 36 (iv) 42
vius eu ls la[;k,¡ ysdj mu la[;kvksa dk ,dkf/kd djus dk vH;kl djksA vc crkvks
uhps fy[kh la[;kvksa dks nks ckj ,d U;wu djus ij dkSu lh la[;k çkIr gksxh\
(i) 16 (ii) 30 (iii) 67 (iv) 75
bUgha la[;kvksa dks 3 ,d ckj U;wu djus ij dkSu lh la[;k,¡ feysxh\
vius eu ls dbZ la[;k,¡ pqudj nks ,oa rhu ckj ,d U;wu djus dk vH;kl djksA
ije fe= dh lgk;rk ls tksM+uk
;fn fdlh vad esa 1] 2] 3 tksM+uk gks rks vko';drk ds vuqlkj ,dkfèkd dj tksM+k tk ldrk gSA
ijUrq tc tksM+s tkus okys nksuksa vad 5 ls cM+s gksa rc ije fe= dh lgk;rk ls tksM+uk vklku gksrk gSA
vkvks] bldk ,d mnkgj.k ns[ksa &
9
$ 7 ---
;gk¡ gesa 9 vkSj 7 dks tksM+uk gSA 9 dk ije fe= vad 1 gS]
vr% 7 ls 1 ysdj 9 esa feyk fn;kA vc 9 $ 1 ¾ 10
vkSj 7 ls 1 fudkyus ij cps 6 10 esa 6 tksM+us ij feyk 16
vFkkZr~ 9
$ 7 - ---
1 6
blh çdkj ije fe= dh lgk;rk ls tksM+us dk vH;kl djks &
(i) 7 + 8 (ii) 8 + 6 (iii) 9 + 8 (iv) 6 + 9
blh çdkj 5 ls cM+s nks vad ysdj mUgsa ije fe= dh lgk;rk ls tksM+us dk vH;kl djksA
fiNyh d{kk esa rqeus xq.kk&Hkkx ds loky fd;s FksA uhps ,sls gh dqN loky fn;s x;s gSaA
lokyksa ds mRrj ikl okys ckDl esa gSA lokyksa dks gy djrs tkvks vkSj mRrj okys [kkuksa esa jax Hkjrs tkvksA tc lkjs mRrj okys [kkuksa esa jax Hkj tk,xk rks rqEgsa feysxk ,d fp=A
1- 46 × 6 ¾ --- 2- 7 × 13 ¾ --- 3- 66 » 2 ¾ --- 4- 11 × 6 ¾ --- 5- 37 × 3 ¾ --- 6- 150 » 5 ¾ --- 7- 128 » 4 ¾ --- 8- 95 × 8 ¾ --- 9- 15 × 5 ¾ --- 10- 120 » 2 ¾ --- 11- 26 × 7 ¾ --- 12- 27 × 4 ¾ ---
13- ,d fMCcs esa 7 xsans j[kh tk ldrh gSaA crkvks 63 xsanksa dks j[kus ds fy, fdrus fMCCkksa dh t:jr gksxh\
14- ,d fd-xzk- 'kDdj 14 #- dh feyrh gSA jktho us vius ?kj ds fy, 5 fd-xzk- 'kDdj [kjhnhA crkvks jktho nqdkunkj dks fdrus #i;s nsxk\
15- ,d ckx esa vke ds 16] ve:n ds 16] larjs ds 16 rFkk iihrs ds Hkh 16 isM+ gaSA crkvks ckx esa dqy fdrus isM+ gSa\
16- ,d Vksdjh esa 72 larjs gSaA bUgsa 6 yksxksa esa cjkcj&cjkcj ck¡Vsa rks izR;sd dks fdrus larjs feysaxs\
30 91
60 70
111
32
75 33
64 760 276 9 182 12 66
108
xq.kk&Hkkx
v/;k; 3
rqeus fiNyh d{kk esa i<+k gS fd xq.kk dk eryc gS ckj&ckj tksM+ukA ,d fMCcs esa 18 pkWd vkrh gS rks ,sls gh 3 fMCcksa esa fdruh pkWd vk,¡xh\
