[1]

f’k{kk funs’kky;

jk"V“h; jkt/kkuh {ks=k] fnYyh ljdkj

ewY; vk/kkfjr lgk;d lkexzh

lu~ 2012-13

fo"k; µ xf.kr

d{kk µ IX

ds funsZ’ku esa

Mk� lquhrk ,l- dkSf’kd

f’k{kk funsf’kdk

leUo;d %

Jherh ’kdqUryk egktu

iz/kkukpk;kZ

jk� m� ek� dU;k fo|ky;

Jh fuokliqjh] ubZ fnYyh 110065

rS;kjdÙkkZ %

1- Jherh lfork fot jktdh; lg f’k{kk mPpre fo|ky; ua� 1] yktir uxj

2- vydk xqIrk …jktdh; mPpre ek/;fed ckfydk fo|ky;] Jh fuokliqjh‰

3- lqeu ’kekZ …jktdh; mPpre ek/;fed ckfydk fo|ky;] Jh fuokliqjh‰

4- J)k ’kekZ …jktdh; lg f’k{kk mPprj fo|ky; taxiqjk‰

5- cchrk [kUuk …jktdh; lg f’k{kk mPprj fo|ky; taxiqjk‰

[2]

jSf[kd lehdj.k

1- fdlh xk¡o ds izkFkfed fo|ky; esa yM+fd;ksa dk ukekadu fiNys o"kZ ls nqxquk gqvk gSA

;fn bl o"kZ ds ukekadu dks ‘y’ }kjk rFkk fiNys ukekadu dks ‘x’ }kjk n’kkZ,¡ rksµ

…d‰ bl lwpuk }kjk jSf[kd lehdj.k cukb,A

…[k‰ ;fn fiNys o"kZ dk ukekadu 35 Fkk rks bl o"kZ dk ukekadu crkb,A

…x‰ ;gk¡ fdu ewY;ksa dks n’kkZ;k x;k gS\

2- lksfu;k vius tUe&fnu ds volj ij ,d vukFkkJe esa pkWdysV ck¡Vrh gSA og izR;sd

cPps dks 5 pkWdysV nsrh gS rFkk O;Ldksa dks dqy 20 pkWdysV nsrh gS\ ;fn cPpksa dh la[;k

dks ‘x’ ls rFkk dqy ck¡Vh xbZ pkWdysV dks ‘y’ ls n’kkZ;k tk, rksµ

…d‰ bldks jSf[kd lehdj.k }kjk n’kkZb,A

…[k‰ ;fn mlus dqy 145 pkWdysV ck¡Vs rks vukFkkJe esa cPpksa dh la[;k Kkr djksA

…x‰ lksfu;k }kjk fdu ewY;ksa dks n’kkZ;k x;k gS\

3- fdlh vkoklh; lkslk;Vh ds fuokfl;ksa }kjk o"kkZ ds ty dks lajf{kr djus gsrq Hkwfexr

VSad esa 30 ?ku lseh@lsd.M dh nj ls bdºk fd;k x;kA ;fn ‘x’ lsd.M esa ‘y’ ?ku lseh

ikuh dks bdºk fd;k x;k rksµ

…d‰ bl tkudkjh dks jSf[kd lehdj.k ds :i esa fyf[k,A

…[k‰ bl lehdj.k dks ekud :i ax+by+c=0 ds :i esa fyf[k,A

…x‰ lkslk;Vh ds lnL;ksa }kjk fdu ewY;ksa dks n’kkZ;k x;k gS\

4- ,d O;fä us dqN nwjh r; djus ds fy, ,d vkWVks fjD’kk fy;kA vkWVks fjD’kk dk fdjk;k

igys fdeh ds fy, 10 #� rRi’pkr~ ;g 7 #i;s izfr fdeh gks tkrk gSA ;fn r; dh

xbZ nwjh ‘x’ fdeh rFkk dqy fdjk;k ‘y’ #i;s gks rksµ

…d‰ bl lwpuk ds vk/kkj ij jSf[kd lehdj.k cukb,A

…[k‰ O;fä 16 fdeh dh nwjh r; djrk gS rFkk vkWVks fjD’kk pkyd dks 120 #i;s ns nsrk

gSA vkWVks pkyd dgrk gS ^^;g lgh fdjk;k ugha gS** rFkk ml O;fä dks cdk;k

jkf’k ns nsrk gSA vkWVks pkyd }kjk nh xbZ cdk;k jkf’k crkb,A

…x‰ vkWVks pkyd }kjk n’kkZ;s tkus okys ewY; crkb,A

[3]

5- ^LoPNrk vfHk;ku* ds vUrxZr ,d eksgYys fuokfl;ksa us feytqy dj vius vM+ksl&iM+ksl

dks LoPN djus dk fu’p; fd;kA bl dk;Z esa cPpksa dh Hkkxhnkjh O;Ldksa dh Hkkxhnkjh ls

20 vf/kd gSA ;fn O;Ldksa dh la[;k dks ‘x’ ekus o cPpksa dh la[;k dks ‘y’ ekus rksµ

…d‰ mijksä lwpuk dks jSf[kd lehdj.k }kjk n’kkZb,A

…[k‰ fuokfl;ksa }kjk izn£’kr ewY; crkb,A

6- jgeku vkSj izdk’k us feydj iz/kkuea=kh jkgr dks"k esa 500 #i;s dk ;ksxnku fn;kµ

…d‰ bl lwpuk dks jSf[kd lehdj.k }kjk n’kkZb,A

…[k‰ bl xfrfof/k esa fdu ewY;ksa dks n’kkZ;k x;k gS\

7- jSf[kd lehdj.k 2(x+1)=3(y–1)–4 dks vkys[k }kjk fn[kkb,A tk¡p dhft, fd fcUnq

(–3, +1) bl js[kk ij fLFkr gS ;k ugha\

;gk¡ ij fdu ewY;ksa dks n’kkZ;k x;k gS\

8- d{kk esa v/;kfidk us ewy fcUnq ls xqtjus okyh js[kk ds fy, lgh fodYi <w¡<us dks dgkµ

jSf[kd lehdj.k fuEu gSµ

y+x=1, x+3y=2, x+y=0

jsgkuk us bldk lgh mÙkj x+y=0 pqukA fuEu esa ls dkSu&lk ewY; n’kkZ;k x;k gSµ

…d‰ lPpkbZ …[k‰ lekurk …x‰ bZekunkjh

…?k‰ ln~Hkko

9-

–3 –2 –1 0 1 2 3 4

x=a

vkÑfr (i)

–3 –2 –1 0 1 2 3 4X X

3

2

1

–1

–2

Y

Y

x=b

vkÑfr (ii)

…d‰ ¯ij cuh vkÑfr;ksa (i) o (ii) esa a rFkk b dk eku Kkr dfj,A

…[k‰ D;k a=b ? vius mÙkj ds fy, rdZ nhft,A

…x‰ blesa fdu ewY;ksa dks izn£’kr fd;k x;k gS\

[4]

10- …d‰ isV“ksy dh dher 4 #i;s izfr yhVj dh nj ls gj N% eghus esa c<+ jgh gSA ;fn isV“ksy

dh dher fnlEcj 2011 esa ‘x’#i;s gks rFkk isV“ksy dk orZeku ewY; ‘y’#i;s gks

rks fnlEcj 2012 esa isV“ksy dh dher dks n’kkZus ds fy, jSf[kd lehdj.k cukb,A

…[k‰ isV“ksy dh dher esa yxkrkj o‘f) ds dkj.k dbZ yksxksa us isV“ksy dh txg CNG dk

iz;ksx vkjEHk dj fn;k gSA CNG dk ewY; izfro"kZ 3 #i;s dh nj ls c<+rk gSA ;fn

fnlEcj 2011 esa CNG dk ewY; ‘a’ #i;s rFkk orZeku ewY; ‘b’ #i;s gks rks

fnlEcj 2012 dk ewY; Kkr djus ds fy, jSf[kd lehdj.k cukb,A

…x‰ yksxksa }kjk isV“ksy dh txg CNG ds iz;ksx ls fdu ewY;ksa dks n’kkZ;k x;k gS\

jSf[kd lehdj.k

mÙkjekyk

1- …d‰ y=2x

…[k‰ y=2×35=70

…x‰ LorU=krk] flyx lekurk

1- …d‰ y=5x+20

…[k‰ 145=5x+20

125=5x x=25

…x‰ [kq’kh] ln~Hkko

3- …d‰ y=30x

…[k‰ 30x–y+0=0

…x‰ i;kZoj.k lqj{kk] lg;ksx

4- …d‰ y=10+7(x–1)

=10+7x–7

y=7x+3

[5]

…[k‰ y=7×16+3

=112+3=115 #i;s cdk;k jkf’k = 120–115 = 5 #i;s

…x‰ bZekunkjh] lPpkbZ

5- …d‰ y = x+20

…[k‰ lg;ksx] [kq’kh] ln~Hkko] i;kZoj.k lqj{kk

6- …d‰ x+y = 500

…[k‰ lg;ksx] lgk;rkFkZ

7- …d‰ lehjd.k

2(x+1)=3(y–1)–4

2x+2=3y–3–4

2x–3y+9=0

fcUnq (–3, +1) lehdj.k esa j[kus ij

= –6 – 3 + 9 = 0 = R.H.S.

