guru mantra

vkSlriz-1 & fdlh ijh{kk esa 8 fo/;kfFkZ;ksa }kjk izkIr vadks dk vkSlr 51 gS rFkk vU; 9 fo/;kfFkZ;ksa ds vkSlr vad 68 gSA iwjs 17 fo/;kfFkZ;ksa }kjk izkIr vadks dk vkSlr gS\

¼1½ 59 ¼2½ 5-9 ¼3½ 60¼4½ 60-5

Ikz-2 & ;fn 6 fo/;kfFkZ;kas dk vkSlr Hkkj 50 fdxzk- 2 fo/;kfFkZ;ksa dk vkSlr Hkkj 51 fdxzk- rFkk 2 fo/;kfFkZ;ksa 55 fdxzk- gS rks dqy fo/;kfFkZ;kas dk vkSlr Hkkj gksxk \

¼1½ 61 fdxzk- ¼2½ 51-5 fdxzk- ¼3½ 52 fdxzk-¼4½ 51-2 fdxzk-

Ikz-3 & fdlh X ds vuqHkkx A ds 32 yM+dks ds vadks dk vkSlr 60 gS tcfd d{kk X ds vuqHkkx B ds 40 yM+dks ds vadks dk vkSlr 33 gSA nksuks vuqHkkxks dks feykus ij vadks dk vkSlr gksxk \

¼1½ 44 ¼2½ 45 ¼3½ 46 12

¼4½ 4512

Ikz-4 & ;fn 20 izs{k.kksa x1 , x2 ,……. x20 dk vkSlr y gks rc ] x1−101 , x2 101 , x3101…….x20−101 dk vkSlr fdruk

gksxk \ ¼1½ y−20 ¼2½ y−101 ¼3½ 20y ¼4½ 101

y

Ikz-5 & ;fn pkj izs{k.kkas dk vkSlr 20 gks vkSj muesa ls izR;sd esa ,d vpj c tksM+ fn;k tk, ] rks mudk vkSlr 22 gks tkrk gSA rnuqlkj c dk eku fdruk gS\

¼1½ 6 ¼2½ &2 ¼3½ 2¼4½ 16

Ikz-6 & 4 yM+dks rFkk 3 yM+fd;ksa us vkSlru 120 :Ik, [kpZ fd,A muesa yM+dks us ;fn vkSlru 150 :Ik, fd, gks rks yM+fd;ksa dk vkSlr [kpZ fdruk Fkk \

¼1½ 80 :Ik, ¼2½ 60 :Ik, ¼3½ 90 :i, ¼4½ 100 :i,

Ikz-7 & 6 ests vkSj 12 dqflZ;k¡ 7800 :Ik, esa [kjhnh gSA ;fn ,d est dk vkSlr ewY; 750 :Ik, gks rks ,d dqlhZ dk vkSlr ewY; fdruk gS \

¼1½ 8 ¼2½ 10 ¼3½ 12¼4½ 14

Ikz-8 & ,d d{kk esa A rFkk B nks xqV gS ftuesa d`e”k% 42 rFkk 28 Nk= gSA ;fn xqV A dk vkSlr Hkkj 25 fdxzk- gks vkSj xqV B dk Hkkj 40 fdxzk- gks rks d{kk ds lHkh Nk=ks dk vkSlr Hkkj fdruk

gksxk \¼1½ 69 ¼2½ 31 ¼3½ 70¼4½ 30

Ikz-9 & 50 la[;kvks dk vkSlr 38 gSA ;fn nks la[;k,¡ vFkkZr 45 rFkk 55 gVk nh tk,¡ rks “ks’k la[;kvks dk vkSlr fdruk jg tk,xk \

¼1½ 35 ¼2½ 32-5 ¼3½ 37-5¼4½ 36

Ikz-10 & 30 la[;kvks dk vkSlr 15 gSA buesa ls izFke 18 la[;kvks dk 10 rFkk vxyh 11 la[;vks dk vkSlr 20 gS vafre la[;k gksxh \

¼1½ 56 ¼2½ 52 ¼3½ 60¼4½ 50

Ikz-11 & fdlh ijh{kk esa 120 izR;kf”k;ksa }kjk izkIr vadks dk vkSlr 35 gSA mRrh.kZ izR;kf”k;ksa }kjk izkIr vadks dk vkSLkr 39 gS vkSj vuqRrh.kZ izR;kf”k;ksa }kjk izkIr vadks dk vkSlr 15 gS ijh{kk esa mRrh.kZ izR;kf”k;ksa dh la[;k fdruh gS \

¼1½ 100 ¼2½ 120 ¼3½ 150¼4½ 140

Ikz-12 & 30 la[;kvks dk vkSlr 40 gS vkSj vU; 40 la[;kvks dk 30 gSA lHkh la[;kvks dk vkSlr gS\

¼1½ 34 27 ¼2½ 35 ¼3½34

¼4½ 34-5Ikz-13 & fdlh d{kk ds 15 fo/;kfFkZ;ksa dh vkSlr vk;q 15 o’kZ gSA buesa ls 5 fo/;kfFkZ;ksa dh vkSlr vk;q 14 o’kZ gS A buesa ls 5 fo/;kfFkZ;ksa dh vkSlr vk;q 14 o’kZ gS rFkk vU; 9 fo/;kfFkZ;ksa dh vkSlrvk;q 16 o’kZ gSA 15 osa fo/;kfFkZ;k dh vk;q gS \

¼1½ 11 o’kZ ¼2½ 15 o’kZ ¼3½ 15 27 o’kZ

¼4½ 14 o’kZ Ikz-14 & 15 la[;kvks dk vkSlr 7 gSA ;fn igyh 8 la[;kvks dk vkSlr 6-5 gS rFkk vafre 8 la[;kvks dk vkSlr 9-5 gS rks chp dh la[;k gS \

¼1½ 40 ¼2½ 38 ¼3½ 48¼4½ 50

Ikz-15 & vkB la[;kvks dk vkSlr 20 gS igyh nks la[;kvks dk vkSlr 15 12 vkSj vxyh rhu dk 21 1

3gSA ;fn NBoha la[;k lkroha ls 4 de rFkk

vkBoha ls 7 de gks rks vkBoh la[;k gksxhA ¼1½ 18 ¼2½ 22 ¼3½ 25

¼4½ 27Ikz-16 & 20 la[;kvks dk vkSlr 12 gS igyh 12 la[;kvks dk vkSlr 11 gS rFkk vxyh 7 la[;kvks dk vkSlr 10 gS vafre la[;k gksxh \

¼1½ 40 ¼2½ 38 ¼3½ 48¼4½ 50

Ikz-17 & fdlh d{kk ds fo/;kfFkZ;ksa ds izkIrkadks dk vkSlr 68 gS d{kk esa yM+fd;ksa ds izkIrkadks dk vkSlr 80 rFkk yM+dks ds izkIrkadks dk vkSlr 60 gSA d{kk esa fdrus izfr”kr fo/;kFkhZ yM+ds gS \

¼1½ 40 ¼2½ 60 ¼3½ 65¼4½ 11

Ikz-18 & 7 nh gqbZ la[;kvks esa ls igyh pkj la[;kvks dk vkSlr 4 gS rFkk vfUre pkj la[;kvks dkvkSlr Hkh 4 gSA ;fn lHkh lkr la[;kvks dk vkSlr 3 gks ] rks pkSFkh la[;k gksxh \

¼1½ 3 ¼2½ 4 ¼3½ 7¼4½ 11

Ikz-19 & pkj la[;kvks esa ls igyh rhu dk vkSlr 18 rFkk vfUre rhu dk vkSlr 16 gS ;fn vfUre la[;k 19 gks ] rks izFke la[;k gS \

¼1½ 19 ¼2½ 18 ¼3½ 20¼4½ 25

Ikz-20 & 11 la[;kvks dk vkSlr 35 gSA ;fn izFke 6 la[;kvks dk vkSlr 32 gks vkSj vaafre 6 la[;kvks dk vkSlr 37 gks ] rks NBh la[;k D;k gS \

¼1½ 28 ¼2½ 29 ¼3½ 30¼4½ 27

Ikz-21 & 11 ifj.kkeksa dk vkSlr 50 gSA ;fn muesa igys 6 ifj.kkeksa dk vkSlr 49 gks vkSj vafre 6 ifj.kkeksa dk vkSlr 52 gks ] rks NBk ifj.kke fdruk gksxk \

¼1½ 48 ¼2½ 50 ¼3½ 52¼4½ 56

Ikz-22 & 20 la[;kvks dk vkSlr 15 gS vkSj muesa izFke ik¡p dk 12 gSA rnuqlkj ] “ks’k la[;kvks dk vkSlr fdruk gS \

¼1½ 16 ¼2½ 15 ¼3½ 14¼4½ 13

Ikz-23 & ukS la[;kvks dk vkSlr 50 gSA igyh ik¡p la[;kvks dk vkSlr 54 gS vkSj vfUre rhu la[;kvks dk vkSlr 52 gSA rks NBh la[;k gS \

¼1½ 30 ¼2½ 34 ¼3½ 24¼4½ 44

Ikz-24 & A vkSj B dh vkSlr ekfld vk; 14]000 :i;s gS B vkSj C dh vkSlr ekfld vk; 15]600 :Ik;s rFkk C vkSj A dh vkSlr ekfld vk; 14]400 :Ik;s gS C dh ekfld vk; gS \

¼1½ 16000 :0 ¼2½ 15000 :0 ¼3½ 14000 :0¼4½ 15]500 :0

Ikz-25 & ;fn X vkSj Y dh vkSlr ekfld vk; 5050 :0 gSA Y vkSj Z dh vkSlr vk; 6250 :0 gS rFkk X vkSj Z dh vkSlr vk; 5200 : gSA X dh ekfld vk; gksxh \

¼1½ 4050 : ¼2½ 3500 : ¼3½ 4000 : ¼4½ 5000

Ikz-26 & nks la[;kvks A vkSj B dk vkSlr 20 ] B rFkk C dk vkSlr 19 vkSj C RkFkk A dk vkSlr 21 gS A dk eku D;k gS \

¼1½ 24 ¼2½ 22 ¼3½ 20¼4½ 18

Ikz-27 & 100 ls de lHkh fo’ke la[;kvks dk vkSlr gksxk \

¼1½ 49-5 ¼2½ 50 ¼3½ 50-5¼4½ 51

Ikz-28 & lkr yxkrkj vkus okys /ku iw.kkZadks dk vkSlr 26 gSA bu iw.kkZadks esa lcls NksVk gS \

¼1½ 21 ¼2½ 23 ¼3½ 25¼4½ 26

Ikz-27 & pkj yxkrkj vkus okyh le la[;kvks dk vkSlr 27 gS muesa lcls cM+h la[;k la[;k gksxkh \

¼1½ 28 ¼2½ 26 ¼3½ 32¼4½ 30

Ikz-28 & m ls vjaHk gksus okys 5 d`fed iw.kkZadks dk vkSlr n gSA

rnuqlkj ¼m+¿2½ ls vkjaHk okys 6 d`fed iw.kkZdks dk vkSlr D;k gksxk \

¼1½ 2n+52 ¼2½ ¼n+2½ ¼3½ ¼n+3½

¼4½ 2n+92

Ikz-29 & lkr la[;kvks dk vkSlr 18 gS rnuqlkj ;fn muesa ,d la[;k 17 gks vkSj mls 31 esa fn;k tk, rks vkSlr fdruk gks tk,xk \

¼1½ 21-5 ¼2½ 19-5 ¼3½ 20¼4½ 21

Ikz-30 & pkj d`fed le la[;kvks dk vkSlr 9 gSA rnuqlkj muesa lcls cM+h la[;k dkSu lh gS \

¼1½ 12 ¼2½ 6 ¼3½ 8¼4½ 10

Ikz-31 & izFke ik¡p vHkkT; la[;kvks dk vkSlr fdruk gksrk gS \¼1½ 5-3 ¼2½ 5-6 ¼3½ 5¼4½ 3-6

Ikz-32 & mu izFke N% ¼/kukRed½ fo’ke la[;kvks dk vkSlr fdruk gS ftuesa izR;sd 7 }kjk foHkkT; gks \

¼1½ 42 ¼2½ 43 ¼3½ 47¼4½ 49

Ikz-33 & izFke nl vHkkT; la[;kvks dk vkSlr crkb,A¼1½ 10-1 ¼2½ 10 ¼3½ 12-9¼4½ 13

Ikz-34 & rhu la[;k,¡ l izdkj gS fd nwljh la[;k igyh la[;k nqxuh gS vkSj rhljh ls frxquh gSA ;fn rhuks la[;kvks dk vkSlr 44 gks ] rks cM+h la[;k gS \

¼1½ 24 ¼2½ 72 ¼3½ 36¼4½ 108

Ikz-35 & igyh rhu la[;kvks dk vkSlr pkSFkh la[;k dk frxquk gSA ;fn lHkh pkjks la[;kvks dk vkSlr 5 gks rks pkSFkh la[;k Kkr dhft, \

¼1½ 4-5 ¼2½ 5 ¼3½ 2¼4½ 4

Ikz-36 & rhu la[;kvks dk vkSlr 77 gSA igyh la[;k nwljh la[;k dh nqxquh vkSj nwljh la[;k rhljh dh nqxquh gSA igyh la[;k gksxh \

¼1½ 33 ¼2½ 66 ¼3½ 77¼4½ 132

Ikz-37 & rhu la[;kvks esa ls igyh la[;k nwljh la[;k dh nwxquh gS vkSj rhljh dh vk/kh gSA ;fn rhuks la[;kvks dk vkSlr 56 gks rks igyh vkSj rhljh la[;k dk varj gksxk \

¼1½ 12 ¼2½ 20 ¼3½ 24¼4½ 48

Ikz-38 & nl la[;kvks dk vkSlr 7 gSA ;fn izR;sd la[;k dks 12 ls xq.kk fd;k tk, ] rks izkIr gksus okyh ubZ la[;kvks dk vkSlr gksxk \

¼1½ 7 ¼2½ 19 ¼3½ 82¼4½ 84

Ikz-39 & rhu la[;kvks dk vkSlr 40 gSA buesa igyh la[;k ] nwljh dh nqxquh gS vkSj rhljh la[;k dh frxquh gSA rnuqlkj lcls cM+h la[;k vkSj lcls NksVh la[;k dk varj fdruk gS \

¼1½ 30 ¼2½ 36 ¼3½ 46¼4½ 60

Ikz-40 & rhu la[;kvks esa ls nwljh la[;k igyh dh nqxquh gS rFkk rhljh la[;k dh frxquh gSA ;fn rhuks la[;kvks dk vkSlr 44 gS rks igyh vkSj rhljh la[;k dk varj gS \

¼1½ 24 ¼2½ 18 ¼3½ 12¼4½ 6

Ikz-41 & ik¡p la[;kvks dk vkSlr 27 gSA ;fn muesa ls ,d la[;k fudky nh tk, rks vkSLkr 25 gks tkrk gSA fudkyh xbZ la[;k gS \

¼1½ 25 ¼2½ 27 ¼3½ 30¼4½ 35

Ikz-42 & 14 Nk=ks ds izkIrkadks dk vkSlr 71 Fkk ysfdu ckn esa irk pyk fd ,d Nk= ds izkIrkad 56 dh ctk; 42 vkSj nwljs ds 32 dh ctk; 74 p<+k fn, x, FksA vr% lgh vkSlr crkb, \

¼1½ 67 ¼2½ 68 ¼3½ 69¼4½ 71

Ikz-43 & fdlh d{kk esa 50 fo/;kFkhZ gSA 50 fdxzk- Hkkj okyk ,d fo/;kFkhZ pyk tkrk gS rFkk mlds Lfkku ij ,d u;k fo/;kFkhZ vk tkrk

gS ftlls d{kk dk vkSlr Hkkj 12 fdxzk- c<+ tkrk gS u, fo/;kFkhZ

dk Hkkj gS \¼1½ 70 fdxzk- ¼2½ 72 fdxzk- ¼3½ 75 fdxzk-¼4½ 76 fdxzk-

Ikz-44 & tc 60 fdxzk- Hkkj okys ,d O;fDr dks ,d u, O;fDr ls izfrLFkkfir fd;k tkrk gS rks 25 O;fDr;ks ds vkSlr Hkkj esa 1 fdxzk- dh ozf) gks tkrh gSA u, O;fDr dk Hkkj gS \

¼1½ 50 fdxzk- ¼2½ 61 fdxzk- ¼3½ 86 fdxzk-¼4½ 85 fdxzk-

Ikz-45 & nl nh bqbZ la[;kvks dk vkSlr Kkr djrs le; ,d fo/;kFkhZ us xyrh ls ,d la[;k 46 dsLFkku ij 64 fy[k fy;k rFkk viuk lgh vkSlr 50 fudky fn;kA nh gqbZ la[;kvks dk lgh vkSlr gS \

¼1½ 48-2 ¼2½ 48-3 ¼3½ 49-1¼4½ 49-3

Ikz-46 & 10 la[;kvks dk vkSlr 15 ifjdfyr fd;k x;k gSA ckn es irk yxrk gS fd vkSlr ifjdfyr djrs le; ,d la[;k 36 djs xyrh ls 26 i<+ fy;k x;k Fkk lgh vkSlr gS \

¼1½ 20 ¼2½ 18 ¼3½ 14¼4½ 16

Ikz-47 & 27 la[;kvks dk vkSlr 60 gSA ;fn ,d la[;k cnydj 28 dh ctk; 82 dj nh tk, ] rks vkSlr fdruk gks tk,xk \

¼1½ 56 ¼2½ 58 ¼3½ 62¼4½ 64

Ikz-48 & 20 enksa dk vkSlr 47 gSA ckn esa irk pyk fd ,d en dks 62 ds LFkku ij xyrh ls 26 fy[k fy;k x;k rnuqlkj lgh vkSlr Kkr dhft, \