18 $ 18 $ 18 ¾ 54 ;kuh 18 × 3 ¾ 54 rqeus ;g Hkh ns[kk Fkk fd 6 × 5 ¾ 5 × 6
dksbZ Hkh nks la[;k,¡ ysdj mudk xq.kuQy fudkyksA la[;kvksa dk Øe cnyus ls xq.kuQy ugha cnyrkA ;kuh 3 × 4 ¾ 4 × 3
vxj dksbZ 2 la[;k,¡ ,slh [kkst ldks ftlds fy, ;g lgh u gks rks lcdks crkukA vc uhps fn;s gq, lokyksa dks tYnh ls gy djksA
1- 8 × 8 ¾ 64 8 × 9 ¾ ---
2- 12 × 9 ¾ 108 9 × 12 ¾ ---
3- 19 × 10 ¾ 190 20 × 10 ¾ ---
4- 20 × 5 ¾ 100 20 × 4 ¾ --- 5- 29 × 4 ¾ 116 30 × 4 ¾ --- 6- 26 × 8 ¾ 208 26 × 7 ¾ --- NwVh gqbZ la[;k <w¡<ks+
xq.kk djus ds vyx&vyx rjhds
,d drkj esa 23 dqflZ;k¡ gS ,slh gh 9 drkjksa esa fdruh dqflZ;k¡ gksaxh\
ehuk] Vhuw nksuksa us vyx&vyx rjhds ls bls fd;k
vkSj fdu&fdu rjhdksas ls bl loky dks gy dj ldrs gks\ djksA
dqN vkSj loky
1- ,d cxhps esa 7 D;kfj;k¡ gSa] izR;sd D;kjh esa xqykc ds 15 ikS/ks yxk, x,A crkvks]
cxhps esa xqykc ds dqy fdrus ikS/ks yxs\
2- ,d Vksdjh esa 25 larjs gSaA crkvks] ,slh gh 5 Vksdfj;ksa esa fdrus larjs gksaxs\
3- ,d nthZ ,d fnu esa 12 'kVZ flyrk gSA crkvks] og 4 fnu esa fdrus 'kVZ fly ysxk\
rqe Hkh bl rjg ds vkSj loky cukvks o vyx&vyx rjhdksa ls gy djds ns[kksA gj loky ds fy, de ls de 4&5 rjhds lkspksA
dSls djsa\
rqeus fiNyh d{kk esa 34 × 7] 126 × 2] ds tSls xq.kk ds loky fd;s gSaA vc 32 × 16 dks djds ns[krs gSaA
1 fdlh Hkh la[;k dk xq.kk tc nks ;k nks ls vf/kd vadksa dh 32 la[;k ls djrs gSa rks igys bdkbZ ds vad dk xq.kk djrs gSaA
× 16 bl loky esa bdkbZ dk vad 6 gS blfy, igys 32 × 6 ¾ 192 192 ¼32 × 6½ vc nwljs vad ;kuh 1 ngkbZ ;kuh 10 dk xq.kk 32 ls djrs gSaA
$320 ¼32 × 10½ 32 × 10 ¾ 320A vc bu nksuksa dks tksM+sa rks mRrj gksxk& 512 512
,d vkSj rjhds ls Hkh ge ;g xq.kk dj ldrs gSaA
32 × 16 ¾ \ bls ge fy[k ldrs gSa& 32 ¾ 30 $ 2 vkSj 16 ¾ 10 $ 6
× 30 2
10 30 × 10 2 × 10 vc bu pkjksa dks tksM+ ysrs gaSA
300 20 300 $ 180 $ 20 $ 12 ¾ &&&&&&
6 30 × 6 2 × 6
180 12
D;k ogh mRrj vk;k tks igys rjhds ls vk;k FkkA
uhps fn, x, iz'uksa dks crk, x, nksuksa rjhdksa ls gy djksA
1- 45 × 23 2- 95 × 89 3- 67 × 72
4- 57 × 69 5- 30 × 29 6- 15 × 49
ns[kks vkSj le>ks