;g fcUnq js[kk ij fLFkr gSA

…[k‰ ftKklk] lPpkbZ] oSKkfud euksn’kk

8- …d‰ lPpkbZ

9- …d‰ a=3, b=3

…[k‰ gk¡

…x‰ oSKkfud euksn’kk] lPpkbZ] Kku

10- …d‰ y=x+8

…[k‰ b=a+3

…x‰ i;kZoj.k lqj{kk

[6]

prqHkq Zt

1-

A

B C28cm

26cm25cm

P

QR

,d fo|ky; esa f’k{kk funs’kky; ds vf/kdkfj;ksa ds vkxeu gsrq Nk=kkvksa dks f=kHkqtkdkj

:i esa jaxksyh cukus dks dgk x;k gSA f=kHkqt ABC dh foek,¡ 26 cm, 28 cm o 25

cm gSA ABC dh Hkqtkvksa ds e/; fcUnqvksa dks tksM+dj ,d f=kHkqt PQR cuk;k x;k

gS ftlds rhuksa vksj ,d gkj ltkuk gSA

…d‰ gkj dh yEckbZ Kkr dhft;sA

…[k‰ bl xfrfof/k }kjk fdl ewY; dks n’kkZ;k x;k gS\

2- d{kk esa v/;kfidk us prqHkZt dh vkÑfr okys jaxhu dkxt lHkh cPpksa dks ck¡V fn,A

mlus buls isij QksflYMx o dflVx }kjk lekUrj prqHkqZt cukus dks dgkµ

…d‰ isij QksflYMx }kjk lekUrj prqHkqZt cukus dh fof/k fyf[k,A

…[k‰ fl) dhft, fd cuh gqbZ vkÑfr lekUrj prqHkqZt gSA

…x‰ blesa fdu ewY;ksa dks n’kkZ;k x;k gS\

3- ABCD ,d le prqHkqZt gS ftlesa ADC=120°.

fcUnq C rFkk D ij vfXu’keu dsUnz gSA O fcUnq ij vkx yxus dh lwpuk feyh gSA

A B

CD

O

120°

…d‰ dkSu&lh vfXu’keu dh Vhe tYnh fcUnq O ij igq¡p ik,xh rFkk D;ksa\

…[k‰ bl xfrfof/k }kjk fdu ewY;ksa dks n’kkZ;k x;k gS\

[7]

4- lksgu viuh v/;kfidk dk vkHkkj izdV djus gsrq mUgsa ,d dkMZ cukdj nsuk pkgrk gSA

dkMZ esa leyEc ds rhu VqdM+s bl izdkj O;ofLFkr fd, x, gS fd AB || HC ||

GD || FE rFkk BC=CD=DE o GF=6 lsehA og bl dkMZ dks ltkus ds fy, ,d

jaxhu Vsi mldh vlekUrj js[kkvksa ij yxkuk pkgrk gSµ

A B

F E

H C

G D

…d‰ mls fdruh jaxhu Vsi dh vko’;drk gksxh] ;fn DE = 4 cm

…[k‰ bl xfrfof/k }kjk lksgu fdu ewY;ksa dks n’kkZrk gS\

5- ,d fdlku ds ikl lekUrj prqHkqZt ABCD dh vkÑfr okyk {ks=k gSA mlds ikyrw

i’kqvksa esa ls ,d xk; dks laØked jksx yx x;k gSA mldh mfpr ns[kHkky gsrq mlus {ks=k

ds ,d dksus esa xk; dks ck¡/k fn;kA ;fn {ks=k ds ,d dksus dk dks.k 65° gks rksµ

A D

CB

65°

…d‰ {ks=k ds rhu vU; dks.k Kkr dfj,A

…[k‰ ;gk¡ izn£’kr fd, x, ewY; crkb,A

6- ,d pkWdysV prqHkqZt ds vkdkj dh gS ftldh foek,¡ 6 lseh] 10 lseh] 5 lseh]

5 lseh gSA blds fod.kZ }kjk bls nks Hkkxksa esa ck¡Vdj ,d efgyk us Hkkx I dks ?kj

esa dke djus okyh ukSdjkuh dks rFkk Hkkx II dks nks cjkcj fgLlksa esa ck¡Vdj vius

[8]

M“kboj o ekyh dks fn;kA

10cm

6 cm

5 cm

5 cm

A B

D

CIII

…d‰ D;k ;g c¡Vokjk mfpr gS\ rdZ }kjk Li"V dfj,A

…[k‰ efgyk }kjk fdu ewY;ksa dks n’kkZ;k x;k gS\

7- ,d prqHkqZt ds xq.k/keZ dk fo’ys"k.k djrs gq, d{kk esa ,d fo|kFkhZ us dgk fd prqHkqZt

ds lHkh dks.k vf/kd dks.k ugha gks ldrsµ

…d‰ bl mÙkj dks rdZ }kjk Li"V dfj,A

…[k‰ fo|kFkhZ }kjk fdl ewY; dks n’kkZ;k x;k\

8- xf.kr dh iz;ksx’kkyk esa lHkh fo|kfFkZ;ksa dks fuEu yEckbZ ds 4 rhys fn, x, 8 lseh] 8

lseh] 5 lseh] 5 lsehA fo|k£Fk;ksa dks buls fofHkUu izdkj ds prqHkqZt cukus dks dgk x;kµ

…d‰ bu rhfy;ksa dk iz;ksx dj fdruh izdkj ds prqHkqZt cusaxs\

…[k‰ cuus okys prqHkqZtksa ds izdkj fyf[k,A

…x‰ bl xfrfof/k }kjk fo|kFkhZ ds fdu ewY;ksa ds ckjs esa irk pyrk gS\

9- ,d leyEc prqHkqZt ABCD esa DC || AB rFkk A=B=45°. v/;kfidk cPpksa

ls D dk eki Kkr djus ds fy, dgrh gS ujs’k us bldk tokc 135° fn;kµ

D C

A B

…d‰ D;k ;g mÙkj lgh gS\ rdZ nsdj Li"V djsaA

…[k‰ blesa fdu ewY;ksa dks n’kkZ;k x;k gS\

[9]

10- d{kk esa lekUrj prqHkqZt ds xq.k/keZ dh ppkZ ds nkSjku v/;kfidkvksa us x o y ds

chp lEcU/k iwNkA lekUrj prqHkqZt esa x o y fp=k }kjk n’kkZ, x, gSA v/;kfidk

us blds rhu fodYi fn,µ

(i) x > y (ii) x < y (iii) x = y

A B

CD

yx

chuk us bldk mÙkj x < y fn;kµ

…d‰ D;k ;g mÙkj lgh gS\

…[k‰ bl mÙkj dks rdZ }kjk fl) dfj,A

…x‰ blesa chuk ds dkSu ls ewY; dks n’kkZ;k x;k gS\

prqHkq Zt

mÙkjekyk

1- …d‰ RQ || BC rFkk RQ =1

2BC

…e/; fcUnq izes; }kjk‰

RQ = 14 cm

QP = 12.5 cm

PR = 13 cm

ifjeki = 14+12.5+13

= 39.5 cm

[10]