¼1½ 48-8 ¼2½ 47-7 ¼3½ 49-9¼4½ 46-6

Ikz-49 & 20 iz{k.kks dk vkSlr eku 75 izkIr gqvk ckn esa irk pyk fd muesa 97 dks 79 i<+ fy;k x;k Fkk rnuqlkj lgh vkSlr eku fdruk Fkk \

¼1½ 75-7 ¼2½ 75-8 ¼3½ 75-9¼4½ 75-6

Ikz-50 & ;fn 30 vkSj 34 o’kZ ds nks O;fDr;ksa LFkku ij 2 u, O;fDr ,d lewg esa “kkfey dj fn, tk, rks 8 O;fDr ds ml lewg dh vkSlr vk;q esa 3 o’kZ dh ozf) gks tkrh gSA rnuqlkj mu nks u, O;fDr;ks dh vk;q fdruh gS \

¼1½ 22 o’kZ ¼2½ 32 o’kZ ¼3½ 44 o’kZ ¼4½ 48 o’kZ

Ikz-51 & 10 enksa dk vkSlr 80 gS tc ,d en dks 50 dh txg 60 fxu fy;k x;k rks lgh vkSlrgksrk \

¼1½ 69 ¼2½ 79-25 ¼3½ 79¼4½ 79-5

Ikz-52 & 14 Nk=kvks vkSj mudh ,d f”kf{kdk dh vkSlr vk;q 15 o’kZ gSA ;fn f”kf{kdk dh vk;q dks gVk fn;k tk, ] rks vkSlr esa 1 o’kZ dh deh gks tkrh gSA rc f”kf{kdk dh vk;q D;k gS \

¼1½ 32 o’kZ ¼2½ 30 o’kZ ¼3½ 29 o’kZ¼4½ 35 o’kZ

Ikz-53 & ,d fdzdsV f[kykM+h dh 10 ikfj;ksa ds juks dk vkSlr 32 FkkA f[kykM+h vxyh ikjh esa fdrus ju cuk, rfd mlds juks dk vkSlr 4 vf/kd gks tk, \

¼1½ 76 ¼2½ 70 ¼4½ 4¼4½ 2

Ikz-54 & ,d fdzdsV f[kykM+h dk mlds }kjk [ksyh xbZ 64 ikfj;ks ds juks dk dksbZ vkSlr Fkk mldh 65 oha ikjh esa mls “kwU; ds Ldksj ij vkmV dj fn;k tkrk gSA blls mldh vkSlr ju la[;k 2 ju de gks tkrh gSA mldh u;h vkSlr ju la[;k gS \

¼1½ 130 ¼2½ 128 ¼3½ 70¼4½ 68

Ikz-55 & fdzdsV ds fdlh f[kykM+h dk mlds }kjk [ksyh xbZ 8 ikfj;ksa esa cuk;s x;s juks dk dksbZ vkSlr gSA ukSaoh ikjh esa og 100 ju

cukrk gSA ftlls mlds juksa dk vkSlr esa 9 dh ozf) gks tkrh gSA mlds juks dk u;k vkSlr gS \

¼1½ 20 ¼2½ 24 ¼3½ 28¼4½ 32

Ikz-56 & fdlh fdzdsV cYysckt dk mlds }kjk [ksyh x;h 11 ifj;ksa ds juksa dk dksbZ vkSlr Fkk 12 oha ikjh esa mlus 90 ju cuk, rFkk blls mlds juksa dk vkSlr 5 de gks x;k ckjgoha ikjh ds ckn mlds juks dk vkSlr gS \

¼1½ 155 ¼2½ 150 ¼3½ 145¼4½ 140

Ikz-57 & fdlh cYysckt us viuh ckgjoha ikjh esa 63 ju cuk, ftlls mlds juks dk vkSlr 2 vf/kd ks tkrk gS ckjgoha ikjh ds ckn mlds juks dk vkSlr gS \

¼1½ 41 ¼2½ 42 ¼3½ 34¼4½ 35

Ikz-58 & ,d fdzdsV f[kykM+h 10 VsLV [ksyus ds ckn 11 osa VsLV esa 100 ju cukrk gSA ifj.kkeLo:Ik ] mlds juks dk vkSlr 5 c<+ tkrk gSA juks dk orZeku vkSlr fdruk gS \

¼1½ 45 ¼2½ 40 ¼3½ 50¼4½ 55

Ikz-59 & ;fn ,d d{kk esa 30 fdxzk- Hkkj dk Nk= pyk tk, vkSj ,d u;k Nk= vk tk, rks d{kk esa 20 Nk=ks dk vkSlr Hkkkj 0-75 fdxzk- vf/kd gks tk,xk rnuqlkj u, Nk= dk Hkkj Kkr dhft, \

¼1½ 35 ¼2½ 40 ¼3½ 45 ¼4½ 50

Ikz-60 & 24 fo/;kfFkZ;ksa dh ,d d{kk dk vkSlr Hkkj 35 fdxzk- gSA ;fn f”k{kd dk Hkkj Hkh lfEefyr dj fy;k tk, ]rks vkSlr Hkkj 400 xzke c<+ tkrk gSA f”k{kd dk Hkkj fdruk gS \

¼1½ 50 fdxzk- ¼2½ 55 fdxzk- ¼3½ 45 fdxzk-¼4½ 53 fdxzk-

Ikz-61 & fdlh dk;kZy; esa Jfedks dk ekfld vkSlr osru 8500 : gSA ;fn 7 rduhdh fo”ks’kKks dk ekfld vkSlr osru 10]000 : gks vkSj “ks’k Jfedks dk ekfld vkSlr osru 7]800 : gks rks dk;Z”kkyk esa dk;Zjr Jfedks dh dqy la[;k gS \

¼1½ 18 ¼2½ 20 ¼3½ 22¼4½ 24

Ikz-62 & xf.kr esa 28 fo/;kfFkZ;ksa }kjk izkIr vadks dk vkSlr 50 FkkA 8 fo/;kFkhZ Ldwy NksM+dj pys x, rc “ks’k fo/;kfFkZ;ksa }kjk izkIr vadks dk vkSlr 5 c<+ x;kA Ldwy NksM+dj tkus okys fo/;kfFkZ;ksa }kjk izkIr vadks dk vkSlr fdruk gS \

¼1½ 50-5 ¼2½ 37-5 ¼3½ 42-5¼4½ 45

Ikz-63 & 100 la[;kvks dk vkSlr 44 gS bu 100 la[;kvks RkFkk 4 vU; u;h la[;kvks dks feykdj vkSlr 50 gks tkrk gSA u;h la[;kvks dk vkSlr gksxk \

¼1½ 800 ¼2½ 200 ¼3½ 176¼4½ 24

Ikz-64 & ,d uko esa cSBs gq, 5 O;fDr;ksa dk vkSlr Hkkj 38 fdxzk- gSA mlh uko dk vkSj mlesa cSBs O;fDr;ksa dk vkSlr Hkkj 52 fdxzk- gSA rnuqlkj ml uko dk Hkkj fdruk gS \

¼1½ 228 fdxzk- ¼2½ 122 fdxzk- ¼3½ 232 fdxzk- ¼4½ 242 fdxzk-Ikz-65 & x la[;kvks dk vkSlr y2 rFkk y la[;kvks dk vkSlr x2 gSA rnuqlkj ml lHkh la[;kvks dk dqy vkSlr fdruk gksxk \

¼1½ x3+ y3

x+ y¼2½ xy ¼3½ x

2+ y2

x+ y¼4½ xy2+ y x2

Ikz-66 & 10 dqy xasnks esa dqN yky jax dh gS “ks’k lQsn jax dhA lHkh xasnks dk vkSlr ewY; 28 :- gSA;fn yky xsanks dk vkSlr ewY; 25 :- gks vkSj lQsn xsanks dk vkSlr ewY; 30 :- gks rks lQsn

xssanksdh la[;k D;k gksxh \¼1½ 3 ¼2½ 5 ¼3½ 6¼4½ 7

Ikz-67 & pkj yM+dks A, B, C rFkk D dh vkSlr vk;q 5 o’kZ gS vkSj A, B, D rFkk E dh vkSlr vk;q 6 o’kZ gS muesa C vkB o’kZ dk gS ] rks E dh vk;q fdruh gS \ ¼1½ 12 ¼2½ 13 ¼3½ 14

¼4½ 15

L.C.M. and H.C.F

Ikz-1 & nks la[;kvks dk y0 l0 225 gS rFkk mudk e0 l0 5 gSA ;fn ,d la[;k 25 gks ] rks nwljh la[;k gksxh \

¼1½ 5 ¼2½ 25 ¼3½ 45¼4½ 225

Ikz-2 & nks la[;kvks dk y0 l0 1820 gSA vkSj mudk e0 l0 26 gSA ;fn ,d la[;k 130 gks ] rks nwljh la[;k gS \

¼1½ 70 ¼2½ 1690 ¼3½ 364¼4½ 1264

Ikz-3 & nks la[;kvks dk y0 l0 1920 vkSj mudk e0 l0 16 gSA ;fn ,d la[;k 128 gks ] rks nwljh la[;k Kkr dhft, \

¼1½ 204 ¼2½ 240 ¼3½ 260¼4½ 320

Ikz-4 & nks la[;kvks dk e0 l0 15 RkFkk mudk y0 l0 300 gSA ;fn muesa ls ,d la[;k 60 gks nwljh gksxh \

¼1½ 50 ¼2½ 75 ¼3½ 65¼4½ 100

Ikz-5 & nks la[;kvks dk xq.kuQy 4707 gS ;fn mudk e0 l0 37 gks ] rks muesa cM+h la[;k gksxh \

¼1½ 185 ¼2½ 111 ¼3½ 107¼4½ 101

Ikz-6 & nks la[;kvs dk y0 l0 2079 gS vkSj mudk e0 l0 27 gSA rnuqlkj ;fn muesa ls ,d la[;k 189 gks ] rks nwljh la[;k fdruh gS \

¼1½ 297 ¼2½ 584 ¼3½ 189¼4½ 216

Ikz-7 & og NksVh ls NksVh la[;k ftls 4] 6] 8] 12 vkSj 16 ls Hkkx djus ij izR;sd n”kk esa 2 “ks’k jgs] la[;k gS \

¼1½ 46 ¼2½ 48 ¼3½ 50¼4½ 56

Ikz-8 & 13 dk og lcls NksVk xq.kt ftls 4] 5] 6] 7 vkSj 8 ls Hkkx nsus ij izR;sd n”kk esa 2 “ks’k cprk gS \

¼1½ 2520 ¼2½ 842 ¼3½ 2522¼4½ 840

Ikz-9 & pkj vadks dh ,slh lcls cM+h la[;k Kkr dhft, ftls 15] 18] 21 vkSj 24 ls Hkkx nsus ij d`e”k% 11] 14] 17 vkSj 20 “ks’k cpsA

¼1½ 6557 ¼2½ 7556 ¼3½ 5675¼4½ 7664

Ikz-10 & ;fn fdlh d{kk ds fo/;kFkhZ dks 6 ;k 8 ;k 10 ds iwjs & iwjs lewgks esa j[kk tk lds] rks d{kk esa fo/;kfFkZ;ksa dh fuEure la[;k gksxh \

¼1½ 60 ¼2½ 120 ¼3½ 180¼4½ 240

Ikz-11 & og lcls NksVh la[;k ftls 5] 10] 12 rFkk 15 ls Hkkx nsus ij izR;sd n”kk esa 2 “ks’k jgs fdUrq 7 ls Hkkx sus ij dksbZ “ks’k u jgs ] gS \

¼1½ 189 ¼2½ 182 ¼3½ 175¼4½ 91

Ikz-12 & 6] 12 rFkk 18 esa ls izR;sd ls foHkkftr gksus okyh lcls NksVh iw.kZ oxZ la[;k gS \

¼1½ 196 ¼2½ 144 ¼3½ 108¼4½ 36

Ikz-13 & A, B, C ,d gh le; ,d ozRrkdkj LVsfM;e es ,d gh foUnq ls ,d gh fn”kk esa Hkkxuk “kq djrs gSA A ,d pDdj 252 lsd.M esa iwjk dj ysrk gS ] B 308 lsd.M esa vkSj C 198 lsd.M esaA os vkjafHkd fcUnq ij fdrus le; ckn fQj feysaxs \

¼1½ 26 feuV 18 lsd.M ¼2½ 42 feuV 36 lsd.M¼3½ 45 feuV ¼4½ 46 feuV 12 lsd.M

Ikz-14 & 23,45,67 dk egRre lekiorZd fdruk gS \

¼1½ 48105 ¼2½

2105 ¼3½

1105

¼4½ 24105

Ikz- 15 & fo/;kfFkZ;ksa dh vf/kdre la[;k Kkr dhft, ftlesa 1001 isu vkSj 910 isaflys bl izdkj ck¡Vs tk,¡ fd izR;sd dks feys isuks dh la[;k cjkcj gks ,oa izR;sd dks feys isaflyks dh la[;k cjkcj gks \

¼1½ 91 ¼2½ 910 ¼3½ 1001¼4½ 1911

Ikz-16 & ;fn ukSaoh d{kk ds Nk=ks dh 6] 8] 12] ;k 16 dh iaDr;k¡ cukbZ tkrh gS ] rks dksbZ Hkh Nk= NwVrk ugh gSA rnuqlkj ml d{kk esa Nk=ks dh dqy laHkkfor la[;k fdruh gS \

¼1½ 60 ¼2½ 72 ¼3½ 80¼4½ 96

Ikz-17 & 23 ]

49 ]

56 dk y?kqRre lekioR;Z gS \

¼1½ 827 ¼2½

203 ¼3½

103

¼4½ 2027

Ikz-18 & og lcls cM+h la[;k ftlls 989 vkSj 1327 dks Hkkx nsus ij dè”k% “ks’k 5 vkSj 7 jgrs gS ]fuEu gS \

¼1½ 8 ¼2½ 24 ¼3½ 16¼4½ 32

Ikz-19 & og dkSu lh lcls cM+h la[;k gS ftlds }kjk 25] 73 rFkk 97 dks Hkkx ij izR;sd ds fy, lkeu “ks’k jgs gS \

¼1½ 24 ¼2½ 23 ¼3½ 21¼4½ 6

Ikz-20 & og lcls cM+h la[;k ftlls 43] 91 rFkk 183 dks Hkkx nsus ij izR;sd n”kk esa leku “ks’k jgs gksxh \

¼1½ 9 ¼2½ 8 ¼3½ 4¼4½ 3

Ikz-21 & pkj dèkxr vHkkT; la[;k,¡ tks vkjksgh dè esa gS muesa igyh rhu dk xq.kuQy 385 vkSj vafre rhu dk xq.kuQy 1001 gSA rnuqlkj lcls cM+h vHkkT; la[;k dkSu lh gS \ ¼1½ 11 ¼2½ 13 ¼3½ 17

¼4½ 19Ikz-22 & nks la[;kvs dk xq.kuQy 2160 gS vkSj mudk egRre lekorZd 12 gSA rnuqlkj bl izdkj ds tksM+ks dh laHkkfor la[;k fdruh gS \

¼1½ 1 ¼2½ 2 ¼3½ 3¼4½ 4

Ikz-23 & 28 vkSj 42 ds y- l- vkSj e- l- fdl vuqikr esa gS \¼1½ 6 % 1 ¼2½ 2 % 3 ¼3½ 3 % 2¼4½ 7 % 2

Ikz-24 & rhu la[;k,¡ 2 % 3 % 4 ds vuqikr esa gS rFkk mudk e-l- 12 gSA mudk y- l- gksxkA

¼1½ 144 ¼2½ 192 ¼3½ 96¼4½ 72

Ikz-25 & nks la[;k,sa 3 % 4 ds vuqikr esa gSA muds e-l- rFkk y-l- dk xq.kuQy 2028 gSA la[;kvks dk ;ksxQy gksxkA

¼1½ 68 ¼2½ 72 ¼3½ 86¼4½ 91

Ikz-26 & nks la[;kvks dk vuqikr 4 % 5 gS vkSj mudk egRre lekorZd 8 gSA rnuqlkj mldk y?kqRre lekiorZd fdruk gksxk \

¼1½ 130 ¼2½ 140 ¼3½ 150¼4½ 160

Ikz-27 & nks la[;kvks dk vuqikr 3 % 4 gS vkSj mudk egRre lekiorZd 4 gS rks mudk y?kqRre lekiorZd fdruk gksxk \

¼1½ 12 ¼2½ 24 ¼3½ 36¼4½ 48

Ikz-28 & nks la[;vks dk egRre lekiorZd 5 gSA rnuqlkj mudk y?kqRre lekiorZd fdruk gksxk \

¼1½ 10 ¼2½ 60 ¼3½ 15¼4½ 12

Ikz-29 & nks la[;vks dk e- l - rFkk y-l- dè”k% 18 rFkk 378 gSA ;fn muesa ls ,d la[;k 54 gS rks nwljh gksxh \

¼1½126 ¼2½ 144 ¼3½ 198¼4½ 234

Ikz-30 & nks la[;kvks dk e-l- 15 gS rFkk mudk y- l- 225 gSA ;fn muesa ls ,d la[;k 75 gS rks nwljh gksxh \

¼1½ 105 ¼2½ 90 ¼3½ 60¼4½ 45

Ikz-31 & nks la[;kvks dk egRre leikorZd 96 gS vkSj mudk y?kqRre lekorZd 1296 gSA ;fn muesa ,d la[;k 864 gks rks nwljh la[;k fdruh gS \