346 × 25
1730 ¼346 × 5 ½ $ 6920 ¼346 × 20 ½
8650
vr% 346 × 25 ¾ 6000 $ 1500 $ 800 $ 200 $ 120 $ 30 ;k 346 × 25 ¾ 8650
gy djks
1- 132 × 95 2- 465 × 38 3- 278 × 47
4- 921 × 66 5- 760 × 19 6- 803 × 45
bckjrh loky
Û ,d fo|ky; esa 65 cPps gSaA fidfud ds fy, lHkh us 15&15 #- tek fd;sA crkvks dqy fdrus #i;s tek gq, \
Û jk/kk dks 14 dkWfi;ksa dh vko';drk gSA ;fn izR;sd dkWih dk ewY; 16 #i;s gks rks jkèkk dks fdrus #i;kas dh vko';drk gksxh \
Û ,d NksVs ckWDl esa 12 dqfYQ;k¡ j[kh tk ldrh gSaA ,d cM+s ckWDl esa mlls 15 xquk T;knk dqfYQ;k¡ j[kh tk ldrh gSaA crkvks cM+s ckWDl esa fdruh dqfYQ;k¡ j[kh tk ldrh gSaA
Û lkM+h dh 25 vyx&vyx fMtkbu gSaA izR;sd fMtkbu esa 16 jax gSA nqdkunkj viuh nqdku ds fy, gj rjg dh lkM+h [kjhnuk pkgrk gSA crkvks mls de&ls&de fdruh lkfM+;k¡ [kjhnuh iMa+sxh \
Û ,d dqlhZ dh dher 436 #i;s gS rks oSlh gh 35 dqflZ;k¡ fdrus #i;s esa feyasxh \ Û egs'k ?kj ls 3000 #i;s ysdj cktkj x;k mlus 175 #i;s izfr lsV ds fglkc ls
iqLrd ds 12 lsV [kjhnsA crkvks mlds ikl fdrus #i;s cps \
346 × 25 ¾ \ dks gy djus dk nwljk rjhdk 346 ¾ 300 $ 40 $ 6 vkSj 25 ¾ 20 $ 5
× 300 40 6
20 300 × 20 40 × 20 6 × 20
6000 800 120
5 300 × 5 40 × 5 6 × 5
1500 200 30
mRrj fn;s gq, gSa loky cukvksA
igkM+ksa dk [ksy
;fn rqEgsa ,d ls nl rd ds igkM+s ;kn gSa rks rqe vkxs dh la[;kvksa ds igkM+s cuk ldrs gksA
vkvks 13 dk igkM+k cuk,¡A
10 dk igkM+k 10 20 30 40 50 60 70 80 90 100
3 dk igkM+k 3 6 9 12 15 18 21 24 27 30
13 dk igkM+k 13 26 39 52 65 78 91 104 117 130
13 dk igkM+k cukus ds fy, igys geus 10 dk igkM+k fy[kk fQj 3 dk vkSj fQj mudks tksM+ fn;k rks gesa 13 dk igkM+k feykA
7 $ 6 ¾ 13 gksrk gS] ;fn ge blh rjg 7 o 6 ds igkM+ksa dks tksM+sa rks D;k gksxk\
vkvks djds ns[kksA
7 dk igkM+k 7 14 21 28 35 42 49 56 63 70
6 dk igkM+k 6 12 18 24 30 36 42 48 54 60
13 dk igkM+k 13 --- --- --- --- --- --- --- --- --- D;k rqEgsa 13 dk igkM+k feyk\
D;k rqe nwljh la[;k,¡ ysdj 13 dk igkM+k cuk ldrs gks\ dkSu&dkSu lh la[;k,¡ ysuh gkasxh\
1- ---] --- 2- ---] --- 3- ---] --- 4- ---] --- Åij rqeus 13 dk igkM+k cuk;k gS blh rjg 11] 12] 14--- 20 ds igkM+s Hkh cukvksA