…[k‰ lqUnjrk] [kq’kh] lg;ksxA

2-

A

B

C D

SQ

P

R

…d‰ prqHkqZt ds e/; fcUnqvksa dks feykus ijA

…[k‰ ABD esa P, AB dk rFkk Q, AD dk e/; fcUnq gSA

1PQ || BD & PQ BD

2∴ = ......................(i) …e/; fcUnq izes;‰

blh izdkj RS || BD rFkk

1RS BD

2= .......(ii)

(i) vkSj (ii) ls

PQRS ,d lekUrj prqHkqZt gSA

…x‰ ftKklk] [kq’kh] oSKkfud euksn’kk

3- …d‰ D Vhe igys igq¡psxhA

ODC = 60°, OCD = 30° OC > OD …cM+s dks.k ds lkeus okyh

Hkqtk cM+h gksrh gS‰

…[k‰ bZekunkjh ls yksxksa dh lsok djuk

4- …d‰ AB || HC || GD || FE

rFkk BC = CD = DE

AH = HG = GF

[11]

…rhu lekUrj js[kk,¡ ;fn ,d fr;Zd js[kk ij leku vUr% [k.M cukrh gS rks nwljh

fr;Zd js[kk ij Hkh leku vUr% [k.M cusaxs‰

AF+FE = 18+12

=30 lseh

…[k‰ [kq’kh] lqUnjrk] Kku

5- …d‰ A =C=65°

B = 180°–65°

=115° = D

…[k‰ lgk;rkFkZ] gjsd dh lgk;rk ds fy, rRij jguk

6- …d‰ caVokjk lgh Fkk

…[k‰2BD AD² AB 100 36 64

BD = 8 lseh

{ks� (ABD) 1

6 82

× ×

= 24 oxZ lseh

BCD dk {ks=kQy

a b c 5 5 8S

2 2

+ + + += =

{ks=kQy 9 (9 5) (9 5) (9 8)= × − × − × −

9 4 4 1= × × ×

= 12 oxZ lseh

…x‰ lgk;rkFkZ] lekurk

[12]

7- …d‰ ;fn A = 91°, B = 91°, C = 91° rks D < 90°

A+B+C+D = 360°

…[k‰ oSKkfud euksn’kk] Kku

8- …d‰ rhu izdkj ds prqHkqZt cusaxs

…[k‰ vk;r] lekUrj prqHkqZt] irax

…x‰ oSKkfud euksn’kk] ftKklk

9- …d‰ DC || AB

A+D=180°

D=180°–45°=135°

…[k‰ oSKkfud euksn’kk] lPpkbZ

10- …d‰ gk¡

…[k‰ ADB = DBC = y …,dkarj dks.k‰

D;ksafd BC < CD x < y

…x‰ lPpkbZ

[13]

f=kHkqt o lekUrj prqHkq Zt dk {ks=kQy

1- vkfnoklh yksxksa dh lgk;rkFkZ ,d dY;k.k lfefr }kjk f’kYi esys dk vk;kstu fd;k

x;kA blesa iaMky dks ltkus ds fy, pkjksa vksj cYc dh yM+h yxkbZ tkuh gSA bls ;k rks

,d vk;rkdkj eSnku ds pkjksa vksj yxkuk gS ;k lekUrj prqHkqZt ABCD ds pkjksa vksjA

;fn nksuksa prqHkqZtksa dk {ks=kQy leku gS rksµ

FD E C

BA

…d‰ nksuksa esa ls dkSu&lh vkÑfr pquus ij U;wure [kpZ gksxk o D;ksa\

…[k‰ blesa fdu ewY;ksa dks n’kkZ;k x;k gS\

2- ,d tehu lekUrj prqHkqZt ABCD dh vkÑfr ds :i esa gSA bl tehu dk ekfyd ;gk¡

o‘)kJe] fMLisUljh] LokLF; dsUnz o ikdZ cukuk pkgrk gSA vkÑfr ns[ksa] fcUnq P, fod.kZ

BD ij dksbZ fcUnq gSA

A B

CD

o‘)kJe

ikdZ

P

fMLisUljh

O

…d‰ fl) dhft, fd o‘)kJe o fMLisUljh dks cjkcj dh tehu nh xbZ gSA

…[k‰ tehu ds ekfyd }kjk dkSu ls ewY; n’kkZ, x, gS\

[14]

3- ,d dkWyksuh ds ikl [kkyh tehu dks yksx dwM+k Qsadus ds fy, bLrseky dj jgs FksA tSlk

fd fp=k esa n’kkZ;k x;k gSA dkWyksuh ds yksxksa us feydj ;gk¡ ,d f=kHkqtkdkj rkykc cukus

dk fu’p; fd;kA ;g tehu ,d lekUrj prqHkqZt ABCD ds :i esa FkhA rkykc cukus

ds ckn ckdh cps fgLls ij vkS"k/kh; isM+ mxk, x,A ;fn lekUrj prqHkqZt dk {ks=kQy

200 oxZ eh gks rksµ

A

B

DP

C

Pond

…d‰ vkS"k/kh; isM+ yxk, tkus okyh tehu dk dqy {ks=kQy Kkr dfj,A

…[k‰ dkWyksuh ds fuokfl;ksa }kjk dkSu&lk ewY; n’kkZ;k x;k gS\

4- fo|ky; esa ̂ loZ f’k{kk vfHk;ku* ds vUrxZr ,d jSyh vk;ksftr dh xbZA lHkh fo|k£Fk;ksa

dks ukjs fy[kus ds fy, xÙks dh f=kHkqtkdkj ’khV nh xbZA tSlk fd fp=k esa n’kkZ;k x;k gS

mUgksaus f=kHkqt dh ekf/;dk,¡ [khapdj mls rhu cjkcj {ks=kQy okys f=kHkqtksa esa ck¡V fn;kA

A

B CD

G

EF

…d‰ fl) dhft, AGC dk {ks=kQy¾ AGB dk {ks=kQy¾ BGC dk

{ks=kQy

1

3= …ABC dk {ks=kQy‰

…[k‰ bl xfrfof/k }kjk fo|kFkhZ dkSu ls ewY; n’kkZrs gSa\

[15]

5- ,d fdlku ds ikl oxkZdkj tehu gS ftl ij og ,d gh le; esa ik¡p vyx&vyx

Qly mxkuk pkgrk gSA og tehu ds e/; Hkkx esa xsgw¡ cksuk pkgrk gS] ;g {ks=k dqy

{ks=kQy dk vk/kk gSA ckdh pkj cjkcj f=kHkqtkdkj Hkkxksa esa og vyx&vyx Qlysa

mxkuk pkg jgk gSA

…d‰ vkÑfr }kjk n’kkZb, fd og vius mís’; dks fdl izdkj iwjk dj ldrk gS\

…[k‰ Qlyksa ds fofue; }kjk fdlku fdu ewY;ksa dks izn£’kr djrk gS\

6- ,d xk¡o esa prqHkqZt ABCD dh vkÑfr okyh ,d tehu gSA xk¡o esa lkekftd dk;ZØeksa rFkk

iapk;r dh cSBdksa dks vk;ksftr djus ds fy, ljiap bl Hkwfe ij iDdk bZaVksa dk Q’kZ cuokuk

pkgrs gSa ijUrq ikl gh cPpksa ds fy, ikdZ cuus ds dkj.k mUgksaus Q’kZ f=kHkqt ds vkdkj dk

cukus dk fu’p; fd;kA ;fn AC || DP gks rksµ

…d‰ fl) dhft,µ

{ks� [ ABCD] = {ks� [ABP]

…[k‰ ;gk¡ fdu ewY;ksa dks n’kkZ;k tk jgk gS\

A

B

D

PC

7- ^^jk"V“h; v[k.Mrk fnol** ds volj ij d{kk uoha ds Nk=k ,d iksLVj cukuk pkgrs gSaA