¼1½ 132 ¼2½ 135 ¼3½ 140¼4½ 144

Ikz-32 & nks la[;kvks ds y- l- o e- l- dk xq.kuQy 24 gSA nksuks la[;kvks dk vUrj 2 gSA ;s la[;k,sa Kkr dhft, \

¼1½ 8 vkSj 6 ¼2½ 8 vkSj 10 ¼3½ 2 vkSj 4¼4½ 6 vkSj 4

Ikz-33 & 29 ls cM+h nks la[;kvks dk e- l- 29 vkSj y- l- 4147 gSA bu la[;kvks dk ;ksx gSA

¼1½ 966 ¼2½ 696 ¼3½ 669¼4½ 666

Ikz-34 & ;nks la[;kvks dk ;ksx 216 gS rFkk mudk e- l- 27 gSA ,slh la[;kvks ds fdrus tksM+s gksasxs \

¼1½ 1 ¼2½ 2 ¼3½ 3¼4½ 0

Ikz-35 & nks la[;kvks dk ;ksx 36 gS rFkk muds e- l- rFkk y-l- dè”k% 3 vkSj 105 gSA mu nks la[;kvkss ds O;qRdèksa dk ;ksx gksxk \

¼1½ 13 ¼2½ 911 ¼3½

735

¼4½ 435

Ikz-36 & nks la[;kvks dk ;ksxQy 45 gS rFkk muds e- l- rFkk y- l- d`e”k% 3 rFkk 168 gSA mu la[;kvks ds O;qRd`eksa dk ;ksxQy gksxk \

¼1½ 1537 ¼2½

311 ¼3½

1556

¼4½ 556

Ikz-37 & ;fn P=23 .310 .5 ;Q=25 .3 .7 gks rks P rFkk Q dk egRre lekorZd fdruk gksxk \

¼1½ 2.3 .5 .7 ¼2½ 3.23 ¼3½ 23 .37 ¼4½ 25 .310 .5 .7Ikz-38 & 1500 ls de og cM+h ls cM+h la[;k tks 16 rFkk 18 ls nksuks ls foHkkftr gksrh gS ] gSA

¼1½ 1440 ¼2½ 1404 ¼3½ 1386¼4½ 1368

{ks=ferfrIkz-1 & fdlh oxZ ds fod.kZ dh yEckbZ a lseh- gSA fuEu ls dkSu lk oxZ ds {ks=Qy dks fu:fir= djuk gS ¼oxZ ls-eh- esa½

¼1½ 2a ¼2½ a

√2 ¼3½ a2/2 ¼4½ a2/4

Ikz-2 & ;fn fdlh oxZ ABCD ds fod.kZ AC dh yEckbZ 5-2 ls-eh- gks rks bldk {ks=Qy gksxk \

¼1½ 15-12 oxZ ls-eh- ¼2½ 13-52 oxZ ls-eh- ¼3½ 12-62 oxZ ls-eh- ¼4½ 10-00 oxZ ls-eh-Ikz-3 & nks oxkZs dk ifjeki 24 lseh- vkSj 32 lseh- gSA bu oxkZs ds {ks=Qyksa ds ;ksx cjkcj {ks=Qy okys ,d rhljs oxZ dk ifjeki ¼lseh- esa½ gSA

¼1½ 45 ¼2½ 40 ¼3½ 32¼4½ 48

Ikz-4 & fdlh oxZ dk fod.kZ 4 √2 ls-eh- gSA ,d vU; oxZ dk fod.kZ ftldk {ks=Qy igys oxZ ds {ks=Qy dk nqxquk gS ] fuEu gS \

¼1½ 8√2 ls-eh- ¼2½ 16 ls-eh- ¼3½ √32 ls-eh-¼4½ 8 ls-eh-

Ikz-5 & ik¡p oxksZ ds ifjeki d`e”k% 24 lseh- vkSj 32 lseh- ] 40 lseh- ] 76 lseh- vkSj 80 lseh- gSA ml oxZ dk ifjeki ftldk {ks=Qy bu ik¡pks oxksZ ds {ks=Qyksa ds ;ksx ds cjkcj gS gksxk \ ¼1½ 31 lseh- ¼2½ 62 lseh- ¼3½ 124 lseh-

¼4½ 961 lseh-Ikz-6 & nks oxkZs ds ifjeki 40 lseh- vkSj 32 lseh- gS A ml rhljs oxZ dk ifjeki ftldk {ks=Qy bu nksuks oxkZs ds {ks=Qyks dk varj gS fuEu gSA

¼1½ 24 lseh- ¼2½ 42 lseh- ¼3½ 40 lseh-¼4½ 20 lseh-

Ikz-7 & ;fn nks oxkZs ds {ks=Qkyks dk vuqikr 225 % 256 gks rks muds ifjekiks dk vuqikr gksxk \

¼1½ 225 % 256 ¼2½ 256 % 225 ¼3½ 15 % 16 ¼4½ 16 % 15 Ikz-8 & fdlh oxZ ds {ks=Qy dk mlds fod.kZ ij [khaps x, oxZ ds {ks=Qy ls vuqikr gksxk \

¼1½ 1 % 1 ¼2½ 1 % 2 ¼3½ 1 % 3¼4½ 1 % 4

Ikz-9 & ;fn ,d oxZ ds varo`Zr dk {ks=Qy 9π cm2 gS rks oxZ dk {ks=Qy gksxk \

¼1½ 24 cm2 ¼2½ 30 cm2 ¼3½ 36 cm2

¼4½ 81cm2

Ikz-10 & fdlh oxZ ds ,d fod.kZ dh yackbZ 15√2 lseh- gSA bldk {ks=Qy gksxk \

¼1½ 112-5 cm2 ¼2½ 450 cm2 ¼3½ 225√22

cm2

¼4½ 225 cm2

Ikz-11 & ,d oxZ dk {ks=Qy 200 oxZ eh- gSA ,d u;k oxZ bl izdkj cuk;k x;k gS fd mlds fod.kZ dh yEckbZ igys fod.kZ dh √2 xq.kk gSA u, oxZ dk {ks=Qy gS \

¼1½ 200√2 oxZ eh- ¼2½ 400 √2 oxZ eh- ¼3½ 400 oxZ eh-¼4½ 800 oxZ eh-

Ikz-12 & ,d vk;rkdkj IykaV dh Hkqtkvks esa 5 % 4 dk vuqikr gS vkSj bldk {ks=Qy 500 oxZ eh- gSA IykaV dh ifjeki gS \ ¼1½ 80 eh- ¼2½ 100 eh- ¼3½ 90 eh-

¼4½ 95 eh-Ikz-13 & fdlh vk;rkdkj eSnku dh yEckbZ vkSj PkkSM+kbZ esa 3 % 2 dk vuqikr gSA ;fn bldh ifjeki 80 eh- rks budh pkSM+kbZ gksxh \

¼1½ 18 ¼2½ 16 ¼3½ 10¼4½ 24

Ikz-14 & 42 lseh- f=T;k okys ,d ozRrkdkj rkj dks ,d vk;r ds :Ik rksM+k tkrk gS ftldh Hkqtk,¡ 6 % 5 ds vuqikr esa gSA bl vk;r dh NksVh Hkqtk gksxh \


Ikz-15 & ;fn fdlh vk;r dh YkEckbZ vkSj pkSM+kbZ esa 3 % 2 dk vuqikr gS vkSj bldk ifjeki 20 lseh- gS rks vk;r dk {ks=Qy gksxk \

¼1½ 24 ¼2½ 48 ¼3½ 72¼4½ 96

Ikz-16 & ,d 38 eh- yEcs rFkk 32 eh- pkSM+s vk;rkdkj {ks= ds vUnj dh vksj pkjks rjQ ,d leku pkSM+kbZ okyk ,d iFk cuk;k x;k gSA ;fn iFk dk {ks=Qy 600 m2 gks rks iFk dh pkSM+kbZ gksxh ¼1½ 30

eh- ¼2½ 5 eh- ¼3½ 18-75 eh- ¼4½ 10 eh-Ikz-17 & 18 lseh- rFkk 14 lseh- Hkqtkvks okys vk;r ds vUnj [khaps tkus okys lcls cM+s o`Rr dk {ks=Qy gksxk \

¼1½ 49 cm2 ¼2½ 154 cm2 ¼3½ 378cm2

¼4½ 1078cm2

Ikz-18 & ;fn fdlh vk;r dh yEckbZ rFkk mldh ifjeki 5 % 16 ds vuqikr esa gks rks mldh yEckbZ rFkk pkSM+bZ esa vuqikr gksxk \

¼1½ 5 % 11 ¼2½ 5 % 8 ¼3½ 5 % 4¼4½ 5 % 3

Ikz-19 & fdlh vk;r dh nks layXu Hktk,¡ 4 % 3 ds vuqikr esa gSA ;fn mldk {ks=Qy 192 m2 gS rks mldk ifjeki gksxk ¼ehVj esa½ gksxk \

¼1½ 28 ¼2½ 36 ¼3½ 56¼4½ 60

Ikz-20 & ,d vk;rkdkj eSnku dh pkSM+bZ rFkk yEckbZ 3 % 4 ds

vuqikr esa gSA ml eSnku dk {ks=Qy 112 gsDVs;j gSA rnuqlkj ml

eSnku dh pkSM+kbZ fdruh gS \¼1½ 25 ehVj ¼2½ 50 ehVj ¼3½ 75 ehVj ¼4½ 100 ehVj

Ikz-21 & ;fn fdlh f=Hkqt dk {ks=Qy 1176 cm2 gS vkSj vk/kkj vkSj lacaf/kr ÅapkbZ dk vuqikr 3 % 4 gS rks f=Hkqt dh ÅapkbZ D;k gksxh \


Ikz-22 & 8 ehVj yEcs vkSj 16 ehVj pkSM+s ,d dejs ds Q”kZ dks <dus ds fy, 4 MslhehVj oxZ {ks=Qyokyh dqy fdruh Vkbyks dh vko”;drk gksxh \

¼1½ 200 ¼2½ 260 ¼3½ 280¼4½ 300

Ikz-23 & ,d vk;rkdkj IykaV dk ifjeki 48 eh- gS vkSj {ks=Qy 108m2 gSA IykaV ds vk;kr gS \

¼1½ 36 eh- vkSj 3 eh- ¼2½ 12 eh- vkSj 9 eh- ¼2½ 27 eh- vkSj 3 eh- ¼4½ 18 eh- vkSj 6 eh-

Ikz-24 & ,d vk;r dh yackbZ vkSj pkSM+kbZ nqxquh dj nh xbZ gSA {ks=Qy esa izfr”kr ozf) gS \

¼1½ 150% ¼2½ 200% ¼3½ 300% ¼4½ 400%

Ikz-25 & fdlh f=Hkqt dk vk/kkj 15 lseh- gS vkSj Å¡pkbZ 12 lseh- gSA ,d vU; f=Hkqt dh Å¡pkbZ ftldk {ks=Qy bl f=Hkqt ds {ks=Qy dk nqxquk gS vkSj vk/kkj 20 lseh- gS fuEu gS \

¼1½ 9 lseh- ¼2½ 18 lseh- ¼3½ 8 lseh-¼4½ 12-5 lseh-

Ikz-26 & nks f=Hkqtks esa {ks=Qkyks dk vuqikr 4 % 3 gS vkSj Å¡pkbZvks dk vuqikr 3 % 4 gSA buds vk/kkjks dk vuqikr Kkr dhft, \

¼1½ 16 % 9 ¼2½ 9 % 16 ¼3½ 9 % 12¼4½ 16 % 12

Ikz-27 & fdlh leckgq f=Hkqt dk {ks=Qy 400 √3 oxZ eh- gSA bldk ifjeki gS \

¼1½ 120 eh- ¼2½ 150 eh- ¼3½ 90 eh-¼4½ 135 eh-

Ikz-28 & fdlh f=Hkqt dk {ks=Qy 216 cm2 gS vkSj mldh Hkqtk,¡ 3 % 4 % 5 ds vuqikr esa gSA bl f=Hkqt dk ifjeki gksxk \


Ikz-29 & ;gk¡ nh x;h vkd`fr esa fcUnq D rFkk E d`e”k% f=Hkqt ABC dh Hkqtkvks AB rFkk AC ds e/; fcUnq gSA f=Hkqt ds Nk;kafdr Hkkx dk {ks=Qy dqy f=Hkqt {ks=Qy dk fdruk izfr”kr gS \ A

D E

B C

¼1½ 50% ¼2½ 25% ¼3½ 75% ¼4½ 60%

iz-30 & fdlh leckgq f=Hkqt dh Å¡pkbZ 4 √3 lseh- gSA blds ifjo`Rr ds {ks=Qy dk blds varoZ`Rr ds {ks=Qy dk vuqikr gksxk \

¼1½ 2 % 1 ¼2½ 4 % 1 ¼3½ 4 % 3¼4½ 3 % 2

Ikz-31 & fdlh leckgq f=Hkqt dh Å¡pkbZ 4√3 lseh- gSA blds ifjo`r ds {ks=Qy dk blds vro`Zr ds {ks=Qy esa vuqikr gksxk \

¼1½ 2 % 1 ¼2½ 4 % 1 ¼3½ 4 % 3¼4½ 3 % 2

Ikz-32 & d.kZ 16√2 lseh- okys ledks.k lef}ckgq f=Hkqt dk {ks=Qy gksxk \

¼1½ 144 cm2 ¼2½ 128 cm2 ¼3½ 112 cm2

¼4½ 110 cm2

Ikz-33 & ;fn fdlh leckgq f=Hkqt ds ifjeki dk la[;kRed eku mlds {ks=Qy dk √3 xquk gS rks f=Hkqt dh gj Hkqtk dh yEckbZ gS \ ¼1½ 2 ;wfuV ¼2½ 3 ;wfuV ¼3½ 4 ;wfuV

¼4½ 6 ;wfuVIkz-34 & ,d lef=ckgq f=Hkqt dh izR;sd Hkqtk 6 lseh- gS rnuqlkj mldk {ks=Qy fdruk gS \

¼1½9√3 ¼2½ 6√3 ¼3½ 4√3 ¼4½ 8√3

iz-35 & fdlh leckgq f=Hkqt dk {ks=Qy 4 √3 cm2 gSA f=Hkqt dh izR;sd Hkqtk dh yEckbZ gS \

¼1½ 3 lseh- ¼2½ 2√2 lseh- ¼3½ 2√3 lseh-¼4½ 4 lseh-

Ikz-36 & fdlh ledks.k f=Hkqt dks ledks.k cukus okyh Hkqtk,¡ 5 % 12 ds vuqikr esa gSA ;fn f=Hkqt dk {ks=Qy 270 cm2 gS rks d.kZ dh yEckbZ gksxh \


Ikz-37 & ml f=Hkqt dk {ks=Qy fdruk gksxk ftldh Hkqtk,¡ 9 lseh ] 10 lseh ] rFkk 11 lseh- yach gks

¼1½ 30 cm2 ¼2½ 60 cm2 ¼3½ 30√2 cm2¼4½ 60√2cm2

Ikz-38 & ,d leckgq f=Hkqt dh Å¡pkbZ 15 lseh- gS rnuqlkj mldk {ks=Qy fdruk gksxk \

¼1½ 50√3 oxZ lseh- ¼2½ 70√3 oxZ lseh- ¼3½ 75√3 oxZ lseh- ¼4½ 150√3 oxZ lseh-

Ikz-39 & ,d leprqHkZqt ds fod.kZ 24 lseh- vkSj 10 lseh- gSA bl leprqHkZt dh ifjeki ¼lseh-½ gS \

¼1½ 68 ¼2½ 65 ¼3½ 54¼4½ 52

Ikz-40 & ,d leprqHkZqt dh ifjeki 40 lsehp gSA ;fn nksuks fod.kkZs esa ls ,d dh yEckbZ 12 lseh- gS rks nwljs fod.kZ dh yEckbZ D;k gS \

¼1½ 12 lseh- ¼2½ √136 lseh- ¼3½ 16 lseh- ¼4½ √44 lseh-

Ikz-41 & fdlh leprqHkZqt dk ifjeki 40 eh gS vkSj mldh Å¡pkbZ 5 eh gS bldk {ks=Qy gS \

¼1½ 60 oxZ eh- ¼2½ 50 oxZ eh- ¼3½ 45 oxZ eh- ¼4½ 55 oxZ eh-Ikz-42 & fdlh leprqHkZqt dk ifjeki 40 lseh- gSA ;fn blds ,d fod.kZ dh yEckbZ 12 lseh- gS rks nwljs fod.kZ dh yEckbZ gS \ ¼1½ 14 lseh- ¼2½ 15 lseh- ¼3½ 16 lseh-

¼4½ 12 lseh-Ikz-43 & fdlh leprqHkqZt dk {ks=Qy 150 cm2 gSA mlds ,d fod.kZ dh yEckbZ 10 lseh- gSA nwljs fod.kZ dh yEckbZ gksxh \


Ikz-44 & fdlh ,d prqHkqZt dh Hkqtk,¡ 3 % 4 % 5 % 6 ds vuqikr esa gS rFkk bldk ifjeki 72 lseh- gS bldh lcls cM+h Hkqtk dh yEckbZ ¼lseh-½ gksxh \

¼1½ 24 ¼2½ 27 ¼3½ 30¼4½ 36

Ikz-45 & ;fn fdlh leprqHkqZt dh lekukarj Hkqtkvks dh yackbZ dk vuqikr 3 % 2 gSA muds chp dhU;wure nwjh 15 lseh- gS rFkk leyac prqHkqZt dk {ks=Qy 450 cm2 gSA rnuqlkj lekukarj Hkqtkvks dh yackbZ dk ;ksx fdruk gksxk \ ¼1½ 15 lseh- ¼2½ 36 lseh- ¼3½ 42 lseh-