Hkkx
tc gesa phtksa dks cjkcj&cjkcj ck¡Vuk gksrk gS rc ge Hkkx djrs gSaA rqeus d{kk rhu esa i<+k gS fd ge Hkkx dh fØ;k mlh la[;k dks ckj&ckj ?kVkdj ;k igkM+k cksydj djrs gSaA tSls&15 lsc 5 cPpksa esa cjkcj&cjkcj ck¡Vus gSaA crkvks gj ,d cPps dks fdrus lsc feysaxs\
bl izdkj rqeus ns[kk fd nksuksa rjhdksa ls Hkkx djus ij ik¡pksa cPpksa dks 3&3 lsc feyrs gSaA gy djks
1- 51 » 3 ¾ 17
2- 40 » 4 ¾ &&&&&
3- 150 » 5 ¾ &&&&&
4- 63 » 7 ¾ &&&&&
5- 45 esa ls 5 dks fdruh ckj ?kVk ldrs gSa\
6- 108 phtksa dks 9&9 ds lewg esa ck¡Vs rks fdrus lewg cusaxs\
7- ,d thi esa 8 yksx gh cSB ldrs gSaA 48 yksxksa dks cktkj ys tkus ds fy, fdruh thiksa dh t:jr gksxh\
8- ,d ekyh ds ikl 60 Qwy gSa ;fn og 12 Qwyksa dh ,d ekyk cukrk gS rks crkvks fdruh ekyk,¡ cusaxh\
9- ,d fMCcs esa 10 fdrkcsa vkrh gSa rks crkvks 100 fdrkcksa dks j[kus ds fy, ,sls fdrus fMCcksa dh t:jr gksxh\
3 5 15
15
1 1 1
5 15
5 10
5 5 5 0
17 3 51 3 21 21
0
0
'ks"kQy
D;k 13 yM~Mqvksa dks 4 cPpksa esa cjkcj&cjkcj ck¡V ldrs gks&
rqEgsa irk gSA
;gk¡ 4 Hkktd 13 HkkT;
o 3 HkkxQy gSA
;kuh tc 13 yM~Mwvksa dks 4 cPpksa esa cjkcj&cjkcj ck¡Vk rks gjsd dks 3&3 yM~Mw feys o ,d yM~Mw cp x;kA
bl cps 1 dks 'ks"kQy dgrs gSaA vc uhps fn;s x;s lokyksa dks gy djksA
1- 25 » 4 2- 39 » 6 3- 53 » 8
4- 7 529 5- 9 353 6- 3 654
7- 84 » 4 8- 49 » 7 9- 97 » 6
izR;sd esa HkkT;] Hkktd] HkkxQy vkSj 'ks"kQy vyx&vyx fy[kksA fdu lokyksa esa 'ks"kQy 'kwU; vk;k\ bu lokyksa ds bckjrh loky viuh dkWih esa cukvksA
nks bckjrh loky geus ;gk¡ rqEgkjs fy, cuk, gSa&
1- 25 » 4
f'k{kd us iqLrdky; ls 25 fdrkcsa fudkyh vkSj 4 cPpksa esa cjkcj&cjkcj ck¡V nhA crkvks izR;sd cPps dks fdruh&fdruh fdrkcsa feyh vkSj ck¡Vus ds ckn fdruh fdrkcsa cph\
2- 3 654
3 dqflZ;ksa dk ewY; 654 #- gS] rks ,d dqlhZ dk ewY; fdruk gksxk\
loky cukdj gy djks 484 » 4
4 lkfM+;ksa dh dher --- ---
3 4 13 12 1
40 30 1
4 284
160 124 120 4 4
71 1
4 284 280 4 4
71
4 284 28
4 4
&
&
&
&
&
&
&
0
0 0
0
0 0
0
vyx&vyx rjg ls Hkkx
f'k{kd us cPpksa dks Hkkx dk loky fn;k vkSj dgk lc viuh&viuh dkWih esa djksA cPpksa us ftl rjg ls loky gy fd;s mUgsa rqe Hkh ns[kksA