;g iksLVj lekUrj prqHkqZt ds vkdkj dk gS ftls cjkcj {ks=kQy okys pkj f=kHkqtksa esa

ck¡Vk tk,xk rFkk izR;sd f=kHkqt ij fofHkUu /keksZa }kjk crkbZ xbZ f’k{kk,¡ fy[kh tk,xhA

…d‰ Nk=k iksLVj dks leku {ks=kQy okys pkj f=kHkqtksa esa fdl izdkj ck¡Vsaxs\ vius mÙkj

ds fy, rdZ nhft,A

…[k‰ ;gk¡ n’kkZ, x, ewY; crkb,A

[16]

8- xf.kr dh v/;kfidk us Nk=kksa ds nks lewgksa dks lekUrj prqHkqZt ds vkdkj dk ,d&,d

xÙks dk VqdM+k fn;kA izFke lewg us ml VqdM+s dk {ks=kQy AB dks vk/kkj ekudj Kkr

djuk gS rFkk ml mÙkj dk iz;ksx djds nwljs lewg us vk/kkj DA ds laxr ’kh"kZyEc dk

eku Kkr djuk gSµ

…d‰ lewg II ’kh"kZyEc ‘h’ dk eku fdl izdkj Kkr djsxk\

…[k‰ ;gk¡ fdu ewY;ksa dks n’kkZ;k x;k gS\

9- xf.kr dh ,d v/;kfidk us nks Nk=kksa dks leku eki okys lekUrj prqHkqZt dkVdj fn,

rFkk muls dgk x;k fd blesa ls lekUrj prqHkqZt ds vk/ks {ks=kQy okyh vkÑfr dkVdj

vyx dhft,A

A

D

BY

CX

A

D

BP

C

lquhrk us Hkqtkvksa CD rFkk AB ds e/; jksgu us Hkqtk AB ij fcUnq Pysdj mls

fcUnqvksa dks feykdj viuk mÙkj izLrqr fd;kA C rFkk D ls feyk;k rFkk mÙkj fn;kA

{ks� [ ABCD] = 2×[{ks�(AYXD)] {ks� [ ABCD] = 2×{ks� (DPC)

…d‰ crkb, fd nksuksa esa ls fdldk mÙkj lgh gS\ vius mÙkj dh iqf"V dhft,A

…[k‰ ;gk¡ n’kkZ, x, ewY; crkb,A

lewg (I)lewg (II)

[17]

A

D

B

C

O

10- leprqHkqZt ABCD esa fod.kZ AC=8 lseh rFkk AO=4 lsehA

;g dFku fdl ewY; dks n’kkZrk gSµ

…d‰ lkekftd ewY; …[k‰ lg;ksx

…x‰ lPpkbZ …?k‰ ln~Hkko

vius mÙkj dh iqf"V dhft,A

f=kHkqt o lekUrj prqHkq Zt dk {ks=kQy

mÙkjekyk

1- …d‰ vk;r D;ksafd

vk;r dk ifjeki < lekUrj prqHkqZt ds ifjekiA

…[k‰ lg;ksx] lgk;rkFkZ

2- …d‰ AC dks feykb,

fod.kZ AC o BD dks fcUnq O lef}Hkkftr djrk gSA

AO = OC rFkk BO = OD

APC esa PO ekf/;dk gS

APO dk {ks=kQy = PCO dk {ks=kQy .................. (i)

…ekf/;dk f=kHkqt dks cjkcj {ks=kQy

okys f=kHkqtksa esa ck¡Vrh gS‰

blh izdkj

ADC esa] DO ekf/;dk gS

ADO dk {ks� = DCO dk {ks� .................. (ii)

(i) vkSj (ii) dks tksM+us ij

APO dk {ks� + ADO dk {ks� = PCO dk {ks� + DCO dk {ks�

ADP dk {ks� = DPC dk {ks�

…[k‰ lgk;rkFkZ] [kq’kh] ln~Hkko

A B

CD

P

O

[18]

3- …d‰ 100 oxZ lseh

…[k‰ i;kZoj.k lqj{kk] lg;ksxA

4- …d‰ ABC esa AD ekf/;dk gS

ar (ABD) = ar (ADC) ______ (i)

blh izdkj

ar (GBD) = ar (GDC) ________ (ii)

(i) _ (ii) djus ij

ar (AGB) = ar (AGC)

blh izdkj

ar (AGB) = ar (AGC) = ar (GBC)

…[k‰ lg;ksx] ln~Hkko

5- …d‰

A D

B C

SQ

P

R

xsgw¡

I IV

IIIII

e/; fcUnqvksa dks feykdjA

…[k‰ feŒh dh xq.koÙkk c<+rh gS] i;kZoj.k lqj{kk] [kq’khA

6- …d‰ fn;k gS AC || DP

ADC) dk {ks� = APC dk {ks�

…leku vk/kkj AC rFkk leku lekUrj js[kkvksa AC

vkSj DP ds chp cuus okys f=kHkqtksa ds {ks=kQy leku

gksaxs‰

nksuksa vksj ABC dk {ks� tksM+us ij

ADC dk {ks� + ABC dk {ks� = PC dk {ks� + ABC dk {ks�

(ABCD dk {ks�) = ABP dk {ks�

…[k‰ i;kZoj.k lqj{kk] nwljksa ds fopkjksa ds izfr vknjA

[19]

7- …d‰ lekUrj prqHkqZt ds fod.kZ mls pkj leku {ks=kQy okys f=kHkqtksa esa ck¡Vrs gSaA

…[k‰ jk"V“h; ,drk] HkkbZpkjk] lg;ksxA

8- …d‰ lekUrj prqHkqZt ABCD dk {ks=kQyA

AB×DH = AD×BP

8×3 = 5×h

8 3h

5

× =

24h

5=

h = 4.8 cm.

…[k‰ oSKkfud euksn’kk] lg;ksxA

9- …d‰ nksuksa dk mÙkj lgh gSA

…[k‰ oSKkfud euksn’kk] ftKklk] lg;ksxA

10- ;g dFku lPpkbZ dks n’kkZrk gSA

[20]

o‘Ùk

1- rhu fe=kksa us 3 fiTtk dk vkMZj fn;kA rHkh muds nks fe=k vkSj vk x,A bu ik¡pksa us rhu

fiTtk dks vkil esa fey ck¡V dj [kkus dk QSlyk fd;kµ

…d‰ ;fn rhuksa fiTtk 7 lseh f=kT;k ds gks rks izR;sd fe=k dks feyus okys fgLls dk

{ks=kQy Kkr djksA

…[k‰ fe=kksa }kjk dkSu ls ewY; n’kkZ, x, gSa\

2- fo|ky; esa euk, tk jgs ^ou egksRlo* ds fy, fo|ky; ifjlj ds dksus esa Hkwfe ds ,d

o‘Ùkkdkj fgLls ij o‘{kkjksi.k djuk r; gqvkA fo|k£Fk;ksa ds ik¡p lewgksa dks ,d&,d

fgLlk o‘{kkjksi.k ds fy, …fp=k vuqlkj‰ fn;k x;kA

III

IV V

III

…d‰ fdl lewg dks o‘{kkjksi.k ds fy, vf/kd {ks=kQy feyk vkSj fdruk vf/kd\

…o‘Ùk dh nks f=kT;k,¡ 210 lseh rFkk 105 lseh gS‰

…[k‰ ;gk¡ dkSu ls ewY; n’kkZ, x, gS\

3- Hkkjrh; gkWdh la?k us Hkkjr vkSj ikfdLrku ds chp ,d ln~Hkkouk eSp dk vk;kstu fd;k

ftlesa ,df=kr /ku ,d vukFkkJe dks fn;k tkuk r; gqvkA eSp ds fy, ,d o‘Ùkkdkj eSnku

esa 60 eh-×80 eh- dk VQZ fp=kkuqlkj fcNk;k x;kµ

O80m

60m

…d‰ gkWdh ds eSnku dh f=kT;k Kkr dhft,A

…[k‰ n’kkZ, x, ewY; crkb,A

[21]