¼4½ 60 lseh-Ikz-46 & ;fn fdlh leprqHkZqt dh ,d Hkqtk rFkk mlds ,d fod.kZ dh eki d`e”k% 10 lseh- rFkk 16 lseh- gks rks cm2 esa mldk {ks=Qy gksxk \

¼1½ 60 ¼2½ 64 ¼3½ 96¼4½ 100

Ikz-47 & ,d lekarj prqHkZqt dh nks vklUu Hkqtkvks dh yackbZ 15 lseh- vkSj 18 lseh- gSA ;fn nks NksVh Hkqtkvks ds chp dh nwjh 12 lseh- gS rks cM+h Hkqtkvks ds chp dh gS \


Ikz-48 & ;fn ,d leprqHkqZt ds fod.kZ 8 rFkk 6 gks rks mldh Hkqtk dk oxZ fdruk gksxk \

¼1½ 25 ¼2½ 55 ¼3½ 64¼4½ 36

Ikz-49 & ,d leprqHkZqt dk {ks=Qy 216 cm2 gS vkSj mlds ,d fod.kZ dh yackbZ 24 lseh- gSA rnuqlkj ml leprqHkqZt dk ifjeki fdruk gksxk \

¼1½ 52 ¼2½ 60 ¼3½ 120¼4½ 100

Ikz-50 & ;fn nks ?kuks ds vk;ruks esa 27 % 1 dk vuqikr gS rks budh Hkqtkvks esa vuqikr gS \

¼1½ 3 % 1 ¼2½ 27 % 1 ¼3½ 1 % 3¼4½ 1 % 27

Ikz-51 & fdlh ?kukHk dh Hkqtkvks dk vuqikr 1 % 2 % 3 gSA bldk iz’Bh; {ks=Qy 88 cm2 gSA ?kukHk dk vk;ru gS \

¼1½ 120 cm3 ¼2½ 64 cm3 ¼3½ 48 cm3 ¼4½ 24 cm3

Ikz-52 & ;fn ,d ?ku dk fod.kZ √12 lseh- gS rks mldk vk;ru ¼?ku lseh- esa½ D;k gS \

¼1½ 8 ¼2½ 12 ¼3½ 24¼4½ 3√2

Ikz-53 & 15 lseh- Hkqtkokys fdlh ?ku esa ls 3 lseh- Hkqtkokys dqy fdrus ?ku dkVs tk ldrs gS \

¼1½ 25 ¼2½ 27 ¼3½ 125¼4½ 144

Ikz-54 & ml ?ku dk vk;ru D;k gksxk ftlds fod.kZ dh eki 4 √3 lseh- gS \

¼1½ 16 ¼2½ 27 ¼3½ 64¼4½ 8

Ikz-55 & ;fn nks ?kuks ds v;ruks dk vuqikr 27 % 64 gS rks muds lEiw.kZ i`’Bh; {ks=Qyks dk vuqikr gS

¼1½ 27 % 64 ¼2½ 3 % 4 ¼3½ 9 % 16¼4½ 3 % 8

Ikz-56 & ml lcls yEch NM+ dh yEckbZ Kkr dhft, tks 10 eh- yEckbZ 6 eh- pkSM+kbZ vkSj 4 eh- Å¡pkbZ okys ,d gkWy esa j[kh tk ldrh gS \

¼1½ 2√38 eh- ¼2½ 4 √38 eh- ¼3½ 2√19 eh- ¼4½ 19 eh-

Ikz-57 & ,d ?kukHk dk vk;ru ,d ?ku ds vk;ru dk nqxquk gSA ;fn ?kukHk dh foek,¡ 9 lseh- ] 8 lseh- vkSj 6 lseh- gS rks ?ku dk lEiw.kZ i`’Bh; {ks=Qy gS \

¼1½ 72 cm2 ¼2½ 216 cm2 ¼3½ 432 cm2

¼4½ 108 cm2

Ikz-58 & ydM+yh ds ,d cDls dh eki 20 lseh- × 12 lseh- × 10 lseh- gSA ydM+h dh eksVkbZ 1 lsehgSA bl cDls dks cukus esa yxh ydM+h dk vk;ru ¼?ku lseh- esa½ gS \

¼1½ 960 ¼2½ 519 ¼3½ 2400¼4½ 1120

iz-59 & ,d lkcqu dh fVDdh dk eki 8 lseh- × 5 lseh- × 4 lseh- gSA ,d ckWDl ftldk eki 56 lseh- × 35 lseh- × 28 lseh- gS esa ,lh fdruh fVfd;k¡ iSd dh tk ldrh gS mudh la[;k gksxh \iz-60 & ,d ?kukHk dk vk;ru ,d ?ku ds vk;ru dk nqxquk gSA ;fn ?kukHk dh foek,¡ 9 lseh- ] 8 lseh- vkSj 6 lseh- gks rks ?ku dk lEiw.kZ Ik`’Bh; {ks=Qy gksxk \

¼1½ 72 cm2 ¼2½ 216 cm2 ¼3½ 432 cm2

¼4½ 108 cm2

Ikz-61 & ,d ?kukHk ds rhu layXu ryks ds {ks=Qy d`e”k% x , y , z oxZ bdkbZ gSA ;fn ?kukHk dk vk;ru y ?ku bdkbZ gks rks v , x , y , z esa lgh lEca/k gksxk \

¼1½ v2=xyz ¼2½ v3=xyz ¼3½ v2=x3 y3 z3 ¼4½ v3=x2 y2 z2

Ikz-62 & ;fn fdlh ?ku ds fod.kZ dh yackbZ 8√3 lseh- gS rks mldk iz’Bh; {ks=Qy gS \

¼1½ 192 oxZ lseh- ¼2½ 512 oxZ lseh- ¼3½ 768 oxZ lseh-¼4½ 384 oxZ lseh-

Ikz-63 & 12 ehVj yacs 8 ehVj pkSM+s rFkk 9 ehVj Å¡ps fdlh dejs desa j[kus lcls yacs [kEcs dh yackbZ fdruh gks ldrh gS \

¼1½ 12 ehVj ¼2½ 17 ehVj ¼3½ 19 ehVj ¼4½ 21 ehVj

Ikz-64 & fdlh ?ku ds fod.kZ dh yEckbZ 6 lseh- gSA ?ku dk vk;ru ¼cm3esa½ gksxk \

¼1½ 18√3 ¼2½ 24 √3 ¼3½ 28√3 ¼4½ 30√3

Ikz-65 & ,d ?ku dk fod.kZ 6√3 lseh- gSA rnuqlkj mlds dqy i`’Bh; {ks=Qy rFkk vk;ru dk vuqikr D;k gksxk \

¼1½ 2 % 1 ¼2½ 1 % 6 ¼3½ 1 % 1¼4½ 1 % 2

Ikz-66 & fdlh dejs esa ok;q dk vk;ru 204 ?ku ehVj gSA dejs dh Å¡pkbZ 6 ehVj gSA dejs ds Q”kZ dk {ks=Qy D;k gS \

¼1½ 32 oxZ ehVj ¼2½ 46 oxZ ehVj ¼3½ 44 oxZ ehVj ¼4½ 34 oxZ ehVj

Ikz-67 & ;fn ,d ?ku dk dqy iz’Bh; {ks=Qy 96 oxZ lsaVhehVj gS rks mldk vk;ru gS \

¼1½ 56 ?ku lsaVhehVj ¼2½ 16 ?ku lsaVhehVj ¼3½ 64 ?kulsaVheVj ¼4½ 36 ?ku ehVj Ikz-68 & leku vk;ru ds nks yEc o`Rrh; csyuks dh Å¡pkbZ;ksa dk vuqikr 1 % 2 gS muds v)ZO;klks dk vuqikr gS \

¼1½ √2:1 ¼2½ 2 % 1 ¼3½ 1 % 2¼4½ 1 % 4

Ikz-69 & 85 ehVj yEch ,d NM+ dks nks Hkkxks esa ck¡Vk x;k gSA ;fn ,d Hkkx nwljs dk 2@3 gS rks yEcs Hkkx dh yEckbZ gS \

¼1½ 34 ¼2½ 5632 ¼3½ 85

¼4½ 51Ikz-70 & nks csyuks dh vk/kkj f=T;k,¡ 2 % 3 ds vuqikr esa gS vkSj mudh Å¡pkbZ;ks dk vuqikr 5 % 3 gSmuds vk;ruks dk vuqikr gS \

¼1½ 27 % 20 ¼2½ 20 % 27 ¼3½ 9 % 4¼4½ 4 % 9

Ikz-71 & yksgs dk ,d [kks[kyk ikbi 21 lseh- yEck gS rFkk bldk ckgjh O;kl 8 lseh- gSA ;fn ikbi dh eksVkbZ 1 lseh- gS rFkk yksgs dk Hkkj 8 xzk¿cm3 gks rks ikbi dk Hkkj \

¼1½ 3-696 fdxzk- ¼2½ 3-6 fdxzk- ¼3½ 36 fdxzk- ¼4½ 36-9 fdxzk-Ikz-72 & nks leku vk;ru okys csyuks ds O;kl 3 % 2 ds vuqikr esa gSA mudh Å¡pkbZ;ksa esa vuqikr gksxk

¼1½ 4 % 9 ¼2½ 5 % 6 ¼3½ 5 % 8 ¼4½ 8 % 9

Ikz-73 & nks yEc o`Rrh; csyuks dh f=T;kvks dk vuqikr 2 % 3 gS vkSj mudh Å¡pkbZ 5 % 4 ds vuqikr esa gSA mudsa od`iz’B ds {ks=Qy dk vuqikr gS \

¼1½ 5 % 6 ¼2½ 3 % 4 ¼3½ 4 % 5¼4½ 2 % 3

Ikz-74 & ,d csyu dh f=T;k vkSj Å¡pkbZ;ksa dk vuqikr 5 % 7 gS vkSj mldk vk;ru 550 cm3gSA rnuqlkj mlds od`iz’B dk {ks=Qy fdrus cm2 gS \

¼1½ 110 ¼2½ 444 ¼3½ 220¼4½ 616

Ikz-75 & /kkrq ds rhu Bksl xksyks ftuds O;kl 6 lseh- 8 lseh- vkSj 10 lseh- gS dks fi?kykdj ,d u,Bksl xksys :I esa <kyk x;k gSA u, xksys dk O;kl gS \


Ikz-76 & /kkrq dh rhu Bksl xsanks ftudh f=T;k,¡ 3 lseh- ] 4 lseh- vkSj 5 lseh- gS dks fi?kykdj ,d vU; Bksl xsan cukbZ tkrh gSA bl ubZ xsan dh f=T;k gS \


Ikz-77 & ;fn ,d xksys ds v)Z O;kl dks nqxquk dj fn;k tk, rks bldk vk;ru gks tk,xk \

¼1½ nqxquk ¼2½ pkj xquk ¼3½ 6 xquk¼4½ vkB xquk

Ikz-78 & nks xksys ds i`’Bh; {ks=Qy 4 % 9 ds vuqikr esa gSA muds vk;ruks dk vuqikr gksxk \

¼1½ 2 % 3 ¼2½ 4 % 9 ¼3½ 8 % 27 ¼4½ 64 % 729

Ikz-79 & ;fn nks xksydks ds i`’Bh; {ks=Qyks dk vuqikr 4 % 9 gks rks muds vk;ruks dk vuqikr fdruk gksxk \

¼1½ 19 % 81 ¼2½ 2 % 3 ¼3½ 4 % 9¼4½ 8 % 27

Ikz-80 & ,d xksys rFkk v/kZxksys dk vk;ru cjkcj gSA mudh f=T;kvks dk vuqikr gS \

¼1½ 1 % 2 ¼2½ 1 % 8 ¼3½ 1 :√2¼4½ 1 : 3√2

Ikz-81 & lhls dh ,d xksykdkj xsan dks ftldh f=T;k 10 lseh- gS fi?kykdj 5 feeh- f=T;k okyh lhls dh NksVh xsns cuk nh xbZ gSA

rnuqlkj mu NksVh xsanks dh laHkkfor la[;k fdruh gS ¼π=227 ½

¼1½ 8000 ¼2½ 400 ¼3½ 800¼4½ 125

Ikz-82 & ;fn fdlh xksyk/kZ dk dqy i`’Bh; {ks=Qy 27π oxZ lseh- gS rks xksyk/kZ ds vk/kkj dh f=T;k gS

¼1½ 9√3 lseh- ¼2½ 3 lseh- ¼3½ 3√3 lseh-¼4½ 9 lseh-

Ikz-83 & ,d “kaDokdkj Vadh dh Å¡pkbZ 60 lseh- gS vkSj mlds vk/kkj dk O;kl 64 lseh- gSA 35 : izfr oxZ eh- dh nj ls mls ckgj ls isUV djkus dk O;; D;k gksxk \ ¼1½ :- 52-00 yxHkx¼2½ :- 39-20 yxHkx¼3½ :- 35-20 yxHkx

¼4½ :- 23-94 yxHkx Ikz-84 & nks “kadqvks ds vk;ruks dk vuqikr 2 % 3 gS vkSj muds vk/kkjks dh f=T;kvks dk vuqikr 1 % 2 gSA mudh Å¡pkbZ;ksa dk vuqikr gS \

¼1½ 3 % 8 ¼2½ 8 % 3 ¼3½ 4 % 3¼4½ 3 % 4

Ikz-85 & ;fn 24 lseh- Å¡pkbZ okys ,d yEc o`Rrh; “kadq dk vk;ru 1232 cm3 gS rks mldk od`iz’VBh; {ks=Qy gS \

¼1½ 1254 cm2 ¼2½ 704 cm2 ¼3½ 550cm2 ¼4½ 154 cm2

iz-86 & ,d yEc oRrh; “kadq ds vk/kkj ij O;kl 4 lseh- rFkk mldh Å¡pkbZ 2√3 lseh gSA “kadq dh fr;Zd Å¡pkbZ gksxh \

¼1½ 5 lseh- ¼2½ 4 lseh- ¼3½ 2√3 lseh-¼4½ 3 lseh-

Ikz-87 & nks “kadqvks dh f=T;kvks dk vuqikr 3 % 4 gS vkSj mudh Å¡pkb;ksa dk vuqikr 4 % 3 gSArnuqlkj muds vk;ruks dk vuqikr D;k gksxk \

¼1½ 3 % 4 ¼2½ 4 % 3 ¼3½ 9 % 16¼4½ 16 % 9

Ikz-88 & ,d yEc o`Rrh; “kadq dh Å¡pkbZ vkSj O;kl dk vuqikr 3 % 2

gS vkSj vk;ru 1078 ?ku lseh- gS rks mldh ÅapkbZ gS \ ¼π=227

½Ikz-89 & nks “kadqvks dh f=T;kvks dk vuqikr 3 % 4 gS vkSj mudh ÅapkbZ;ks dk vuqikr 4 % 3 gSA rnuqlkj muds vk;ruks dk vuqikr D;k gksxk \ ¼1½ 3 % 4 ¼2½ 4 % 3 ¼3½ 9 % 16

¼4½ 16 % 9Ikz-90 & ,d “kadq dh f=T;k rFkk ÅapkbZ dk vuqikr 4 % 3 gSA rnuqlkj mldh od`kdkj lrg ds {ks=Qy rFkk dqy lrg ds {ks=Qy dk vuqikr fdruk gksxk \

¼1½ 5 % 9 ¼2½ 3 % 7 ¼3½ 5 % 4¼4½ 16 % 9

Ikz-91 & ,d yac o`Rrh; “kadq dk vk;ru 1232 cm3 gS vkSj mldh Å/okZ/kj Å¡pkbZ 24 lseh- gSA rnuqlkj mlds od`kdkj iz’B dk {ks=Qy fdruk gS \

¼1½ 154 cm2 ¼2½ 550 cm2 ¼3½ 604 cm2

¼4½ 704 cm2

Ikz-92 & 16 lseh- Å¡pkbZ okys ,d Bksl “kadq ds vk/kkj dh ifjf/k 33 lseh- gSA rnuqlkj ml “kadq dk vk;ru fdrus cm3 gS \ ¼1½ 1028 ¼2½ 616 ¼3½ 462

¼4½ 828Ikz-93 & 24 lseh- Å¡pkbZ okys ,d yac o`Rrh; “kadq dk vk;ru 1232 cm3 gSA rnuqlkj mlds od`h; iz’B dk {ks=Qy fdruk gksxk \

¼1½ 550 ¼2½ 704 ¼3½ 924¼4½ 1254

Ikz-94 & ,d yac o`Rrh; “kadq ds vkk/kkj dk ifjeki 8 lseh- gSA ;fn ml “kadq dh Å¡pkbZ 21 lseh- gks rks mldk vk;ru fdruk gksxk \

¼1½ 108 π cm3 ¼2½ 112π cm3 ¼3½ 112 π cm3 ¼4½

108πcm3

Ikz-95 & nks yac ozRrkdkj “kadqvks ds vk;kru 4 % 1 vuqikr esa gS muds O;kl 5 % 4 vuqikr esa gSA rnuqlkj mudh Å¡pkbZ;ksa dk vuqikr D;k gksxk \ ¼1½ 25 % 16 ¼2½ 25 % 64 ¼3½ 64 % 25

¼4½ 16 % 25Ikz-96 & fdlh ifg, dh f=T;k 21 lseh- gSA 924 ehVj dh nwjh r; djus

esa bldks fdrus pDdj yxkus iM+saxs \ ¼π=227 ½

¼1½ 7 ¼2½ 11 ¼3½ 200¼3½ 700

Ikz-97 & fdlh o`Rrh; ifg, dh f=T;k 17-5 eh- gSA 11 fdeh- dh nwjh r; djus esa bldks fdrus pDdj yxkus iM+saxs \