200 » 4 ¾ 50
284 ¾ 200$80$4] 284 » 4 ¾ 80 » 4 ¾ 20
4 » 4 ¾ 1
71
D;k lHkh dk gy lgh gS\ ppkZ djksA rqe Hkh vyx&vyx rjhdksa ls Hkkx ds loky djksA ;g Hkh crkvks fd rqEgsa dkSulk rjhdk ilan gS vkSj D;ksa\
ulhe vkSj lq'khyk ckr dj jgs FksA lq'khyk us dgk D;k rqe tYnh ls crk ldrs gks 1018 esa 11 dk Hkkx nsus ij D;k vk,xk\ ulhe us crk;k yxHkx 100 mRrj vk,xkA
bu lokyksa esa mRrj dk vuqeku dSls yxk ldrs gSaA pyks ns[ksa&
ulhe us dgk 1018 ;kuh 1000 ds djhc gSA vkSj 11 ;kuh 10 ds djhcA vr% ge 1000 » 10 dj ldrs gSaA
vkSj mRrj 100 ds djhc gksxkA
vc rqe bu lokyksa ds mRrj dk vuqeku yxkvksA 1- 97 esa 31 dk Hkkx nsus ij yxHkx D;k mRrj vk,xk\
2- 932 esa 9 dk Hkkx nsus ij yxHkx D;k mRrj vk,xk\
3- 118 ve:nksa ls 8 ve:n dh yxHkx fdruh <sfj;k¡ cu ldrhgS\
4 4
dSls djsa\
rqeus cgqr ls Hkkx ds loky fd;s gSa] D;k rqe crk ldrs gks 372 » 12 ¾ \
;gk¡ 372 dks 12 ls Hkkx djuk gSA lSdM+s esa 3 gSA 3 lSdM+s dks 12 Hkkxksa esa ugha ck¡V ldrsA vr% lSdM+s dks ngkbZ esa cnyrs gSA bl rjg 30 ngkbZ $ 7 ngkbZ feydj 37 ngkb;k¡ gaSA
37 esa 12 dk Hkkx fdruh ckj tk,xkA blds fy, 12 dk igkM+k i<+rs gSaa
12 × 1 ¾ 12 12 × 2 ¾ 24 12 × 3 ¾ 36 12 × 4 ¾ 48
48] 37 ls cM+k gS vr% 12 dk igkM+k rhu ckj gh i<+saxs vkSj 37 esa ls 36 ?kVk,¡xsA 1 ngkbZ cpsxh ftls ge bdkbZ essa cnysaxs A bl rjg 10 $ 2 ¾ 12 bdkb;k¡
vc 12 dk 12 esa Hkkx 1 ckj x;kA bls ,sls Hkh dj ldrs gSaA
20$5$6 ¾ 31
vc rqe bu lokyksa dks gy djks
1- ,d jLlh 132 ehVj yEch gSA vxj ge jLlh ds 12&12 ehVj ds VqdM+s dkVs rks fdrus VqdM+s dVsaxs\
2- ,d fMCcs esa 17 cksry vkrh gSa ,sls 12 fMCcksa esa dqy fdruh cksryssa gksaxh\
31 12 372
36 12 12 00
(12×3=36) (12×1) & 36
&
20 5 6 12 300 72
240 60 60
72 72
(12×20) (12×5) (12×6)
&
&
&
00
00
& 72 & 00 72
3- ,d Vksdjh esa 252 lsc gSaA bu lscksa dks 18 yksxksa esa cjkcj&cjkcj ck¡Vus ij gj O;fDr dks fdrus lsc feysaxsA
4- ,d FkSyh esa ,d #i;s okys 55 flDds gSaA bu flDdksa ls 5&5 #i;s okyh fdruh
<sfj;k¡ cukbZ tk ldrh gSa\
5- 3 ia[ks [kjhnus ds fy, 1650 #- nsus gksrs gSaA crkvks ,d ia[ks dh dher fdruh gS\
6- d{kk&4 dh 12 Nk=kvksa dks dqy feykdj 900 #- Nk=o`fÙk feyhA crkvks gj ,d Nk=k dks fdrus #i;s feys\