…x‰ vukFkkJe dks fn;k x;k /ku lekt dh izxfr ds fy, fdl izdkj lg;ksxh gS\

4- fdlh fo|ky; dh ckgjh nhokj dks jax djokus dk fu.kZ; fy;k x;kA bl dk;Z ds fy,

nhokj ij vyx&vyx jax ds rFkk ,d gh eki 40 lseh f=kT;k okys o‘Ùk cuk, ftu ij

lwfä;k¡ rFkk lkekftd lans’k fy[ks x,A ;fn fo|ky; dh ckgjh nhokj 200 eh- yEch

gS rksµ

200 m

40 cm40 cm 40 cm40 cm

…d‰ nhokj ij fdrus o‘Ùk cuk, x,\

…[k‰ bl izdkj dh xfrfof/k ls Nk=kksa esa fdu ewY;ksa dk lekos’k gksxk\

5- >qXxh >ksaiM+h esa jgus okys cPpksa ds euksjatu gsrq ,d o‘Ùkkdkj eSnku esa esys dk vk;kstu

fd;k x;k ftlesa muds fy, fu%’kqYd Hkkstu dh O;oLFkk dh xbZA Hkkstu forj.k ds fy,

pkj LVkWy A, B, C rFkk D ij fp=kkuqlkj yxk, x,µ

A

90°

C

DB30m

…d‰ fdUgha nks vklUu LVkWy ds chp dh nwjh Kkr dhft, ;fn eSnku dh f=kT;k 30 eh

gksA

…[k‰ D;k bl izdkj ds vk;kstu lekt ds fy, fgrdkjh gS\ lekt esa vU; fdu

lkekftd eqíksa ds fy, bl izdkj ds vk;kstu fd, tk ldrs gSa\

[22]

6- 66 fo|k£Fk;ksa dk ,d lewg fidfud ij x;kA Hkkstu djus ds fy, os ikdZ esa #ds rFkk

,d cM+s o‘Ùkkdkj ?ksjs esa cSB x,A ;fn izR;sd fo|kFkhZ nwljs fo|kFkhZ ls 50 lseh dh

o‘Ùkkdkj nwjh ij cSBk gS rksµ

A

C

B

50 cm

…d‰ fo|k£Fk;ksa }kjk cuk, x, o‘Ùk dh f=kT;k Kkr djksA

…[k‰ fo|k£Fk;ksa }kjk n’kkZ, x, ewY; crkb,A

7- fdlh dkWyksuh ds ,d o‘) nEifÙk us vius o‘Ùkkdkj Hkw[k.M dks fodflr djus dk QSlyk

fd;kA bl dk;Z esa mudh enn gsrq dkWyksuh ds cPps vkxs vk,A fp=kkuqlkj o‘Ùkkdkj

oy; ij ?kkl yxkbZ xbZA ;fn o‘Ùk dh f=kT;k,¡ 245 lseh rFkk 210 lseh gS rksµ

?kkl

iq"i

…d‰ fdrus {ks=kQy ij ?kkl yxkbZ xbZ\

…[k‰ cPpksa }kjk n’kkZ, x, ewY; crkb,A

8- fodykax O;fä;ksa }kjk lapkfyr rhu STD cwFk fp=kkuqlkj fcUnq A, B rFkk C ij

LFkkfir fd, x,A ;s rhuksa ,d nwljs ls lenwjLFk gSa rksµ

[23]

…d‰ BOC dh eki Kkr dhft,A

…[k‰ vkids fopkj esa fodykaxksa dks jkstxkj ds volj miyC/k djkuk D;k lekt dh

izxfr ds fy, fgrdkjh gS\ vius mÙkj dh leh{kk dhft,A

9- xf.kr dh iz;ksxkRed xfrfof/k ds nkSjku Nk=k o‘Ùkkdkj ^^ft;ks cksMZ** dk iz;ksx dj jgs

gSaA o‘Ùk dh fdlh pki }kjk dsUnz ij cuk, x, dks.k dh eki (2a+50°) gSA lk{kh us

blh pki }kjk o‘Ùk ds ’ks"k Hkkx ij cus dks.k dh eki (a+25°) Kkr dhA

…d‰ D;k lk{kh dk mÙkj lgh gS\

…[k‰ BAC dh eki Kkr dhft, ;fn a=30 gksA

…x‰ ;gk¡ dkSu ls ewY; n’kkZ, x, gSa\

10- dsUnz O okys o‘Ùk esa ABCD ,d pØh; prqHkqZt gSA

x+y=90° ;g dFku fdl ewY; dks n’kkZrk gSµ

…d‰ lkekftd ewY;

…[k‰ LorU=krk

…x‰ lR;’khyrk

…?k‰ flyx lekurkA

A

B C

O Dy

x

[24]

vius mÙkj dh leh{kk dhft,A

mÙkjekyk

1- …d‰ 92.4 oxZ lseh …[k‰ vkilh lg;ksx

2- …d‰ lewg III, 8662.5 oxZ lsehA …[k‰ i;kZoj.k lqj{kk] lqUnjrkA

3- …d‰ 50 eh- …[k‰ lgk;rkFkZ] lg;ksx

…x‰ ;g /ku vukFkksa ds fgr ds fy, iz;ksx fd;k tk;sxkA

4- …d‰ 250 …[k‰ lqUnjrk

5- …d‰ 30 2 eh-

…[k‰ gk¡] o‘)kJe ds yksx] vukFkkJe ds cPps] fodykax cPps vkfn ds fy,A

6- …d‰ 5.25 eh- …[k‰ lg;ksx] [kq’kh

7- …d‰ 50050 oxZ lseh …[k‰ lgk;rkFkZ

8- …d‰ 120° …[k‰ gk¡

9- …d‰ gk¡ …[k‰ 55°

…x‰ lPpkbZ] oSKkfud euksn’kkA

10- lR;’khyrk] KkuA

ACD = 90

BAD + BCD = 180 …pØh; prqHkqZt ds dks.k‰

y + x + 90 = 180

x + y = 90°

[25]

jpuk,¡

1- fnYyh V“SfQd iqfyl yksxksa dks V“SfQd fu;eksa ds ckjs esa crkus ds fy, leckgq f=kHkqt

ftldh izR;sd Hkqtk 5 eh gS] ds vkdkj dk ,d cksMZ cuokuk pkgrh gSa] bl f=kHkqt dh

jpuk djsa …eh- dh txg lseh ysa‰ mijksä fØ;kDyki D;k ewY; n’kkZrk gS\

2- jke ds ikl f=kHkqtkdkj tehu gS ftlesa B=30°, C=90° vkSj ifjeki 11 eh gSA

mlus ;g VqdM+k ,d o‘)kJe dks nku esa ns fn;kA bl f=kHkqt dh jpuk djks …lseh esa

Hkqtk,¡ ysdj‰ ;g D;k ewY; n’kkZrk gS\

3- ,d Ldwy ds cPpksa us lQkbZ vH;kl ds fy, ,d jSyh fudkyh mUgksaus AB, BC vkSj

CA esa ekpZ fd;k ftlls ,d f=kHkqt cuk ftlesa BC=8 m, B=45° vkSj AB–

AC=3.5 eh- gSA bl f=kHkqt dh jpuk djksA ;g D;k ewY; n’kkZrk gS\ …lseh esa Hkqtk;sa

ysdj‰

4- ,d dkiksZjsV (Co-operate) gk¯l us f=kHkqtkdkj ikdZ PQR dks gjk&Hkjk cuk, j[kus

ds fy, viuk;k ftlesa QR=7 eh] Q=75° vkSj PQ+PR=13 eh-A f=kHkqt PQR

dh jpuk djks …eh� dh txg lseh esa ysdj‰A ;g D;k ewY; n’kkZrk gS\

5- xzkeh.koklh i’kqvksa ds ikuh ds fy, ,d f=kHkqtkdkj rkykc cuokuk pkgrs gSaA rkykc dh

Hkqtk;sa 5 eh- vkSj 12 eh- gS rFkk muds chp dk dks.k 90° gS bldh jpuk djks …eh�

dh txg lseh esa ysdj‰A bl fØ;kDyki ls vki D;k ewY; fudkyrs gSa\

6- eksgu rFkk lksgu us ,d ledks.k dh jpuk dhA lgh fodYi pqusµ

Mohan Sohan

…d‰ eksgu lgh gSA …[k‰ lksgu lgh gSA

…x‰ nksuksa lgh gSA …?k‰ nksuksa xyr gSA

;g D;k ewY; n’kkZrk gS\

[26]