¼1½ 800 ¼2½ 100 ¼3½ 900¼4½ 1200

Ikz-98 & dlh o`Rr dk {ks=Qy 38-5 oxZ lseh- gSA mlds ifjf/k dh yEckbZ ¼lseh- esa½ gS \

¼1½ 22 ¼2½ 24 ¼3½ 26¼4½ 32

Ikz-99 & 5 v/kZO;klokys o`Rr dk {ks=Qy mldh ifjf/k ds fdrus izfr”kr gksxkh \

¼1½ 200 ¼2½ 225 ¼3½ 240¼4½ 250

Ikz-100 & ,d ifg,okys f[kykSus dk O;kl 14 lseh- gSA rnuqlkj og 15 pDdjks esa fdruh nwjh r; dj ysxk \ ¼1½ 880 lseh- ¼2½ 660 lseh- ¼3½ 600 lseh-

¼4½ 560 lseh-Ikz-101 & fdlh o`Rrkdkj ikdZ ds pkjks vksj ,d leku pkSM+kbZ dk ,d iFk cuk gqvkk gSA bl o`Rrkdkj iFk dh vkarfjd vkSj ckgjh ifjf/k;ksa dk varj 132 ehVj gSA mldh pkSM+kbZ gS \

¼1½ 22 eh- ¼2½ 20 eh- ¼3½ 21 eh-¼4½ 24 eh-

Ikz-102 & o`Rr dk {ks=Qy 144 π oxZ lseh- gS rks mldh f=T;k gksxh \


Ikz-103 & 40 lseh- O;kl okys ,d ifg, }kjk 176 eh- nwjh r; djus esa yxk, x, pDdjks dh la[;k gksxh \ ¼1½ 140 ¼2½ 150 ¼3½ 160

¼4½ 166Ikz-104 & ;nf fdlh o`Rr dh f=T;k esa 1 lseh- dh o`f) dj nh tk, rks mldk {ks=Qy 22 cm2 vf/kd gks tkrk gSA o`Rr dh vkjafHkd f=T;k gS \

¼1½ 6 lseh- ¼2½ 3-2 lseh- ¼2½ 3 lseh-¼4½ 3-5 lseh-

Ikz-105 & ;fn fdlh v)Zo`Rrkdkj {ks= dk ifjeki 144 eh- gks rks {ks= dk O;kl gksxk \

¼1½ 55 ehVj ¼2½ 30 ehVj ¼3½ 28 ehVj ¼4½ 56 ehVj

Ikz-106 & 3 lseh- f=T;k okys fdlh o`Rr dh ifjf/k rFkk mlds {ks=Qy dh eki crkus okyh la[;kvks dk vuqikr gksxk \

¼1½ 1 % 3 ¼2½ 2 % 3 ¼3½ 2 % 9¼4½ 3 % 2

Ikz-107 & 176 ehVj ifjf/k okys fdlh o`Rrkdkj ikdZ ds ckgj pkjks vksj ,d ehVj pkSM+h lM+d cuk;h x;h gSA lM+d dk {ks=Qy gksxk \

¼1½ 1386 m2 ¼2½ 1472 m2 ¼3½ 1512 m2

¼4½ 1760 m2

Ikz-108 & ,d o`Rrkdkj ifg, dk O;kl 7 ehVj gSA rnuqlkj 22 fdeh- rnuqlkj 22 fdeh- rd pyus esa mlds dqy pdz fdrus gksaxs \

¼1½ 100 ¼2½ 400 ¼3½ 500¼4½ 1000

Ikz-109 & nks o`Rrks ds {ks=Qyks dk vuqikr 4 % 7 gSA rnuqlkj mudh f=T;kvks dk vuqikr fdruk gksxk ¼1½ 2 :√7 ¼2½ 4 % 7 ¼3½ 16 % 49 ¼4½ 4 :√7 Ikz-110 & 21 lseh- Hkqtkk okys ,d oxZ ds vanj [khaps tk ldus okys cM+s ls cM+s o`Rr dk {ks=Qy gS \

¼1½ 344-5 oxZlseh- ¼2½ 364-5 oxZlseh- ¼3½ 346-5 oxZ lseh- ¼4½ 366-5 oxZlseh-Ikz-111 & 42 lseh- dh Hkqtk okys ,d leckgq f=Hkqt ds var% o`r dk {ks=Qy gksxk \

¼1½ 231 cm2 ¼2½ 462 cm2 ¼3½ 22√3 c m2¼4½ 924 cm2

Ikz-112 & 120 lseh- ifjeki okys oxZ ds vUrxZr [khaps x, lcls cM+s o`Rr dk {ks=Qy gksxk \

¼1½ 225 π cm2 ¼2½ 220 π cm2 ¼3½ 25 π cm2 ¼4½ 144 π cm2

Ikz-113 & ,d leckgq f=Hkqt ds ifjo`Rr rFkk var% ozr ds {ks=QYkks dk vuqikr fdruk gksxk \

¼1½ 2 % 1 ¼2½ 4 % 1 ¼3½ 8 % 1 ¼4½ 3 % 2

Ikz-114 & ,d oxZ ds vUroZ`r vkSj ifjo`r ds {ks=Qyks dk vuqikr gksrk gS \

¼1½ 1 % 2 ¼2½ 2 % 3 ¼3½ 3 % 4¼4½ 4 % 5

Ikz-115 & ,d leckgq f=Hkqt ftldh Hkqtk 6 lseh- gS ds vr% o`Rk dk {ks=Qy fdruk gksxk \

¼1½ π2 oxZ lseh- ¼2½ √3π oxZ lseh- ¼3½ 6π oxZ

lseh- ¼4½ 3π oxZ leh-iz-116 & ,d oxZ dh var% f=T;k vkSj ifjf=T;k dk vuqikr fdruk gksrk gS \

¼1½ 1 :√2 ¼2½ √2: √3 ¼3½ 1 % 3¼4½ 1 % 2

Ikz-117 & fdlh dejs ds 15 eh- 17 lseh- yEcs vkSj 9 eh- 2 lseh- pkSM+s Q”kZ ij yxkbZ tk ldus okyh oxZ VkbZyks dh U;wure la[;k fdruh gS \ ¼1½ 840 ¼2½ 841 ¼3½ 820

¼4½ 814

Ikz-118 & ,d vk;rkdkj gkWy dh yEckbZ mldh pkSM+kbZ ls 5 eh- vf/kd gSA gkWy dk {ks=Qy 750 m2 gSA gkWy dh yEckbZ Kkr gS \ ¼1½ 15 eh- ¼2½ 22-5 eh- ¼3½ 25 eh-

¼4½ 30 eh- Ikz-119 & ,d dejs ds Q”kZ dk ifjeki 18 eh- gSA dejs dh pkjks nhokjks dk {ks=Qy fdruk gksxk ;fn mldh Å¡pkbZ 3 eh- gS \

¼1½ 21m2 ¼2½ 42 m2 ¼3½ 54 m2

¼4½ 108m2 Ikz-120 & ,d dejs dh pkjks nhokjks dk {ks=Qy 660 oxZ ehVj gS vkSj mldh yEckbZ mldh pkSM+bZ dh nqxquh gSA ;fn dejs dh ÅapkbZ 11 ehVj gks rks mlds Q”kZ dk {ks=Qy fdruk gksxk \ ¼1½ 120 ¼2½ 150 ¼3½ 200

¼4½ 330Ikz-121 & ,d gkWy 15 ehVj yEck vkSj 12 ehVj pkSM+k gSA ;fn ml gkWy ds Q”kZ rFkk Nr ds {ks=Qyksdk ;ksx mldh pkjks nhokjks ds {ks=Qyks ds cjkcj gks rks ml gkWy dk vk;ru fdrus ?ku ehVj

gksxk \¼1½ 720 ¼2½ 900 ¼3½ 1200¼4½ 1800

Ikz-122 & ,d oxZ vkSj o`Rrkdkj eSnku ds ifjeki ,d leku gS ;fn o`Rrkdkj eSnku dk {ks=Qy 3850 oxZ ehVj gks rks oxZ dk {ks=Qy fdrus oxZ ehVj gksxk \

¼1½ 4225 ¼2½ 3025 ¼3½ 2500¼4½ 2025

Ikz-123 & ;fn 12 lseh- vk/kkj okys ,d f=Hkqt dk {ks=Qy 12 lseh- Hkqtk okys ,d oxZ ds {ks=Qy ds cjkcj gks rks f=Hkqt dk “kh’kZyEc gS \


Ikz-124 & lEiw.kZ i`Foh ij Hkwfe dk ikuh ls vuqikr 2 % 1 gS rFkk mRrjh xksyk/kZ ij ;g vuqikr 2 % 3 gSA nf{k.kh xksyk/kZ ij Hkwfe dk ikuh ls vuqikr gksxk \

¼1½ 11 % 4 ¼2½ 4 % 11 ¼3½ 15 % 4¼4½ 4 % 15

Ikz-125 & ,d v)Z xksys vkSj ,d “kadq ds vk/kkj cjkcj gSA ;fn mudh Å¡pkbZ;k¡ Hkh cjkcj gks rks muds od`iz’Bks dk vuqikr gksxk \

¼1½ √2:1 ¼2½ 1 :√2 ¼3½ 1 % 2 ¼4½ 2 % 1

Ikz-126 & ,d oxZ vkSj ,d vk;r ds {ks=Qy cjkcj gSA vk;r dh yEckbZ oxZ dh ,d Hkqtk dh yEckbZ ls 5 lseh- vf/kd gS vkSj mldh pkSM+kbZ oxZ dh Hkqtk dh yEckbZ ls 3 lseh- de gSA vk;r dh ifjeki fdruh gS \ ¼1½ 17 lseh- ¼2½ 26 lseh- ¼3½ 30 lseh-

¼4½ 34 lseh-Ikz-127 & ,d ?ku ds vk;ru dk ml xksys tks ?ku esa iw.kZr;k fQV fd;k tk ldsxk ds vk;ru ls vuqikr gksxk \

¼1½ π % 6 ¼2½ 6 % π ¼3½ 3 % π¼4½ π % 3

Ikz-128 & ,d rkj dks ,d oxZ ds vkdkj esa eksM+us ij vko`r {ks= dk {ks=Qy 121 cm2 gSA ;fn mlh rkj dks ,d o`r ds vkdkj esa eksM+k tk, rks o`r dk {ks=Qy gksxk \ ¼1½ 144 cm2 ¼2½ 180 cm2 ¼3½ 154 cm2

¼4½ 176 cm2

Ikz-129 & ,d yac o`Rrh; csyu ,d v/kZ xksyk vkSj ,d yac o`Rrh; “kadq ,d gh vk/kkj ij fLFkr gS vkSj mudh ÅapkbZ cjkcj gS muds vk;ru dk vuqikr gS \ ¼1½ 3 % 6 % 1 ¼2½ 3 % 4 % 1 ¼2½ 3 % 2 % 1 ¼4½ 4 % 3 % 1Ikz-130 & fdlh oxZ ds fod.kZ ij ,d leckgq f=Hkqt cuk;k x;k gSA oxZ ds {ks=Qy ds lkFk f=Hkqt ds {ks=Qy dk vuqikr gS \

¼1½ √3 :2 ¼2½ √2: √3 ¼3½ 2 :√3 ¼4½ 1 :√2Ikz-131 & ,d ?ku rFkk xksys ds lEiw.kZ i`’B {ks= cjkcj gSA muds vk;ruks dk vuqikr gksxk \

¼1½ π % 6 ¼2½ √π % √6 ¼3½ √6 :√π¼4½ 6 % π

Ikz-132 & lhlk ds ,d Bksl ?ku ls ftlds fdukjs dk eki 44 lseh- gS 4 lseh- O;kl dh fdruh xksykdkj xksfy;k¡ cu ldrh gS \

¼1½ 2541 ¼2½ 2451 ¼3½ 2514¼4½ 2415

Ikz-133 & ml csyu dh Å¡pkbZ D;k gS ftlds vk;ru vkSj f=T;k ogh gS tks 12 lseh- O;kl okys xksyd ds gS \


Ikz-134 & ;fn fdlh vk;r dh yEckbZ 25% c<+ tk, vkSj pkSM+kbZ 20% ?kV tk, rks vk;r ds {ks=Qy esa fuEu esa ls dkSu lk ifjorZu gks tk,xk \

¼1½ 5% ozf) ¼2½ 5% gzkl ¼3½ vifjofrZr ¼4½ 10% ozf)

Ikz-135 & ;fn fdlh yEc o`Rrkdkj csyu ds vk/kkj dh f=T;k rFkk mldh Å¡pkbZ nksuks esa 20% dh o`f) dh tk, rks mlds vk;ru esa fdruh o`f) gksxh\

¼1½ 20% ¼2½ 40% ¼3½ 60% ¼4½ 72%

Ikz-136 & ,d vk;r dh yEckbZ dks 10% de fd;k tkrk gS rFkk mldh pkSM+bZ esa 10% dh ozf) dh tkrh gS vk;r dk {ks=Qy fdrus izfr”kr cny tk,xh \

¼1½ 0% ¼2½ 1% ¼3½ 5% ¼4½ 100% Ikz-137 & ;fn fdlh vk;r dh izR;sd Hkatk dks 20% c<+;k tk, rks mlds {ks=Qy esa fdrus izfr”kr dh o`f) gksxh \

¼1½ 40% ¼2½ 42% ¼3½ 44% ¼4½ 46%

Ikz-138 & ,d vk;r dh yEckbZ eas 10% dh oz) rFkk mldh pkSM+kbZ esa 10% dh deh dh tkrh gSA u;s vk;r ds {ks=Qy esa gksxh \ ¼1½ u dksbZ deh u dksbZ ozf) ¼2½ 1% dh ozf)

¼3½ 1% dh deh ¼4½ 10% dh dehIkz-139 & ;fn fdlh yEc o`Rrkdkj csyu ds v)ZO;kl esa 50% dh deh rFkk bldh Å¡pkbZ esa 60% dh ozf) dh tk, rks blds vk;ru esa deh gks tk,xh \

¼1½ 10% ¼2½ 60% ¼3½ 40% ¼4½ 20%

Ikz-140 & ;fn fldh leckgq f=Hkqt dh Hkqtkvks esa d`e”k% 20% ] 30% ] 50% dh ozf) djds ,d u;k f=Hkqt cuk;k x;k gks rks

leckgq f=Hkqt dh ifjeki esa ozf) gksxh \

¼1½ 25% ¼2½ 33 13% ¼3½ 75%

¼4½ 100% Ikz-141 & ;fn fdlh vk;r dh izR;sd Hkqtk dks 50% c<+ fn;k tk, rks bldk {ks=Qy c<+ tk,xk \

¼1½ 50% ¼2½ 125% ¼3½ 100% ¼4½ 250%

Ikz-142 & fdlh vk;r dh YeckbZ rFkk pkSM+kbZ esa d`e”k% 20% rFkk 25% dh o`f) dh tkrh gSA ifj.kkeh vk;r ds {ks=Qy esa o`f) gksxh \ ¼1½ 60% ¼2½ 50% ¼3½ 40%

¼4½ 30%

Ikz-143 & ;fn fdlh “kadq dh Å¡pkbZ esa 100% dh o`f) dh tk, rks blds vk;ru esa o`f) gksxh \

¼1½ 100% ¼2½ 200% ¼3½ 300% ¼4½ 400%

Ikz-144 & v)ZO;kl 1 lseh- ] 2 lseh- rFkk 3 lseh- okyh rhu xksykdkj xsanks dks fi?kykdj ,d vdsyh xksykdkj xasn cuk;h x;h xbZ gSA bl izfd;k esa 25% lkexzh cckZn gqbZ gSA u;ha xsan dk

v)ZO;kl gksxk \ ¼1½ 6 lseh- ¼2½ 5 lseh- ¼3½ 3 lseh-¼4½ 2 lseh-

Ikz-145 & ;fn fdlh o`Rr dk O;kl 8% c<+k fn;k tk, rks {ks=Qy esa fdruh o`f) gksxh \

¼1½ 16-64% ¼2½ 6-64% ¼3½ 16% ¼4½ 16-46%

Ikz-146 & ,d vk;r dh yackbZ 60% c<+kbZ xb gSA rnuqlkj mldh pkSM+bZ fdruh de djuh gksxh] rkfd vk;r dk {ks=Qy vifjofrZr jgs \ ¼1½ 37-5% ¼2½ 60% ¼3½ 75%

¼4½ mDr esa dksbZ ugh

izfr”krrkiz-1 & ;fn fdlh la[;k dk 20% ] 120 gks rks mlh la[;k dk 120% gksxk \

¼1½ 20 ¼2½ 120 ¼3½ 480¼4½ 720

Ikz-2 & ;fn x dk 8% ] y ds 4% ds leku gks rks x dk 20% leku gS \¼1½ y ds 10% ¼2½ y ds 16% ds ¼3½ y dk 80% ds ¼4½ y ds 50% ds

Ikz-3 & ;fn x dk eku y ds eku ls 25% de gks rks y dk eku x ds eku ls vf/kd gS \

¼1½ 3313 % ¼2½ 25% ¼3½ 75%

¼4½ 6622 %

Ikz-4 & C dh vk; B dh vk; ls 20% vf/kd gS vkSj B dh vk; A dh vk; ls 25% vf/kd gSA C dh vk; A dh vk; ls fdrus izfr”kr vf/kd gS \ ¼1½ 150% ¼2½ 50% ¼3½ 25%

¼4½ 35% Ikz-5 & ;fn fdlh fo/kky; esa dqy fo?;kfFkZ;ksa ds 60% yM+ds gks vkSj yM+fd;ksa dh la[;k 972 gks rks ml fo/;ky; esa dqy fdrus yM+ds gS \