rqe [kqn Hkh ,sls iz'u cukvksA gy djds vius nksLrksa o f'k{kdksa dks fn[kkvksA uhps cus pkSdksj esa dqN la[;k,¡ o fpg~uksa ds dkMZ j[ks gq, gSaA jfo us bUgsa Bhd ls tek;k Fkk ysfdu deyk us bUgsa fcxkM+ fn;kA D;k rqe bUgsa fQj ls Bhd dj ldrs gks\
¾ 10 » 2 5
45 » 3 ¾ 15
3 × 12 4 ¾
3 3 9 » ¾
20 » 5 ¾ 4
crkvks rks dkSu&ls gy lgh gSa o dkSu&ls xyrA tks gy xyr gS mUgsa lqèkkjks vkSj ;g Hkh crkvks dh xyrh djus okys us dgk¡ xyrh dhA
1- 10 2- 3-
7 81 7 1
33 3 99
9 09
9 0
114 4 96 4 5 4 16
16 00
1 6 90
6 3
07 8 56 0 56
12 4 58
4 8
8 0
4- 5- 6-
rqeus igys Hkh bckjrh loky cuk, gSaA vc uhps fy[ks rF;ksa ds fy, Hkh bckjrh loky cukvksA
1- 125 » 5 2- 53 × 4 3- 15 $ 15 $ 15
4- 763 & 365 5- 256 » 12 6- 105 » 15
7- 108 × 13 8- 256 $ 200 $ 300 9- 63 × 9
,sls gh vkSj loky rqe [kqn Hkh cukvksA Lo;a Hkh djks o nksLrksa dks Hkh djus dks nksA
d{kk&3 esa rqeus 1 1 3 1, , ,
2 4 4 3 ds ckjs esa i<+k gSA rqEgsa ;kn gksxk ge 1
2 dks vk/kk dgrs gSa vkSj fp= esa bl rjg iznf'kZr djrs gSa &
1
2 ¾ vk/kk ¾
,slk gh ckdh rhu la[;kvksa ds lkFk Hkh djksA 1
4 ¾ ,d pkSFkkbZ ¾ 3
4 ¾ &&&&&&&&& ¾ 1
3 ¾ &&&&&&&&& ¾
'kgukt vkSj ekyk us dqN fp= o dqN vkd`fr;k¡ cukbZa gSaA buds j¡xs gq, Hkkx dqy ds fdrus&fdrus gSa\ gj ,d ds uhps fy[kksA
&&&&&& &&&&&& &&&&&& &&&&&&
&&&&&& &&&&&& &&&&&& &&&&&&
fHkUu
v/;k; 4
&&&&&& &&&&&& &&&&&& &&&&&&
&&&&&& &&&&&& &&&&&& &&&&&&
va'k vkSj gj
rqEgsa ;g Hkh ;kn gksxk fd 2
8 esa 2 dks va'k dgrs gS vkSj 8 dks gjA vc bu fHkUuksa esa va'k vkSj gj crkvksA 3 2 1 1 1, , , ,
4 3 2 3 4
tc dksbZ fHkUu fp= ls iznf'kZr gks rks mlesa va'k vkSj gj dks dSls igpkusa] vkvks bl mnkgj.k esa ns[ksa &
mnkgj.k& 1
4 dks ge fp= esa ,sls crk ldrs gSaA fHkUu dk va'k 1 ¾ jaxk gqvk fgLlkA fHkUu dk gj 4 ¾ fd;s x;s dqy fgLlsA ,slk gh 2
3] 1
2] 1 3 o 3
4 ds fy, Hkh djksA
,d oLrq ds dqy ftrus cjkcj fgLls fd;s x;s og gqvk gj vkSj ftrus fgLls jaxs og gqvk va'kA
bu fp=ksa dks ns[kks vkSj crkvks ,d vkd`fr ds fdrus cjkcj fgLls fd;s vkSj fdrus fgLls jaxs\ fQj buesa gj vkSj va'k Hkh crkvksA
&&&&&& &&&&&& &&&&&& &&&&&&
va'k --- gj ---