7- dfork us va/k fo|ky; dks nku djus ds fy, ,d f=kHkqtkdkj dkyhu cuk;k ftldh

Hkqtk;sa 5 eh-] 5 eh- vkSj 6 eh- gSA bl f=kHkqt dh jpuk djks …eh� dh txg lseh esa

ysdj‰A mijksä iz’u fdl ewY; dks n’kkZrk gS\

8- A ds fy, lgh fodYi pqusµ

…d‰

160 60

2+ × …[k‰

160 60

4+ ×

…x‰

160 60

3+ × …?k‰

160 60

5+ ×

;g D;k ewY; n’kkZrk gS\

9- xjhc yksxksa dks lnhZ ls cpkus ds fy, iSaFkj Dyc us ,d VSaV cuk;k ftldk njoktk

f=kHkqtkdkj FkkA bldh Hkqtk;sa 3 eh- 4 eh- vkSj 5 eh- gSA f=kHkqtkdkj njokts dh jpuk

djksA …eh� dh txg lseh esa ysdj‰

blls vki D;k ewY; fudkyrs gks\

10- ,d fjVk;MZ vkehZ vQlj ds ikl ledks.k f=kHkqt ds vkdkj dk Hkwfe dk VqdM+k gS

ftldh ,d Hkqtk 13.5 eh- vkSj d.kZ rFkk nwljh Hkqtk dk ;ksx 15.5 eh- gSA mlus bls

vukFkkJe dks nku ns fn;kA bl f=kHkqt dh jpuk djks …Hkqtk;sa lseh esa ysa‰A bu fopkjksa

ls D;k ewY; fudyrk gS\

mÙkjekyk

1- …d‰ lgh jpuk

…[k‰ yksxksa dks mudh lqj{kk ds fy, ;krk;kr ds fu;eksa ls tkx:d djukA

2- …d‰ lgh jpuk

…[k‰ nku izo‘fÙk dks izksRlkfgr djuk

3- …d‰ lgh jpuk

…[k‰ i;kZoj.k dks lkQ lqFkjk cukuk

A

[27]

4- …d‰ lgh jpuk

…[k‰ …1‰ i;kZoj.k dks lkQ lqFkjk cukuk

…2‰ leqnk; lsok

5- …d‰ lgh jpuk

…[k‰ lekt lsok

6- …d‰ eksgu lgh gS

…[k‰ lPpkbZ ewY;

7- …d‰ lgh jpuk

…[k‰ nku dh izo‘fÙk dks izksRlkfgr djuk] lekt lsok

8- …d‰

160 60

4+ ×

…[k‰ lPpkbZ ewY;

9- …d‰ lgh jpuk

…[k‰ leqnk; lsok

10- …d‰ lgh jpuk

…[k‰ lekt lsok

[28]

i‘"Bh; {ks=kQy vkSj vk;ru

1- yEc ’kadq ds vk;ru ds lw=k dks bl izdkj Hkh fy[kk tk ldrk gSµ

2 31 1v h h

3 3= π − πl

mijksä dFku dkSu&lk ewY; n’kkZrk gSµ

…d‰ lPpkbZ ewY; …[k‰ lkekftd ewY;

…x‰ nwljksa ds fopkjksa ds izfr vknj …?k‰ lekurk

2- d{kk X ds 50 fo|k£Fk;ksa us o‘)kJe esa tkdj ogk¡ jgus okys o‘)ksa ds lkFk lkjk fnu

O;rhr djus dk fu’p; fd;kA migkj ds fy, izR;sd fo|kFkhZ us csyukdkj Qwynku xÙks

ls cuk;kA izR;sd Qwynku dks 4.2 cm f=kT;k vkSj 11.2 cm ¡̄pkbZ dk gksuk gSA

…d‰ 20 #i;s izfr 100 m² ds nj ls xÙkk [kjhnus ij fo|k£Fk;ksa dks fdruk O;; djuk

iM+sxk\

…[k‰ fo|k£Fk;ksa }kjk dkSu&lk ewY; n’kkZ;k x;k gS\

3- NSS ds Lo;a lsodksa us ck<+ izHkkfor {ks=k esa frjiky ls cus ’kadq ds vkdkj ds ,d racw

dks yxk;kA racw dh ¡̄pkbZ 4 m rFkk mlds vk/kkj dk O;kl 6 m gSA

…d‰ 1.5 m pkSM+s frjiky dh fdruh yEckbZ yxsxh\ ;g ekudj pfy, fd bldh

flykbZ vkSj dVkbZ esa 10% frjiky vfrfjä yxsxk (=3.14 dk iz;ksx dhft,A)

…[k‰ Lo;a lsod dkSu ls ewY; n’kkZrs gSa\

4- fdlh xgjs [kqns xìs dks iqu% pØ.k IykfLVd ls cus 50 [kks[kys ’kadqvksa ls fuekZ.k LFky

ls vyx fd;k x;k gSA izR;sd ’kadq ds vk/kkj dk O;kl 40 cm gS vkSj ¡̄pkbZ 1 m gSA

…d‰ ;fn bu ’kadqvksa dh ckgjh i‘"Bksa dks isaV djokuk gS vkSj isaV dh nj 12 #i;s izfr

m² gS] rks budks isaV djkus esa fdruh ykxr vk,xh\

(=3.14 vkSj 1.04 1.02= dk iz;ksx dhft,)

…[k‰ ewY;ksa dk uke crkb,A

[29]

5- QSDVjh ds ekfyd v’ouh vius lHkh deZpkfj;ksa dks ltk gqvk xksyk HksaV esa nsuk pkgrk

gSA xksys dk O;kl (2a+5) cm gSA lts gq, xksys dks yEc o‘Ùkh; csyu] tks xksys dks

iw.kZr;k ?ksjs gq, gS] esa iSd fd;k x;k gSA …nsf[k, vkÑfr‰ ;fn csyu dh ¡̄pkbZ 21 cm

gS rksµ

…d‰ ‘a’ dk eku Kkr dhft,A

…[k‰ xksys dk i‘"Bh; {ks=kQy Kkr dhft,A

…x‰ v’ouh }kjk n’kkZ, ewY; crkb,A

6- ,d vkoklh; dkWyksuh dh tula[;k 5400 gS izfrfnu izfr O;fä dh 60 yhVj ikuh dh

vko’;drk gSA o"kkZ ds ikuh dk lgh mi;ksx djus ds fy, fuoklh mldk laj{k.k djuk

pkgrs gSaA ty laj{k.k ds fy, 48 m×27 m×25 m ekiksa okyh ,d Vadh cukbZ xbZA

…d‰ Vadh dk ikuh fdrus fnu ds fy, i;kZIr gksxk ;fn o"kkZ ds le; Vadh esa ty Lrj

dh ¡̄pkbZ 5 m gSA

…[k‰ O;fä;ksa ds lewg }kjk n’kkZ, x, ewY; crkb,A

7- ,d vLirky ds ,d jksxh dks izfrfnu 7 cm O;kl okys ,d csyukdkj dVksjs esa lwi

(soup) fn;k tkrk gSA fdlh ,d fnu dU;k egkfo|ky; dh dU;kvksa us ;g r; fd;k

fd og jksfx;ksa ds fy, lwi cuk,xhA ;fn og dVksjk lwi ls 5 cm ¡̄pkbZ rd Hkjrh gS] rks

bl vLirky esa 300 jksfx;ksa ds fy, ml fnu fdruk lwi rS;kj fd;k x;k gS\

dU;kvksa }kjk dkSu&lk ewY; n’kkZ;k x;k gS\

8- fdlh lkslk;Vh esa jgus okys fuokfl;ksa us vgkrs esa fLFkr ^^dSalj funku dsUnz** ds gkWy

dks isaV djus dk fu’p; fd;kA ;fn vk;rkdkj gkWy ds Q’kZ dk ifjeki 250 m gS rFkk

[30]