¼1½ 1258 ¼2½ 1458 ¼3½ 1324¼4½ 1624

Ikz-6 & ,d O;fDr tks viuh vk; dk 6623 % [kpZ djrk gS og izfr 1200 :

cpkrk gSA mldk O;; izfr ekl gS \ ¼1½ 1200 ¼2½ 2400 ¼3½ 3000

¼4½ 3200Ikz-7 & ;fn x] y dk 80% rks x dk fdruk izfr”kr y gS \

¼1½ 75% ¼2½ 80% ¼3½ 100% ¼4½ 125%

Ikz-8 & ;fn A] B ls 40% vf/kd gS B] C ls 20% de gS rc A :C gS \¼1½ 28 % 25 ¼2½ 26 % 25 ¼3½ 3 % 2¼4½ 3 % 1

Ikz-9 & fdlh fo/;ky; esa dqy fo?;kfFkZ;ksa dk 70% yM+fd;k¡ gSA yM+dks dh la[;k 510 gSA rks fo/kky; esa dqy fo/;kfFkZ;ksa dh la[;k gS \

¼1½ 850 ¼2½ 1700 ¼3½ 1830¼4½ 1900

Ikz-10 & ;fn fdlh la[;k ds 75% esa 75 tksM+dj ogh la[;k izkIr gks tk, rks og la[;k Kkr dhft,

¼1½ 225 ¼2½ 270 ¼3½ 300¼4½ 325

Ikz-11 & x dk 30% ] 72 gSA x dk eku gS \¼1½ 216 ¼2½ 240 ¼3½ 480¼4½ 640

Ikz-12 & ;fn la[;k x vU; la[;k y ls 10% de gS rFkk y la[;k 125 ls 10% vf/kd gS ] rks x cjkcj gS \ ¼1½ 150 ¼2½ 143 ¼3½ 140-55

¼4½ 123-75Ikz-13 & nks la[;k,¡ fdlh rhljh la[;k ls d`e”k% 25% vkSj 20% de gSA igyh la[;k nwljh la[;k dk fdrus izfr”kr gS \

¼1½ 5% ¼2½ 75% ¼3½ 80% ¼4½ 93-75%

Ikz-14 & fdl la[;k dk 18% la[;k 75 ds 12% ds cjkcj gS \¼1½ 50 ¼2½ 100 ¼3½ 2

¼4½ 32

Ikz-15 & 65 xzke 2 fdxzk- ds fdrus izfr”kr ds cjkcj gS \

¼1½ 134 ¼2½

652 ¼3½

158

¼4½ 138

Ikz-16 & 1 ?kaVk 45 feuV dh le;kof/k ,d fnu dk fdruk izfr”kr gS \¼1½ 7-218 ¼2½ 7-291 ¼3½ 8-3¼4½ 8-24

Ikz-17 & o’kZ 2008 esa 31% deZpkfj;ksa us dj dk Hkqxrku fd;k dj u nsus okys “ks’k deZpkjh 20]700 gSA

Rknuqlkj deZpkjh;ksa dh dqy la[;k fdruh gS \¼1½ 31]160 ¼2½ 64]750 ¼3½ 30]000¼4½ 66]775

Ikz-18 & ,d O;fDr dks 20% osruo`f) izkIr gksus ij mldk osru 24]000 :i, gks x;k gSA rnuqlkj mldk iwoZ osru fdruk Fkk \

¼1½ 20]000 :- ¼2½ 21]000 :- ¼3½ 16]000 :-¼4½ 18]000 :-

Ikz-19 & ,d oLrq dk ewY; 25% de dn fn;k x;k gSA rnuqlkj ;fn ml ij igys okyk ewY; nqckjk ykxw djuk gks rks de fd, x, ewY; esa fdrus izfr”kr o`f) djuh gksxh \

¼1½ 25% ¼2½ 30% ¼3½ 33%

¼4½ 3313%

Ikz-20 & 400 yhVj rsy ds ,d daVsuj esa fjlko ds dkj.k 8% dk uqdlku gqvk A daVsuj esa fdruk rsy cpk \

¼1½ 320 yhVj ¼2½ 368 yhVj ¼3½ 332 yhVj ¼4½ 32 yhVj

Ikz-21 & ,d fMCcs esa 100 uhys xksys] 50 yky xksys vkSj 50 dkys xksys gSA 25% uhys xksys vkSj 50%yky xksys fudky fy, x,A rc dkys xksyks dk izfr”kr gS \

¼1½ 50% ¼2½ 25% ¼3½ 3313

¼4½ 40% Ikz-22 & okf’kZd ijh{kk esa egqvk dks xf.kr esa lqfiz;ks ls 10% de vad feysA egqvk dk 81 vad feys rks lqfiz;ks ds vad gS \

¼1½ 90 ¼2½ 87 ¼3½ 88¼4½ 89

Ikz-23 & ;fn 120 ,d la[;k dk 20% gks rks ml la[;k dk 120% fdruk gksxk \

¼1½ 360 ¼2½ 720 ¼3½ 20¼4½ 120

Ikz-24 & phuh ds ewY; esa 20% dh o`f) gksrh gSA phuh dh [kir fdrus izfr”kr de dh tk, rkfd ml ij gksus okyk [kpkZ igys ftruk gh jgs \

¼1½ 20 ¼2½ 10 ¼3½ 1623

¼4½ 15Ikz-25 & ;fn [kk/kkUu ewY;ksa esa 10% dh o`f) gks tk, rks fdlh O;fDr dk mudk miHkksx fdrus izfr”kr djuk gksxk] rkfd mldk [kpZ u c<+us ik, \

¼1½ 9111% ¼2½ 10% ¼3½ 11

19%

¼4½ lwpuk,a vi;kZIr gS

Ikz-26 & osru esa fdrus izfr”kr dh dVkSrh dh tk, fd og osru esa dh xbZ 20 izfr”kr dh o`f) dks lekIr dj ns \

¼1½ 20 ¼2½ 1623 ¼3½ 33

13 ¼4½ 18

Ikz-27 & u, ctV esa feV~Vh ds rsy dk ewY; 25% c<+ x;kA dksbZ O;fDr feV~Vh ds rsy dh [kir esa fdrus izfr”kr dh deh djs fd mldk bl en esa O;; u c<+s \

¼1½ 20% ¼2½ 25% ¼3½ 50% ¼4½ 40%

Ikz-28 & fdlh oLrq ds ewY; esa 15% dh o`f) gks tkrh gSA ;fn dksbZ miHkksDrk ml oLrq ij fd, tkus okys O;; dks igys ftruk gh j[kuk pkgs rks mls ml oLrq dh [kir esa fdrus izfr”kr dh deh dj nsuh pkfg, \

¼1½ 15% ¼2½ 13113% ¼3½ 16

23%

¼4½ 102023%

Ikz-29 & ;fn fdlh miHkksDrk oLrq ds ewY; esa 50% dh o`f) gksrh tk, rks bldh [kir es fdrus Hkkx deh dh tk, rkfd bldh [kir ij gksus okyk O;; igys ftruk gh jgs \

¼1½ 14 ¼2½

13 ¼3½

12

¼4½ 23

Ik-30 & phuh ds Hkko 25% dh o`f) gksrh gSA ;fn dksbZ ifjokj phuh ij fd, tkus okys vius O;; dks igys tSlk gh j[kuk pkgs rks ifjokj }kjk phuh ds [kir esa fdrus deha djuh gksxh \ ¼1½ 25% ¼2½ 20% ¼3½ 80%

¼4½ 75% Ikz-31 & phuh ds ewY; esa 25% o`f) gqbZ gSA dksbZ ifjokj viuh phuh dh [kir esa fdrus izfr”kr dh deh djs rkfd mlds ifjokfjd ctV ij bldk dksbZ izHkko u gks \

¼1½ 25% ¼2½ 2212% ¼3½ 20%

¼4½ 1712%

Ikz-32 & fdlh oLrq ds ewY; esa 25% dh dVkSrh dh xbZ bls blds vkjafHkd ewY; ij ykus ds fy, u, ewY; esa fdrus izfr”kr dh ozf) djuh iM+sxh \

¼1½ 9111 ¼2½ 11

19 ¼3½ 33

13 ¼4½ 36

23

Ikz-33 & nw/k dh dheV 20% c<+ xbZ gSA O;; dks mruk gh j[kus ds fy, orZeku miHkksx esa fdruh deh djuh gksxh \

¼1½ 10% ¼2½ 20% ¼3½ 18%

¼4½ 1623%

Ikz-34 & ;fn fdlh fHkUu va”k esa 20% dh o`f) vkSj mlds gj es 5% dh

deh dj nh tk, rks ubZ fHkUu dk eku 52 gks tkrk gSA izkjafHkd

fHkUu gS \

¼1½ 2419 ¼2½

318 ¼3½

9548

¼4½ 4895

Ikz-35 & ,d fHkUu ds va”k esa 20% o`f) dj nh xbZ gS vkSj mlds gj

esa 20% dj deh dj nh xbZ gSA vr% fHkUu dk eku 45 gks tkrk gSA

rnuqlkj ewy fHkUu D;k gS \

¼1½ 23 ¼2½

815 ¼3½

711

¼4½ 45

Ikz-36 & ,d xk¡o dh tula[;k 25]000 gSA mlesa 15 Lf=;k¡ gS vkSj

“ks’k iq:’k gSA muesa 5% iq:’k rFkk 40% fL=;k¡ vf”kf{kr gSA rnuqlkj dqy f”kf{kr yksxks dk izfr”kr fdruk gS \

¼1½ 75% ¼2½ 88% ¼3½ 55% ¼4½ 85%

Ikz-37 & A dh vk; B dh vk; ls 10% vf/kd gSA eku fyft, B dh vk; A dh vk; ls x% de gS rks x dk eku Kkr dhft, \

¼1½ 9111% ¼2½ 10

111% ¼3½ 11%

¼4½ 10% Ikz-38 & x dh vk; y dh vk; ls 20% vf/kd gSA y dh vk; x dh vk; ls fdrus izfr”kr de gS \

¼1½ 8313% ¼2½ 16

23% ¼3½ 83

23%

¼4½ 1613%

Ikz-39 & ;fn jke dh vk; “;ke dh vk; ls 1212% vf/kd gS rks “;ke dh vk;

jke dh vk; ls fuEu de gS \

¼1½ 1119% ¼2½ 13

12% ¼3½ 87

12%

¼4½ 8819%

Ikz-40 & B dks A ls 20% de vad izkIr gq,A A dks B ls fdrus izfr”kr vf/kd vad izkIr gq, \

¼1½ 20 ¼2½ 25 ¼3½ 12¼4½ 80

Ikz-41 & ;fn x dh dekbZ y ls 25% vf/kd gks rks y dh dekbZ x ls fdruk izfr”kr de gS \

¼1½ 16 ¼2½ 10 ¼3½ 20¼4½ 25

Ikz-42 & ;fn A dk osru B ds osru ls 25 vf/kd gS rks B dk osru A ds osru ls fdruk izfr”kr de gS \

¼1½ 3313% ¼2½ 25% ¼3½ 20%

¼4½ 1623%

Ikz-43 & fdlh O;fDr ds osru esa igys 20% dh o`f) dh xbZ vkSj fQj mlesa 20% dh deh dh xbZA mlds osru esa ifjorZu gS \

¼1½ 4% deh ¼2½ 4% o`f) ¼3½ 8% deh¼4½ 20% o`f)

Ikz-44 & fdlh la[;k esa igys 20% dh o`f) dh xbZ vkSj fQj 10% dh deh dh xbZA “kq) izfr”kr o`f) ;k deh Kkr dhft, \ ¼1½ 10% o`f) ¼2½ 10% deh ¼3½ 8% o`f)``

¼4½ 8% deh Ikz-45 & fdlh oLrq ij yxs dj esa 10% dh deh dh xbZ vkSj mldh [kir 10% c<+ tkrh gS \ ml ij izkIr jktLo esa izfr”kr ifjorZu Kkr dhft, \

¼1½ 10% o`f) ¼2½ 2% deh ¼3½ 1% deh¼4½ 11% ozf)

Ikz-46 & fdlh la[;k esa 10% dh o`f) dj nh tkrh gS vkSj fQj mles 10% dh deh dj nh tkrh gSA vafre :Ik esa ml la[;k esa & ¼1½ dksbZ ifjorZu ugh gksxk ¼2½ 1% dh deh gks tkrh gS

¼3½ 1% dh o`f) gks tkrh gS ¼4½ 0-1% dh o`f) gks tkrh gS Ikz-47 & fdlh oLrq dk ewY; 75 :- Fkk igys ewY; esa 20% dh o`f) dh xbZ rFkk ckn esa bles 20% dh deh dj nh xbZA oLrq dk orZeku ewY; gS \

¼1½ 72 :- ¼2½ 60 :- ¼3½ 75 :-¼4½ 90 :-

Ikz-48 & fdlh la[;k esa 10% dh o`f) dh tkrh gS rFkk mlds mijkar 10% dh deh dh tkrh gS la[;k esa D;k okLfod ifjorZu gksxk \

¼1½ u o`f) u deh ¼2½ 2% dh deh ¼3½ 1% dh o`f)¼4½ 1% dh deh

Ikz-50 & :- 100 dh ,d oLrq dh dher igys 10% c<+k nh tkrh gS rRi”pkr 10% vkSj c<+k nh tkrhgSA rnuqlkj dqy o`f) fdrus :- dh gks tkrh gS \

¼1½ 20 ¼2½ 21 ¼3½ 110¼4½ 121

Ikz-51 & fufru ds osru esa 10% dh deh dj nh x;h rFkk iqu% de gq, osru esa 10% dh o`f) dj nh x;hA mlds vkjafHkd osru dh rqyuk esa mlk u;k osru gksxk \

¼1½ cjkcj ¼2½ 1% vf/kd ¼2½ 1% de¼4½ 5% de

Ikz-52 & A dk osru 10% c<+k;k x;k vkSj fQj 10% ?kVk;k x;kA osru esa ifjorZu gS \

¼1½ 0% ¼2½ 1% deha ¼3½ 1% o`f)¼4½ 2% deha

Ikz-53 & fdlh dkWyst esa Nk= vkSj Nk=kvks dk vuqikr 3 % 2 gSA ;fn Nk=ks ds 20% rFkk Nk=kvks ds 25% O;Ld gS rks mu fo/;kfFkZ;ksa dh izfr”krrk tks O;Ld ugh gS fuEufyf[kr gS \ ¼1½ 58% ¼2½ 67-5% ¼3½ 78%

¼4½ 82-5% Ikz-54 & fdlh Ldwy ds yM+dks dh la[;k vkSj yM+fd;ksa dh la[;k dk vuqikr 4 % 1 gSA ;fn yM+dks ds 75% dks rFkk yM+fd;ksa ds 70% dks N=o`fRr feyrh gS rks mu fo/;kfFkZ;ksa dk izfr”kr ftUgs

Nk=ozfRr ugh feyrh gS fuEu gS \¼1½ 50 ¼2½ 28 ¼3½ 75¼4½ 26

Ikz-55 & fdlh d{kk esa yM+fd;ksa dh la[;k yM+dks dh la[;k ls 20% vf/kd gSA bl d{kk esa dqy 66 fo/;kFkhZ gSA ;fn d{kk esa 4 vkSj yM+fd;ka HkrhZ dj yh tk,¡ rks yM+ds vkSj yM+fd;ksa dh

la[;kvks dk vuqikr gksxk \¼1½ 1 % 2 ¼2½ 3 % 4 ¼3½ 1 % 4¼4½ 3 % 5

Ikz-56 & fdlh ifjokj esa pkoy eNyh rFkk [kk?k rsy ij fd, tkus okys O;; 12 % 17 % 3 ds vuqikr esa gSA bu oLrqvks ds ewY; esa d`e”k%

20% ] 30% rFkk 50% dh o`f) gks tkrh gSA ifjokj ds bu oLrqvks ij fd, tkus okys O;; esa dqy fdruh o`f) gks tk,xh \

¼1½ 1418% ¼2½ 7

18% ¼3½ 56

18%

¼4½ 2818%

Ikz-57 & ;fn A dk 20% ¿ B dk 30% ¿ C dk 16 gks rks A :B:C gksxk \

¼1½ 2 % 3 % 16 ¼2½ 3 % 2 % 16 ¼3½ 10 % 15 % 18 ¼4½ 15 % 10 % 18Ikz-58 & jek ds O;; rFkk cpr esa 5 % 3 dk vuqikr gSA ;fn mldh vk; esa 12% rFkk O;; esa 15% dh o`f) gks tk, rks mldh cpr esa fdrus izfr”kr dh o`f) gksxh \

¼1½ 12 ¼2½ 7 ¼3½ 8¼4½ 13

Ikz-59 & A ,B rFkk C ds osru dk vuqikr 1 % 3 % 4 ds vuqikr esa gSA ;fn muds osru esa d`e”k% 5 izfr”kr ] 10 izfr”kr rFkk 15 izfr”kr dh o`f) dh tk, rks muds c<+s gq, osru fdl vuqikr esa

gksaxs \¼1½ 20 % 66 % 95 ¼2½ 21 % 66 % 95 ¼3½ 21 % 66 % 92¼4½ 19 % 66 % 92

iz-60 & fdlh dkWyst esa yM+dks rFkk yM+fd;ksa dh la[;k,a 3 % 2 ds vuqikr esa gSA ;fn 20% yM+ds rFkk 25% yM+fd;k¡ ckfyx gS rks fdrus izfr”kr fo/;kFkhZ ckfyx ugh gS \

¼1½ 58 ¼2½ 78 ¼3½ 6623

¼4½ 8313

Ikz-61 & nks la[;kvks dk varj mu nksuks esa cM+h la[;k ds 20% ds cjkcj gSA ;fn NksVh la[;k 20 gks rks cM+h la[;k D;k gksxh \

¼1½ 25 ¼2½ 45 ¼3½ 50¼4½ 80

Ikz-62 & mls la[;kvks dk varj 1660 gSA ;fn ,d la[;k dk 612% nwljh

la[;k ds 812% ds cjkcj gS rks NksVh la[;k D;k gS \

¼1½ 7055 ¼2½ 5395 ¼3½ 3735¼4½ 2075

Ikz-63 & ;fn nks la[;k,¡ fdlh vU; la[;k d`e”k% 20% vkSj 50% gS rks mu nksuks la[;kvks esa vuqikr gS \

¼1½ 5 % 2 ¼2½ 2 % 5 ¼3½ 1 % 5¼4½ 1 % 2

Ikz-64 & nks la[;kvks esa ls cM+h la[;k dk 40% NksVh la[;k ds 60% ds cjkcj gSA ;fn bu la[;kvks dk ;ksx 150 gks rks cM+h la[;k gksxh \

¼1½ 70 ¼2½ 80 ¼3½ 90¼4½ 60

Ikz-65 & ,d la[;k ls 15 ?kVkus ij og ?kV dj 80% jg tkrh gSA ml la[;k dk 40% D;k gS \

¼1½ 75 ¼2½ 60 ¼3½ 30¼4½ 90

Ikz-66 & nks la[;kvks dk vUrj cM+h la[;k ds 25% ds cjkcj gSA ;fn NksVh la[;k 30 gS rks cM+h la[;k gksxh \

¼1½ 40 ¼2½ 45 ¼3½ 48¼4½ 50

Ikz-67 & 498 fdl la[;k ls 17% de gS \¼1½ 610 ¼2½ 580 ¼3½ 600¼4½ 620

Ikz-68 & ,d la[;k esa ls 10% de djus ij og 30 gks tkrh gSA rnuqlkj og la[;k D;k gS \

¼1½ 3312 ¼2½ 33

13 ¼3½ 40 ¼4½ 35

Ikz-69 & nks la[;kvks dk ;ksx 520 gSA ;fnmuesa cM+h la[;k dks 4% de dj fn;k tk, vkSj NksVh la[;k dks 12% c<+k fn;k tk, rks izkIr la[;k,¡ ,d leku gksaxhA rnuqlkj muesa ls NksVh la[;k dkSu lh gS \

¼1½ 280 ¼2½ 210 ¼3½ 240¼4½ 300

Ikz-70 & Xyksljhu ds 50 yhVj ds ,d uewus esa 20% dh v”kq) feykoV ikbZ xbZA buesa fdruh “kq) Xyksljhu feykbZ tk, rkfd v”kq)rk dh izfr”krrk 5% jg tk, \

¼1½ 155 yhVj ¼2½ 150 yhVj ¼3½ 150-4 yhVj ¼4½ 149 yhVj

Ikz-71 & 25 yhVj ued ds ,d ?kksy esa ued dh ek=k 6% gSA rnuqlkj ml ?kksy esa fdruk ikuh vkSj feyk;k tk, fd ued ek=k 5% gks tk, \

¼1½ 4 yhVj ¼2½ 5 yhVj ¼3½ 6 yhVj ¼4½ 8 yhVj

Ikz-72 & 75 xzke phuh ds ,d ?kksy es 30% phuh gSA rnuqlkj ml ?kksy esa fdruh phuh vkSj feyk;h tkuh pkfg, fd ?kksy esa phuh dk izfr”kr 70% gks tk,

¼1½ 125 xzke ¼2½ 100 xzke ¼3½ 120 xzke ¼4½ 130 xzke Ikz-73 & 30% vYdksgy ?kksy ds 6 yhVj esa ,d yhVj “kq) vYdksgy feyk;k x;kA ?kksy esa ty dk izfr”kr gS \

¼1½ 50% ¼2½ 65% ¼3½ 60% ¼4½ 40%

iz-74 & 80% cksfjd vEy okys 100 feyh ikuh ds ?kksy esa fdruk vkSj feyk;k tk, fd ?kksy esa cksfjd vEy 50% gks tk, \ ¼1½ 30 feyh- ¼2½ 40 feyh- ¼3½ 50 feyh-

¼4½ 60 feyh-Ikz-75 & pk; ds ewY; esa 10% dh deh gksus ij ,d O;kikjh 22500 :Ik, esa 25 fdxzk- vf/kd pk; [kjhn ldrk gSA pk; dk izfr fdxzk- de gqvk ewY; fdruk Fkk \ ¼1½ 70 :- ¼2½ 80 :- ¼3½ 90 :-

¼4½ 100 :-Ikz-76 & lscks dh dher esa gksus ij ,d O;fDr 1-25 :- ds ctk; 1 :- esa 3 lsc [kjhn ysrk gSA dher esa deha dk % fdruk gksxk ¼yxHkx½ \

¼1½ 20 ¼2½ 25 ¼3½ 30

¼4½ 3313

Ikz-77 & pkkoy dh dher esa 20% dh deha gks tkus ij ,d xzkgd 800 :- esa 12-5 fdxzk- pkoy T;knk [kjhn ysrk gSA rnuqlkj pkoy dh ewy dher izfr fdxzk- fdruh gS \

¼1½ 14 :- ¼2½ 16 :- ¼3½ 12 :-¼4½ 15 :-

Ikz-78 & ,d oLrq dh dher esa 10% dh deh gks tkus ij ,d O;fDr :- 225 esa ml oLrq dk 25 fdxzk- T;knk [kjhn ldrk gSA rnuqlkj ml oLrq dh ewy dher izfr fdxzk- fdruh Fkh \

¼1½ 2 :- ¼2½ 1 :- ¼3½ 2-50 :- ¼4½ 1-50 :-Ikz-79 & fdlh uxj dh orZeku tula[;k 180000 gSA ;fn blesa 10% okf’kZd dh nj ls o`f) gksrh gS rks 2 o’kZ ckn mldh tula[;k gks tk,xh \

¼1½ 207800 ¼2½ 227800 ¼3½ 217800¼4½ 237800

Ikz-80 & ,d oLrq ds ewY; esa gj o’kZ mlds ewY; ds 10% dh nj ls gzkl gksrk gSA ;fn oLrq dk orZeku ewY; 729 :- gS rks 3 o’kZ iwoZ mldk ewY; Fkk \

¼1½ 1250 ¼2½ 1000 ¼3½ 1125¼4½ 1200

Ikz-81 & fdlh dLcs dh tula[;k izfro’kZ 4% c<+ tkrh gSA ;fn bldh orZeku tula[;k 50]000 gks rks 2 o’kZ ckn ;g fdruh gksxh \

¼1½ 53]900 ¼2½ 54]000 ¼3½ 54]080¼4½ 54]900

Ikz-82 & fdlh eky ds ewY; esa 10% okf’kZd dh o`f) fxjkoV vkrh gSA ;fn ;g rhu o’kZ igys [kjhnk\ x;k gks rFkk bldk orZeku ewY; 5]832 :- gks rks [kjhnrs le; bldk D;k ewY; Fkk \

¼1½ 7200 :- ¼2½ 7862 :- ¼3½ 8000 :-¼4½ 8500 :-

Ikz-83 & fdlh e”khu ds ewY; esa izfro’kZ 5% dk gzkl gksrk gSA ;fn mldk orZeku ewY; 2]00]000 :- gS rks nks o’kZ ckn mldk ewY; gksxk \

¼1½ 1]80]500 :- ¼2½ 1]99]000 :- ¼3½ 1]80]000 :- ¼4½ 2]10]000 :-Ikz-84 & fdlh ijh{kk esa 1000 yM+ds vkSj 800 yM+fd;k¡ FkhA yM+dks dk 60% vkSj yM+fd;ksa dk 50% mRrh.kZ gq,A tks ijh{kkFkhZ vuqRrh.kZ gq, mudk izfr”kr Kkr dhft, \

¼1½ 46-4 ¼2½ 48-4 ¼3½ 44-4¼4½ 49-6

Ikz-85 & fdlh ijh{kk esa 60% Nk= vaxzth esa mRrh.kZ gz, gS] 70% fgUnh esa vkSj 40% nksuks esaA rc vaxzsth vkSj fgUnh nksuks esa vuqRrh.kZ Nk=ks dk izfr”kr D;k Fkk \

¼1½ 10 ¼2½ 20 ¼3½ 25¼4½ 30

Ikz-86 & ,d mEehnokj dk sfdlh ijh{kk esa mRrh.kZ gksus ds fy, 40% vad izkIr djus t:jh gSA ;fn 220 vad izkIr djusokys mEehnokj 20 vadks ls vuqRrh.kZ gks x;k rks ml ijh{kk ds vf/kdre vad D;k Fks \

¼1½ 1200 ¼2½ 800 ¼3½ 600¼4½ 450

Ikz-87 & ,d izR;k”kh fdlh ijh{kk esa 20% vad izkIr djds 30 vadks ls Qsy gks tkrk gS ijUrq vU; izR;k”kh 32% vad izkIr djds ikl gksus okys vadks ls 42 vad vf/kd izkIr djrk gSA rc ikl gksus ds fy, vadks dk izfr”kr gS\

¼1½ 52% ¼2½ 50% ¼3½ 33% ¼4½ 25%

Ikz-88 & fdlh ijh{kk esa 52% fo/;FkhZ fgUnh rFkk 42% vaxzth esa Qsy gq,A ;fn 17% fo/;kFkhZ bu nksuks fo’k;ks esa Qsy gq, gks rks fdrus izfr”kr fo/;kFkhZ nksuks fo’k;ksa esa Qsy gq, \

¼1½ 38% ¼2½ 33% ¼3½ 23% ¼4½ 18%

Ikz-89 & fdlh ijh{kk esa 80% izR;k”kh vaxzsth rFkk 85% xf.kr esa ikl gq,A ;fn 73% izR;k”kh bu nksuks fo’k;ksa esa ikl gq, gks rks fdrus izfr”kr izR;k”kh bu nksuks fo’k;ks esa Qsy gq, \

¼1½ 8 ¼2½ 15 ¼3½ 27¼4½ 35

Ikz-90 & fdlh ijh{kk esa ikl gksus ds fy, vf/kdre vadks ds 36% vad ykuk vko”;d gSA ,d fo/;kFkhZ us 113 vad izkIr fd;s rFkk og 85 vadks ls Qsy gks x;kA ijh{kk esa vf/kdre vad gS \

¼1½ 500 ¼2½ 550 ¼3½ 565¼4½ 620

Ikz-91 & ,d ijh{kk esa ijh{kkfZFkZ;ksa ds 52% vaxzth esa vuqRrh.kZ gq, vkSj 42% xf.kr esaA rnuqlkj ;fn nksuks fo’k;ksa esa 17% vuqRrh.kZ jgs gks]rks mu nksuks fo’k;kssa esa mRrh.kZ ijh{kkfFkZ;ksa dk izfr”kr fdruk Fkk \

¼1½ 23 ¼2½ 21 ¼3½ 25¼4½ 22

Ikz-92 & uhye viuh vk; dk 20% edku ds fdjk, ij rFkk “ks’k dk 70% ?kjksyw enksa ij [kpZ djrh gSA ;fn og 3600 :- dh cpr djrh gS rks mldh dqy vk; fdruh gS \

¼1½ 15000 :- ¼2½ 10500 :- ¼3½ 10050 :-¼4½ 10000 :-

Ikz-93 & jk/kk vius osru dk 40% Hkkstu ij 20% edku ds fdjk, ij] 10% euksjatu ij rFkk 10% ifjogu ij O;; djrh gSA ;fn ekg ds var esa mldh cpr 1500 :Ik;s gS mldk ekfld osru :i;s gS \

¼1½ 8000 ¼2½ 7500 ¼3½ 6000¼4½ 10000

Ikz-94 & ,d O;fDr ds ikl dqN /kujkf”k gSA mlus ml jkf”k dk 20% ,d oLrq [kjhnus esa [kpZ fd;k vkSj “ks’k dk 5% ifjogu ij blds ckn mlus :- 120 nku dj fn,A rnuqlkj ;fn mlds ikl :- 1400 “ks’k cps gks rks mlds }kjk ifjogu ij fd;k [kpZ fdruk Fkk \

¼1½ 76 :- ¼2½ 61 :- ¼3½ 95 :-¼4½ 80 :-

Ikz-95 & fdlh Qy fod`srk ds ikl dqN lsc FksA og 40% lsc csp nsuk gS vkSj fQj Hkh mlds ikl 420 lsc cps jgrs gSA izkjEHk esa mlds ikl lsc Fks \

¼1½ 588 lsc ¼2½ 600 lsc ¼3½ 672 lsc¼4½ 700 lsc

Ikz-96 & ;fn fdlh fo/kky; esa 70% fo/;kFkhZ yM+ds gSA vkSj yM+fd;ksa dh la[;k 504 gS] rks yM+dks dh la[;k gS \ ¼1½ 1176 ¼2½ 1008 ¼3½ 1208

¼4½ 3024Ikz-97 & fdlh ijh{kk esa 70% izR;k”kh vaxzth esa ikl gq, ] 80% xf.kr esa ikl gq, rFkk 10% nksuks fo’k;ksa esa Qsy gq,A ;fn nksuks fo’k;ksa esa 144 izR;k”kh ikl gq, ] rks izR;kf”k;ksa dh dqy la[;k Fkh

¼1½ 125 ¼2½ 200 ¼3½ 240¼4½ 375

Ikz-98 & fdlh ijh{kk nsuks okyks esa 640 yM+ds vkSj 360 yM+fd;k¡ FkhA yM+dks ds 60% rFkk yM+fd;ksa ds 80% ijh{kkFkhZ lQy jgsA Qsy gksus ijh{kkfFkZ;ksa dk izfr”kr Fkk \

¼1½ 20 ¼2½ 60 ¼3½ 30-5¼4½ 32-8

Ikz-99 & fdlh ijh{kk esa 34% ijh{kkFkhZ xf.kr esa Qsy gq, rFkk 42% vaxzth esa Qsy gq,A ;fn 20% nksuks fo’k;ksa esa Qsy gq,A rks nksuks fo”;ksa esa ikl gksus okys ijh{kkfFkZ;ksa dk izfr”kr Fkk \

¼1½ 54 ¼2½ 50 ¼3½ 44¼4½ 56

Ikz-100 & ,d la[;k esa igys 20% rFkk iqu% 20% dh o`f) dh x;h gSA c<+h gqbZ la[;k dks fdrus izfr”kr de fd;k tk, ] rkfd ;g izkjfEHkd la[;k ds cjkcj gks tk, \

¼1½ 3059% ¼2½ 19

1131% ¼3½ 40%

¼4½ 44% Ikz0-101 & ,d pquko esa dsoy nks mEehnokj FksA muesa ls ,d mEehnokj dks 40% er feys vkSj og ,d vU; mEehnokj ls 298 erks ls gkj x;k rnuqlkj Mkys x,s euks dh la[;k fdruh Fkh \

¼1½ 745 ¼2½ 1460 ¼3½ 1490¼4½ 1500

Ikz-102 & fdlh flusek gkWy dh lhaVks dh la[;k esa 25% dh o`f) dj nh xbZA izR;sd fVdV ds ewY; esa Hkh 10% dh o`f) dj nh xbZA bu ifjorZuks ds ifj.kkeLo:Ik flusek gkWy ls izkIr gksus okyh vk; esa o`f) gksxh \

¼1½ 37-5% ¼2½ 45-5% ¼3½ 47-5% ¼4½ 49-5%

Ikz-103 & fdlh oLrq dk ewY; igys 20% ?kVkdj 30% c<+ fn;k tkrk gSA ifj.ker% ;fn mldk : 416ewY; gks tk, rks ml oLrq dk ewy ewY; fdruk gS \

¼1½ 350 :- ¼2½ 405 :- ¼3½ 400 :-¼4½ 450 :-

vuqikr lekuqikr iz-1 & 1 % 2 % 3 % 4 ds vuqikr esa pkj la[;k,a gSA mu la[;kvks dk ;ksx 16 gSA igyh o pkSFkh la[;k dk ;ksx cjkcj gS \

¼1½ 5 ¼2½ 8 ¼3½ 10¼4½ 80

Ikz-2 & nks la[;kvks esa 3 % 8 dk vuqikr gS vkSj mudk varj 115 gSA rc nksuks la[;kvks esa ls NksVh la[;k gS \

¼1½ 181 ¼2½ 194 ¼3½ 69¼4½ 78

Ikz-3 & fdlh ckWDl esa dsoy 1 :Ik;k rFkk 50 iSls okys dqy feykdj 210 flDds gSA muds d`ekuqlkj ekuksa dk vuqikr 13 % 11 gSA ,d :Ik;s okys flDds dh la[;k gksxh \

¼1½ 65 ¼2½ 66 ¼3½ 77¼4½ 78

Ikz-4 & 215 % 20.5 dk vuqikr fdlds vuqikr ds cjkcj gS \¼1½ 2 % 1 ¼2½ 3 % 1 ¼3½ 6 % 1¼4½ 3 % 2

iz-5 & ;fn A % B = 3 % 4 ] B % C = 5 % 7 vkSj C % D = 8 % 9 gS rks vuqikr A % D cjkcj gksxk \

¼1½ 3 % 7 ¼2½ 7 % 3 ¼3½ 21 % 10¼4½ 10 % 21

Ikz-6 & ;fn a : b = 5 % 7 vkSj c : d = 2a : 3b gS rks ac : bd gksxk \¼1½ 20 % 38 ¼2½ 50 % 147 ¼3½ 10 % 21¼4½ 50 % 151

Ikz-7 & ;fn A : B = 3 : 5 rFkk B : C = 4 : 7 gks rks A : B : C gksxk \¼1½ 6 % 9 % 14 ¼2½ 3 % 5 % 7 ¼3½ 12