¡̄pkbZ 6 m gks rksµ

…d‰ 8 #i;s izfr m² dh nj ls pkjksa nhokjksa ij isaV yxkus dh ykxr Kkr dhft,A

…[k‰ fuoklh dkSu&lk ewY; n’kkZrs gSa\

9- lquh/kh] pUnzek rFkk i‘Foh ds O;kl ds chp lEcU/k Kkr djuk pkgrh gSA miyC/k

vkadM+ksa ls ;g irk gS fd i‘Foh dk vk;ru pUnzek ds vk;ru dk 64 xquk gSA lquh/kh

bl fu"d"kZ ij igq¡ph fd pUnzek dk O;kl i‘Foh ds O;kl dk yxHkx ,d&pkSFkkbZ gSA

…d‰ mlds dFku dks fl) dhft,A

…[k‰ bl iz;ksx }kjk lquh/kh dkSu&lk ewY; n’kkZrh gS\

10- Jheku rFkk Jherh jes’k va/k fo|ky; ds 100 fo|k£Fk;ksa esa nw/k forfjr djuk pkgrs

gSaA forj.k ds fy, nks fodYi gSµ

fodYi A : i;kZoj.k 10.5 f=kT;k okyk v/kZ xksyk

fodYi B : IykfLVd dk 7 cm f=kT;k okyk v/kZ xksykA

…d‰ fodYi A esa fdrus yhVj nw/k dh vko’;drk gS\

…[k‰ fodYi B esa dqy fdrus yhVj nw/k dh vko’;drk gS\

…x‰ Jheku rFkk Jherh jes’k us fodYi A dks forj.k ds fy, pqukA muds }kjk

dkSu&lk ewY; n’kkZ;k x;k gS\

mÙkjekyk

1- …d‰

2- …d‰ Rs. 3511.20

…[k‰ lkekftd ewY;] lg;ksx] o‘) yksxksa dh ns[kHkkyA

3- …d‰ yEckbZ = 34.54 m

…[k‰ lkekftd ewY;] lgk;rkFkZZ

4- …d‰ dqy ewY; = 384.34 #i,

…[k‰ i;kZoj.k lqj{kk] lkekftd ewY;

[31]

5- …d‰ 8

…[k‰ xksys dk i‘"Bh; {ks=kQy = 1386 cm²

…x‰ lkekftd lkeatL;

6- …d‰ dqy fnu = 20 fnu

…[k‰ lg;ksx] lgk;rkFkZ] i;kZoj.k lqj{kk

7- …d‰ 57.750 l

…[k‰ lkekftd lkeatL;] [kq’kh

8- …d‰ Rs. 12000

…[k‰ Rs. 240

…x‰ lg;ksx] lkekftd ewY;] lkeatL;

9- …d‰ /kjrh dk vk;ru = 64 × pUnzek dk vk;ru

3 31 2

3 4R 64 R

4 3π = × π

( )331 2R 4R⇒ =

( ) ( )3 3

1 22R 4 2R⇒ = ×

( ) ( )3 3

1 2D 4D⇒ =

D1

= 4D2

1

4× …/kjrh dk O;kl‰ = pUnzek dk O;kl

…[k‰ ftKklk] tkuus dh Hkkouk] oSKkfud euksn’kk

…v‰ 242 litres

…c‰ 71.9 yhVj

…l‰ i;kZoj.k lqj{kk] lkekftd ewY;A

[32]

lkaf[;dh

1- ,d fo|ky; esa yxkrkj 6 o"kksZa rd fo|k£Fk;ksa dh la[;k fuEufyf[kr Fkhµ

o"kZ 2000 2001 2002 2003 2004 2005

fo|k£Fk;ksa dh la[;k 1620 2060 2540 3250 3500 3710

…d‰ mijksä vkadM+ksa dk ek/; Kkr djksA

…[k‰ mijksä vkadM+ksa dk n.M vkys[k cukvksA

…x‰ mijksä iz’u D;k ewY; izn£’kr djrk gS\

2- fiNys 100 o"kksZa esa Hkkjr esa ck?k dh fuEufyf[kr fLFkfr Fkhµ

o"kZ 1900 1960 2002 2007

ck?kksa dh la[;k 40,000 18,000 3,642 1,411

…d‰ mijksä vkadM+ksa dk ,d n.M vkys[k cukvksA

…[k‰ mijksä iz’u fdl ewY; dks n’kkZrk gS\

3- fuEufyf[kr vkadM+s 1998-99 ls 2002-03 rd Hkkjr }kjk pqdk, x, _.k …gtkj

djksM+ #i;s esa‰ dks n’kkZrk gSµ

o"kZ 1998-99 99-2000 2000-01 2001-02 2002-03

_.k 70 84 98 106 120

…gtkj djksM+ #i;s‰

…d‰ mijksä vkadM+ksa dk ckjEckjrk cgqHkqt cukb,A

…[k‰ mijksä vkadM+ksa ls vki D;k ewY; fudkyrs gks\

[33]

4- fuEu n.M vkys[k fnYyh ljdkj }kjk ykMyh ;kstuk ij cuk, x, ctV dks n’kkZrk gSµ

;kstuk tuojh 2008 esa ’kq# gqbZA

…d‰ fdl o"kZ esa ctV lcls de Fkk\

…[k‰ fdl o"kZ esa ctV lcls vf/kd Fkk\

…x‰ mijksä n.M vkys[k ls D;k ewY; izn£’kr gksrk gS\

5- ou egksRlo ds nkSjku 25 fo|ky;ksa esa ls izR;sd fo|ky; esa 25 ikS/ks yxk, x,A ,d

eghus ckn yxk, x, ikS/kksa esa ls cp x, ikS/kksa dh la[;k fuEu Fkhµ

16 20 23 10 610 12 7 9 1515 22 11 13 2117 9 4 10 12

20 15 18 18 22

…d‰ bu vkadM+ksa dks ,d ckjEckjrk caVu lkj.kh ds :i esa izLrqr dhft,A (0-5 dk oxZ

varjky ysdj)

…[k‰ mijksä fØ;kdyki D;k ewY; n’kkZrk gS\

0

200,0

400,0

600,0

800,0

1000,0

1200,0

5, 4

9060 9160

10300

2007-08 2008-09 2009-10 2010-11

vuqekfur ctV

…#i;s fefy

;u esa‰

[34]

6- 10 fo|k£Fk;ksa dk ,d lewg va/k fo|ky; x;kA ogk¡ nku esa izR;sd fo|kFkhZ us 100,

120, 125, 50, 75, 100, 150, 100, 75, 85 #i;s fn,A

…d‰ bu vkadM+ksa dk ek/;] cgqyd rFkk ekf/;dk Kkr djksA

…[k‰ mijksä ls vki D;k ewY; fudkyrs gks\

7- fuEufyf[kr vkadM+s fnYyh esa 2001 ls 2010 rd fctyh dh [kir n’kkZrs gSaµ

o"kZ 2001 2005 2006 2009 2010

fctyh dh [kir …esxkokV esa‰ 2831 3490 3626 4408 4581

8- fuEufyf[kr vkadM+s Hkkjr esa fMifFkfj;k ds dsl vkSj fMifFkfj;k dh otg ls gksus okyh

e‘R;q dks n’kkZrs gSaµ

o"kZ 2005 2006 2007 2008 2009

fMifFkfj;k dsl 47 50 45 190 340

fMifFkfj;k ds dkj.k e‘R;q 1 0 0 30 82

fuEufyf[kr iz’uksa dk mÙkj nksµ

…d‰ fdl o"kZ esa fMifFkfj;k ds dsl lcls de Fks\

…[k‰ fdl o"kZ esa fMifFkfj;k ds dkj.k dksbZ Hkh e‘R;q ugha gqbZ\

…x‰ mijksä vkadM+s D;k ewY; n’kkZrs gSa\

9- fuEufyf[kr vkadM+s Hkkjr esa dkyh [kkalh (Whoopig cough) dks n’kkZrk gSµ

o"kZ 2005-06 2006-07 2007-08 2008-09 2009-10

dsl 470 50 30 60 826

…d‰ mijksä vkadM+ksa dk ckjEckjrk cgqHkqt cukvksA

…[k‰ mijksä vkadM+s D;k ewY; izn£’kr djrs gSa\

10- 10 O;fä;ksa ls ;g iwNk x;k fd vius leqnk; ds lkekftd dk;Z djus esa os ,d lIrkg

esa fdruk le; nsrs gSaA mudk dguk gS Øe’k% 10, 7, 13, 10, 20, 15, 10, 14, 12,

16 ?k.VsA ,d lIrkg esa muds }kjk lkekftd dk;Z esa yxk, x, le; dk ek/; cgqyd

rFkk ekf/;dk Kkr djksA

mijksä iz’u ls vki D;k ewY; fudkyrs gks\

[35]