% 20 % 21 ¼4½ 12 % 20 % 35

Ikz-8 & ;fn A = B dk 45 rFkk B = C dk

52 gks rks A : C dk vuqikr gksxk \

¼1½ 1 % 2 ¼2½ 2 % 1 ¼3½ 2 % 3¼4½ 1 % 3

Ikz-9 & ;fn 2A = 3B = 4C gks rks A : B : C gksxk \¼1½ 2 % 3 %4 ¼2½ 4 % 3 % 2 ¼3½ 6 % 4 %

3 ¼4½ 3 % 4 % 6Ikz-10 & ;fn A : B = 2 : 3, B : C = 4 : 5 rFkk C : D = 5 : 9 gks rks A : D cjkcj gksxk \

¼1½ 11 % 17 ¼2½ 8 % 27 ¼3½ 5 % 9¼4½ 2 % 9

Ikz-11 & ;fn A : B : C = 2 : 3 : 4 gks rks AB:BC:CA cjkcj gS \

¼1½ 8 % 9 % 16 ¼2½ 8 % 9 % 12 ¼3½ 8 % 9 % 24 ¼4½ 4 % 9 % 16Ikz-12 & 738 :Ik, dks A, B, C esa bl izdkj forfjr fd;k x;k gS fd mudk vuqikr 2 % 3 % 4 gSA rnuqlkj muesa B dk fdruk fgLlk gS \ ¼1½ 328 :- ¼2½ 246 :- ¼3½ 264 :-

¼4½ 164 :-Ikz-13 & og la[;k dkSu lh gS] ftls ;fn 7] 16] 43] 79 esa tksM+k tk, rks os la[;k,a lekuqikrh gks tk,

¼1½ 2 ¼2½ 3 ¼3½ 5¼4½ 1

Ikz-14 & fdlh fHkUu ds va”k vkSj gj 2 % 3 ds vuqikr esa gS] ;fn va”k esa ls 6 ?kVk;k tk,] rks ifj.kke ;g og fHkUu gS ftldk eku

izkjfEHkd fHkUu dk 23 gSA izkjfEHkd fHkUu dk va”k gS \

¼1½ 6 ¼2½ 18 ¼3½ 27¼4½ 36

Ikz-15 & nks la[;kvks ds chp 5 % 4 dk vuqikr gSA rnuqlkj] ;fn igyh dk 40% dk eku 12 gks] rks nwljh la[;k dk 50% fdruk gksxk \

¼1½ 12 ¼2½ 24 ¼3½ 18¼4½ 20

Ikz-16 & ;fn ¼p - q½ dk 50% = ¼p + q½ 30% gks] rks p : q cjkcj gksxk \¼1½ 5 % 3 ¼2½ 4 % 1 ¼3½ 3 % 5¼4½ 1 % 4

Ikz-17 & nks fo/;kfFkZ;ksa dh vk;qvks dk vuqikr 3 % 2 gSA muesa ls ,d nwljs ls 5 o’kZ cM+k gSA NksVs fo/;kFkhZ dh vk;q fdruh gS \

¼1½ 2 o’kZ ¼2½ 10 o’kZ ¼3½ 212 o’kZ

¼4½ 15 o’kZ Ikz-18 & nks Hkkb;ksa dh orZeku vk;q dk vuqikr 1 % 2 gS rFkk 5 o’kZ igys ;g vuqikr 1 % 3 FkkA 5 o’kZ Ik”pkr mudh vk;q dk vuqikr fdruk gksxk \ ¼1½ 1 % 4 ¼2½ 2 % 3 ¼3½ 3 % 5

¼4½ 5 % 6Ikz-19 & pkj o’kZ iwoZ A rFkk B dh vk;q 11 % 14 s vuqikr esa Fkh rFkk pkj o’kZ ds ckj mudh vk;q 13 % 16 ds vuqikr esa gksxhA A h orZeku vk;q gS \ ¼1½ 48 o’kZ ¼2½ 26 o’kZ ¼3½ 44 o’kZ

¼4½ 28 o’kZ Ikz-20 & fdlh la[;k dk 0-6 nwljh la[;k ds 0-08 ds cjkcj gSA nksuks la[;vks ds vuqikr gS \

¼1½ 3 % 4 ¼2½ 4 % 3 ¼3½ 2 % 15¼4½ 2 % 9

Ikz-21 & nks la[;kvks dk ;ksx 40 gS vkSj mudk varj 4 gSA la[;kvks dk vuqikr D;k gS \

¼1½ 21 % 19 ¼2½ 22 % 9 ¼3½ 2 % 15¼4½ 11 % 18

Ikz-22 & nks la[;kvks dk vuqikr 10 % 7 gS vkSj mudk vUrj 105 gSA mu la[;kvks dk ;ksx gS \

¼1½ 595 ¼2½ 805 ¼3½ 1190¼4½ 1610

Ikz-23 & nks /kukRed iw.kkZadks dk xq.kuQy 1575 gSA rFkk mudk vuqikr 9 % 7 gSA buesa NksV iw.kkZad gS

¼1½ 25 ¼2½ 35 ¼3½ 45¼4½ 70

Ikz-24 & rhu la[;kvks dk ;ksx 68 gSA ;fn igyh la[;k dk nwljh ls vuqikr 2 % 3 rFkk nwljh dk rhljh ls vuqikr 5 % 3 gks] rks la[;k gksxh \ ¼1½ 30 ¼2½ 58 ¼3½ 20

¼4½ 48Ikz-25 & nks la[;k,¡ ,lh gS fd mudk vUrj mudk ;ksx rFkk mudk xq.kuQy 1 % 7 % 24 ds vuqikr esa gSA la[;kvks dk xq.kuQy gS \

¼1½ 24 ¼2½ 36 ¼3½ 48¼4½ 60

Ikz-26 & nks la[;kvks dk ;ksxQy vSj muds varj dk vuqikr 5 % 1 gSA cM+h la[;k vkSj NksVh la[;k ds chp dk vuqikr gS \

¼1½ 2 % 3 ¼2½ 3 % 2 ¼3½ 5 % 1¼4½ 1 % 5

Ikz-27 & rhu d{kkvks ds fo/;kfFkZ;ksa dh la[;kvks dk vuqikr 2 % 3 % 5 gSA izR;sd d{kk esa 40 fo/;kFkhZ vkSj cM+k fn, tkus ij ;g vuqikr 4 % 5 % 7 gks tkrk gSA izkjEHk esa dqy fo/;kfFkZ;ksa dh la[;k Fkh \

¼1½ 100 ¼2½ 180 ¼3½ 200¼4½ 400

Ikz-28 & rhu d{kkvks ds fo/;kfFkZ;ksa dh la[;kvks dk vuqikr 2 % 3 % 5 gSA ;fn izR;sd d{kk esa 20 fo/;kFkhZ c<+k fn, tk,¡] rks ;g vuqikr 4 % 5 % 7 gks tkrk gSA c<+ksRrjh ls igys fo/;kfFkZ;ksa dh

dqy la[;k Fkh \¼1½ 10 ¼2½ 90 ¼3½ 100¼4½ 110

Ikz-29 & rhu d{kkvks esa fo/;kfFkZ;ksa dh la[;kvks dk vuqikr 2 % 3 % 5 gSA izR;sd d{kk esa 20 fo/;kFkhZ c<+ fn, tkus ij ;g vuqikr 4 % 5 % 7 gks tkrk gSA izkjEHk esa dqy fo/;kfFkZ;ksa dh la[;k Fkh \ ¼1½ 50 ¼2½ 90 ¼3½ 100

¼4½ 150Ikz-30 & rhu d{kkvks esa fo/;kfFkZ;ksa dh la[;k 2 % 3 % 4 ds vuqikr esa gSA ;fn izR;sd d{kk esa 12 fo/;kFkhZ c<+ tk,] rks ;g vuqikr 8 % 11 % 14 esa ifjofrZr gks tkrk gSA vkjaHk esa rhuks d{kkvks esa dqy feykdj fo/;kfFkZ;ksa dh la[;k Fkh \

¼1½ 162 ¼2½ 108 ¼3½ 96¼4½ 54

Ikz-31 & rhu d{kkvks esa Nk=ks dh la[;k dk vuqikr 2 % 3 % 5 gSA izR;sd d{kk esa 20 Nk=ks dh ozf) gksus ij vuqikr 4 % 5 % 7 gks tkrk gSA rnuqlkj bl ozf) ls igys Nk=ks dh la[;k fdruh Fkh

¼1½ 160 ¼2½ 120 ¼3½ 100¼4½ 10

Ikz-32 & rhu la[;k,¡ 1 % 2 % 3 ds vuqikr esa gSA muesa izR;sd esa 5 tksM+us ij ubZ la[;k,¡ 2 % 3 % 4 ds vuqikr esa gks tkrh gSA rnuqlkj os la[;k,¡ dkSu lh gS\ ¼1½ 10] 20] 30 ¼2½ 15] 30] 45 ¼3½ 1] 2] 3 ¼4½ 5] 10] 15Ikz-33 & 200 xzke dh , feJ/kkrq esa tLrk vkSj rk¡ck 5 % 3 ds vuqikr esa gSA blesa fdrus xzke rk¡ckfeyk;k tk, rkfd ;g vuqikr 3 % 5 gks tk, \

¼1½ 133 13 ¼2½

1200 ¼3½ 72

¼4½ 66 Ikz-34 & dk¡ls esa rk¡cs vkSj tLrs dk vuqikr 13 % 7 gSA 100 fdxzk- dk¡ls esa fdruk tLrk gksxk\

¼1½ 20 fdxzk- ¼2½ 55 fdxzk- ¼3½ 35 fdxzk- ¼4½ 40 fdxzk-Ikz-35 & 30 yhVj “kksjs ds vEy esa vEy vkSj ikuh dk vuqikr 2 % 3 gSA blesa fdruk ikuh vkSj feyk;k tk, rkfd vEy vkSj ikuh dk vuqikr 2 % 5 gks tk,\ ¼1½ 10 yhVj ¼2½ 15 yhVj ¼3½ 18 yhVj ¼4½ 12 yhVj Ikz-36 & cjkcj /kkfjrkvks ds rhu crZu gSA igys crZu esa xa/kd ds vEy vkSj ikuh dk vuqikr 3 % 2 gS nwljs crZu esa ;g vuqikr 7 % 3 gS rFkk rhljs crZu esa ;g vuqikr 11 % 4 gSA ;fn bu lHkh dks feyk fn;k tk, rks bl feJ.k esa xa/kd ds vEy vkSj ikuh dk vuqikr gksxk \ ¼1½ 61 % 29 ¼2½ 61 % 28 ¼3½ 60 % 29

¼4½ 59 % 29Ikz-37 & A vkSj B dh ekfld vk; 5 % 6 ds vuqikr esa gSA rFkk muds ekfld O;; dk vuqikr 3 % 4 gSA ;fn os izfr ekl d`e”k% 1800 : vkSj 1600 : dh cpr djrs gS] rks B dh ekfld vk; Kkr dhft, \

¼1½ 3400 :- ¼2½ 2700 :- ¼3½ 1720 :-¼4½ 7200 :-

Ikz-38 & nks O;fDr;ksa dh vk; dk vuqikr 5 % 3 gS rFkk muds O;; dk vuqikr 9 % 5 gSA ;fn os d`e”k% 1300 :- vkSj 900 :- dh cpr djrs gS rks izR;sd dh vk; Kkr dhft, \

¼1½ 4]000 ] 2]400 ¼2½ 3]000 ] 1]800 ¼3½ 5]000 ] 3]000¼4½ 4]500 ] 2]700

Ikz-39 & A vkSj B dh okf’kZd vk; 4 % 3 ds vuqikr esa gS rFkk muds okf’kZd O; dk vuqikr 3 % 2 gSA ;fn buesa ls izR;sd o’kZ ds var esa 600 :i;s dh cpr djrk gS] rks A dh vk; gS \

¼1½ 4]800 :Ik;s ¼2½ 1]800 :Ik;s ¼3½ 1]200 :Ik;s ¼4½ 2]400 :Ik;s

Ikz-40 & nks O;fDr;ksa dh vk; dk vuqikr 5 % 3 gS rFkk muds O;; dk vuqikr 9 % 5 gSA ;fn os dè”k% 26 :- vkSj 1800 :- dh cpr djrs gS] rks mudh vk; gS \

¼1½ 800] 4800 ¼2½ 6000 ] 6000 ¼3½ 1000 ] 6000¼4½ 9000 ] 5400Ikz-41 & fdlh cDls esa 180 :- 1 :- 50 iSls vkSj 25 iSls ds flDdks ds :Ik es j[ks gq, gS ftudk vuqikr esa 2 % 3 % 4 gSA 50 iSls okys flDdks dh la[;k fdruh gS \

¼1½ 60 ¼2½ 120 ¼3½ 150¼4½ 180

Ikz-42 & ;fn 378 flDds ,d :Ik;s ] 50 iSls rFkk 25 iSls ds flDdks ds :I esa gS rFkk buds eku 13 % 11 % 7 ds vuqikr esa gS rks 50 iSls ds flDdks dh la[;k fdruh gS \

¼1½ 132 ¼2½ 128 ¼3½ 136¼4½ 133

Ikz-43 & 225 :- dh ,d jkf”k ,d :Ik;s 50 iSls vkSj 25 iSls ds flDdks ds :i esa gS budh la[;k,¡ mlh dè esa gS 8 % 5 % 3 vuqikr esa gSA ,d :i;s ds flDdks dh la[;k gS \ ¼1½ 80 ¼2½ 112 ¼3½ 160

¼4½ 172Ikz-44 & ,d ckWDl esa 1 :- ] 50 iSls rFkk 25 iSls okys flDds 8 % 5 % 3 ds vuqikr esa gSA ;fn ckWDl esa dqy /ku jkf”k 112-50 :- gks ] rks 50 iSls okys flDdks dh la[;k gS \

¼1½ 80 ¼2½ 50 ¼3½ 30¼4½ 42

Ikz-45 & fdlh ckWDl esa dsoy 1 :Ik;k rFkk 50 iSls okys dqy feykdj 210 flDds gSA muds dèkuqlkj ekus dk vuqikr 13 % 11 gSA 1 :- okys flDdks dh la[;k gksxh \

¼1½ 65 ¼2½ 66 ¼3½ 77¼4½ 78

Ikz-46 & A vkSj B ds ikl 2 % 1 ds vuqikr esa /ku gSA ;fn A ] B dks 2 :- ns nsrk gS rks ;g /ku muds ikl 1 % 1 ds vuqikr esa gks tkrk gSA izkjEHk esa muds ikl fdruk /ku Fkk \

¼1½ 12 :- ] 6 : ¼2½ 16 :- ] 8 :- ¼3½ 8 :- ] 4 :- ¼4½ 6 :- ] 3 :-Ikz-47 & 1]240 :Ik;s dh ,d /kujkf”k A , B vkSj C esa bl izdkj ck¡fV, fd A dk Hkkx % B dk Hkkx = 6 % 5 rFkk B dk Hkkx % C dk Hkkx = 10 % 9 gSA C dk Hkkx Kkr dhft, \

¼1½ 480 :- ¼2½ 360 :- ¼3½ 400 :-¼4½ 630 :-

Ikz-48 & dksbZ /kujkf”k 2 % 7 % 9 ds vuqikr esa P , Q vkSj R dks ck¡Vh tkuh gSA P vkSj Q ds Hkkxks dk ;ksx R ds Hkkx ds cjkcj gSA P vkSj Q ds Hkkxks dk varj fdruk gS \ ¼1½ 5000 :- ¼2½ 7500 :- ¼3½ 9000 :-

¼4½ lwpuk vi;kZIr gS

Ikz-49 & 117 :- dks P, Q, R esa 12: 13:14 ds vuqikr esa ck¡Vus ds Lfkku ij

xyrh ls 2 % 3 % 4 dsvuqikr esa ck¡V fn;k x;kA blesa dkSu YkkHk esa jgk \

¼1½ dsoy P ¼2½ dsoy Q ¼3½ dsoy R ¼4½ Q vkSj R nksuks

Ikz-50 & og U;wure iw.kkZad D;k gS ftls ;fn 6 % 7 vquikr ds vadks ls ?kVk;k tk, rks ifj.kke 16 % 21

Lks de vuqikr esa vk, \¼1½ 5 ¼2½ 4 ¼3½ 3¼4½ 2

Ikz-51 & ,d Vªd 1 feuV esa 550 eh- dh nwjh r; djrk gSA tcfd ,d cl 33 fdeh- dh nwjh 45 feuV esa r; djrh gSA mudh xfr dk vuqikr gksxk\

¼1½ 4 % 3 ¼2½ 3 % 5 ¼4½ 3 % 4¼4½ 50 % 3

Ikz-52 & 286 fo/;kfFkZ;ksa okys ,d fo/;ky; esa yM+ds rFkk yM+fd;ksa dh la[;k,¡ 8 % 5 ds vuqikr es gSA ;fn 22 vU; yM+fd;k¡ fo/;ky; esa nkf[kyk ys ysa] rks yM+ds rFkk yM+fd;ksa dh la[;kvks dk vuqikr gks tk,xk \

¼1½ 12 % 7 ¼2½ 10 % 7 ¼3½ 8 % 7¼4½ 4 % 3

Ikz-53 & 6] 14] 18 rFkk 38 esa ls izR;sd esa dkSu lh la[;k tksM+us ij ifj.kkeh la[;k,¡ ,d lekuqikr cuk,axh \

¼1½ 1 ¼2½ 2 ¼3½ 3¼4½ 4

Ikz-54 & 12 rFkk 18 dk rhljk lekuqikfrd fdruk gksxk \¼1½ 3 ¼2½ 6 ¼3½ 27¼4½ 144

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