500

2000

o"kZ

1000

1500

2000

2500

3000

3500

4000

2001 2002 2003 2004 2005

fo|kfFkZ;ksa dh la[;k

0

5,000

1900

10,000

15,000

20,000

25,000

30,000

35,000

40,000

1960 2002 2007

o"kZ …ck?kksa dk laj{k.k‰

ck?kksa dh la[;k

0

mÙkjekyk

1- …d‰ 2780

…[k‰

…x‰ f’k{kk ds izfr tkx:drkA

2- …d‰

[36]

20

98-99

40

60

80

100

120

99-00 00-01 01-02 02-03

_.k …gtkj djksM+ #i;s esa‰

o"kZ

0

…[k‰ ck?kksa dks cpkvks …laj{krk‰

3- …d‰

…[k‰ gesa vkRefuHkZj gksus dk iz;kl djuk pkfg;sA

4- …d‰ 2007-08 esa ctV lcls de FkkA

…[k‰ 2010-11 esa ctV lcls vf/kd FkkA

…x‰ (i) yM+fd;ksa dks cpkuk

(ii) Ldwyksa esa yM+fd;ksa dh la[;k esa c<+ksÙkjh

(iii) ekrk firk esa flQZ yM+dh gksus dh vlqj{kk dks de djukA

5- …d‰ oxZ vUrjky ikS/kks a dh la[;k

0-5 1

5-10 4

10-15 7

15-20 7

20-25 6

…[k‰ o‘{kkjksi.k ls i‘Foh dh lqj{kk

[37]

500

2001

1000

1500

2000

2500

3000

3500

4000

4500

5000

2005 2006 2009 2010

o"kZ

fctyh dh cpr

0

6- …d‰ 50, 75, 75, 85, 100, 100, 120, 125, 150

ek/; = 98

cgqyd = 100

ek/;d = 100

…[k‰ lkekftd dk;ksZ ds fy, nku nsus dh vknrA

7- …d‰

…[k‰ fctyh dh cpr

8- …d‰ 2007 esa fMifFkfj;k dh chekjh lcls de FkhA

…[k‰ 2006 rFkk 2007 esa fMifFkfj;k dkj.k dksbZ e‘R;q ugha gqbZA

…x‰ (i) Vhdkdj.k dk;ZØe dks Bhd ls ykxw djukA

(ii) lekt lsok

[38]

9- …d‰

…[k‰ (i) Vhdkdj.k dk;ZØe dks Bhd ls ykxw djukA

(ii) lekt lsok

10- …d‰ vkjksgh Øe esa j[kus ijµ

7, 10, 10, 10, 12, 13, 14, 15, 16, 20

ek/; = 12.7

cgqyd = 10

ek/;d = 12.5

…[k‰ lekt lsok

[39]

izkf;drk

1- 2 cPpksa okys 1500 ifjokjksa dk ;kn‘PN;k p;u fd;k x;k gS vkSj fuEufyf[kr vkadM+s

fy[k fy, x, gSµ

ifjokjksa esa yM+fd;ksa dh la[;k 2 1 0

ifjokjksa dh la[;k 800 500 200

…d‰ ml ifjokj dh izkf;drk Kkr djsa ftlesa nks yM+fd;k¡ gks\

…[k‰ bu vkadM+ksa ls D;k lh[k feyrh gS\

2- LorU=krk fnol ds volj ij 1200 fo|k£Fk;ksa esa ls 900 fo|k£Fk;ksa us dk;ZØe esa Hkkx

fy;kµ

…d‰ LorU=krk fnol esa Hkkx ysus okys fo|kfFkZ;ksa dh izkf;drk Kkr djsaA

…[k‰ buls D;k ewY; fudyrk gS\

3- lhrk dgrh gS fd ’kCn ‘MADAM’ esa M rFkk ‘A’dh izkf;drk cjkcj gSA D;k og

lgh gS\

blls D;k ewY; fudyrk gS\

4- 1000 ifjokjksa esa ls 750 ifjokjksa dk ,d cPpk gS rFkk ckdh dk nks cPpksa okyk ifjokj

gSA izkf;drk Kkr djsaµ

…d‰ ,d cPps okys ifjokj dhA

…[k‰ nks cPpksa okys ifjokj dhA

…x‰ buls D;k ewY; fudkyrs gks\

5- ,d dLcs esa tUek"Veh ds volj ij 1000 yksxksa esa ls 920 yksx efUnj x;sA efUnj u

tkus okys yksxksa dh izkf;drk Kkr djsaA

bl dk;Z ls D;k lh[k feyrh gS\

6- ou egksRlo ds volj ij ,d Ldwy esa 100 cPpksa us Hkkx fy;k vkSj fuEu ikS/ks yxkus

esa ,d nwljs dh lgk;rk dhµ

[40]

ikS/kksa dk uke xqykc eksxjk pesyh tlehu

ikS/kksa dh la[;k 32 28 16 24

izkf;drk Kkr djsaµ

…d‰ xqykc ds ikS/ks yxkus dhA

…[k‰ tklehu ds ikS/ks yxkus dhA

…x‰ bl dk;Z ls D;k ewY; fudyrk gS\

7- eksgu ,d eghus esa 30,000 #i;s dekrk gS vkSj 25,000 #i;s [kpZ dj nsrk gSA mldh

cpr dh izkf;drk Kkr djsaA

8- ,d uxj esa 1000 yksxksa esa ls 998 yksx i<+s fy[ks gSA izkf;drk Kkr djsa fd pquk gqvk

O;fäµ

…d‰ i<+k fy[kk gSA

…[k‰ vui<+ gSA

…x‰ blls vki D;k ewY; fudkyrs gks\

9- d{kk ukSoh ds 15 cPpksa ds jä lewg ;s gSµ

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, AB

,sls cPps dh izkf;drk Kkr djks ftudk jä lewgµ

…d‰ O gks

…[k‰ A gks

…x‰ buls D;k ewY; fudyrk gS\

10- yktir uxj ds pkSjkgs ij 100 yksxksa esa ls 9 yksxksa us V“SfQd ykbZV dk mYya?ku fd;kA

mYya?ku u djus okys yksxksa dh izkf;drk Kkr djksA

blls D;k lh[k feyrh gS\

[41]

mÙkjekyk

1- …d‰

800 8

1500 15=

…[k‰ dU;k dks izkFkfedrkA

2- …d‰

900 3

1200 4=

…[k‰ ns’k izse dh HkkoukA

3- …d‰

2P(M) P(A)

5= =

…[k‰ lPpkbZ ewY;

4- …d‰

3

4 ;k

750

1000

…[k‰

250

1000 ;k

1

4

…x‰ …1‰ tula[;k fu;U=k.k

…2‰ NksVk ifjokj] lq[kh ifjokj

5- …d‰

80

1000 ;k

2

25

…[k‰ /kk£ed ewY;A

6- …d‰

32

100 ;k

8

25

…[k‰

24

100 ;k

6

25

…x‰ (i) i;kZoj.k lqj{kk

(ii) vkilh lg;ksx dh Hkkouk

[42]

7- …d‰

5000

30000 ;k

1

6

…[k‰ cpr dh vknr

8- …d‰

998

1000 ;k

499

500

…[k‰

2

1000 ;k

1

500

…x‰ ’kgjksa esa lk{kjrk nj vf/kd gSA

9- …d‰

7

15

…[k‰

4

15

…x‰ …1‰ nku dh Hkkouk

…2‰ lekt lsokA

10- …d‰

91

100

…[k‰ V“SfQd fu;eksa ds izfr lekt dh tkx:drk vkSj vius thou dh lqj{kk