‘mÜ¶{‘h$ narjm, 2019-20 j{uv ‘m°s>b nona 1€¦ · rbse math model paper 1 n¥îr>...

RBSE Math Model Paper 1 n¥îR> g§»¶m 1

RBSE Ho$ gm°ëdS> ‘m°S>b nona/S>oñH$dH©$ S>mCZbmoS> H$aZo Ho$ {bE h‘mar do~gmBQ> www.rbse.online na {d{OQ> H$a|&

No of Questions : 30 Zm‘m§H$

No of Pages : 3

‘mÜ¶{‘H$ narjm, 2019-20

J{UV

‘m°S>b nona 1g‘¶ … 3 4

1 KÊQ>o nyUmªH$ … 80

narjm[W©¶m| Ho$ {bE gm‘mÝ¶ {ZX}e-

1. g^r àíZ H$aZo A{Zdm¶© h¢&

2.

^mJ àíZ g§»¶m A§H$ àË¶oH$ àíZ

A 1-10 1

~ 11-15 2

g 16-25 3

X 26-30 6

3. àíZ H«$‘m§H$ 27 d 29 ‘| AmÝV[aH$ {dH$ën h¢&

4. àíZ H«$‘m§H$ 26 H$m boIm{MÌ J«m’$ nona na ~ZmBE&

^mJ-A

1. gyÌ EH$m{YHo$Z nyd}U H$m à¶moJ H$aVo hþE 31 31 31 3

2# H$m ‘mZ kmV H$s{O¶o&

2. gyÌ namdË¶© ¶moO¶oV² Ûmam g‘rH$aU xx

3 42 1

31

++ = H$m hb kmV H$s{OE&

3. 140 g§»¶m H$mo A^mÁ¶ JwUZIÊS>m| Ho$ JwUZ’$b Ho$ ê$n ‘| ì¶³V H$s{OE&

4. cos sin67 232 2c c-^ h H$m ‘mZ ³¶m h¡?

5. {H$gr g‘¶ gy¶© H$m CÝZ¶Z H$moU 60c h¡ VWm Cgr g‘¶ EH$ Iå^o H$s N>m¶m H$s bå~mB© 100 ‘rQ>a h¡&

Q>m°da H$s D±$MmB© ³¶m hmoJr?

6. {Ì^wO Ho$ AÝXa Cg {~ÝXþ H$m {~ÝXþnW kmV H$s{O¶o Omo {H$ {Ì^wO H$s VrZm| ^wOmAm| go g‘mZ Xÿar na hmo&

7. d¥Îm H$s gVh na pñWV {~ÝXþ na {H$VZr ñne© aoImE± ItMr Om gH$Vr h¢?

8. EH$ nmgo Ho$ ’|$H$Zo na g‘ A§H$ AmZo H$s àm{¶H$Vm kmV H$s{OE&

9. àVrH$ Zo nhbr, Xÿgar, Vrgar ¶mVm¶mV bmBQ> H$mo H«$‘e… 5, 12, 19 goH$ÊS> ‘| nma {H$¶m hmo Ed§ AJa dh

Bgr H«$‘ go ¶mVm¶mV bmBQ> H$mo nma H$aVm h¡ Vmo 10dt ¶mVm¶mV bmBQ> H$mo dh {H$VZo g‘¶ ‘| nma H$aoJm?

http://www.rbse.online


RBSE Ho$ gm°ëdS> ‘m°S>b nona àmßV H$aZo Ho$ {bE 9460443210 H$mo AnZr ³bmg Ho$ ìhmQ²>gEßn J«wn ‘| ES> H$a|&

10. EH$ ~g ñQ>¡ÊS> na gmYmaU ~gm| H$s g§»¶m S>rb³g ~gm| H$s g§»¶m H$r {VJwZr h¡, ¶{X gmYmaU ~gm| H$s g§»¶m

x h¡ Vmo 5 df© ~mX S>rb³g ~gm| H$s g§»¶m {b{IE&

^mJ-~

11. gyÌ {Z{bI‘² H$m à¶moJ H$aVo hþE 111034 889' H$m ‘mZ kmV H$s{OE&

12. Xmo g§»¶mAm| H$m b.g. 42 Am¡a ‘.g. 7 h¡& ¶{X BZ‘| go EH$ g§»¶m 14 hmo Vmo Xÿgar g§»¶m ³¶m hmoJr?

13. EH$ d¥Îm H$s {ÌÁ¶m 3.5 go‘r. h¡& d¥Îm H$s n[a{Y VWm joÌ’$b kmV H$s{OE&

14. EH$ KZ H$m gånyU© n¥îR>r¶ joÌ’$b 1014 dJ© ‘rQ>a h¡& KZ H$s ^wOm kmV H$s{OE&

15. EH$ grYo d 12 ‘rQ>a D±$Mo nmob Ho$ erf© na EH$ CCTV H¡$‘am bJmZm h¡ Vm{H$ nmob Ho$ erf© go 13 ‘rQ>a Xÿa

ÑpîQ> aoIm Ho$ AmJo ^r ¶mVm¶mV XoIm Om gHo$& Bg pñW{V ‘|-

1. nmob Ho$ nmX go dh Xÿar {OgHo$ AmJo go ¶mVm¶mV {XImB© XoVm h¡, ³¶m hmoJr?

2. nmob Ho$ Mmam| Amoa AXe©Zr¶ d¥Îm H$m joÌ’$b {H$VZm hmoJm?

^mJ-g

16. EH$ {ÛKmV ~hþnX kmV H$s{OE {OgHo$ eyÝ¶H$m| H$m ¶moJ VWm JwUZ’$b H«$‘e… 1/4 Am¡a 1- h¢&

17. Xmo A§H$m| dmbr {H$VZr g§»¶mE± 3 go {d^mÁ¶ h¡?

18. Am±Yr Ho$ H$maÊm EH$ d¥j H$m D$nar ^mJ Qy>Q>H$a j¡{VO Vb na 60c H$m H$moU ~ZmVm h¡& d¥j H$m {eIa

j¡{VO Vb na d¥j H$s O‹S> go 10 ‘rQ>a H$s Xÿar na {‘bVm h¡& Qy>Q>Zo go nhbo d¥j H$s D±$MmB© kmV H$s{OE&

.3 1 732=^ h

19. EH$ ABCT ‘|, ‘mpÜ¶H$mE± ,AD BE Am¡a CF {~ÝXþ G na à{VÀN>oX H$aVr h¢& ¶{X AG 6= go‘r.,

BE 9= go‘r. Am¡a .GF 4 5= go‘r. hm|, Vmo GD Am¡a BG kmV H$s{O¶o&

20. AmH¥${V ‘| ¶{X OA OB OC OD$ $= h¡ Vmo Xem©BE A C+ += d B D+ +=

21. AmH¥${V ‘|, Hw$N> H$moUm| H$mo , ,a b c Am¡a d go {MpÝh²V {H$¶m J¶m h¡& BZ H$moUm| Ho$ ‘mn kmV H$s{OE&

22. 4 go‘r. {ÌÁ¶m Am¡a O Ho$ÝÐ dmbo d¥Îm, {Og na Xmo ñne© aoImE± PT Am¡a PQ Bg àH$ma hm| {H$

TOQ 120c+ = hmo, H$s aMZm H$s{OE&



23. EH$ d¥Îm H$s n[a{Y EH$ dJ© H$o n[a‘mn Ho$ ~am~a h¡& ¶{X dJ© H$m joÌ’$b 484 dJ© ‘rQ>a hmo Vmo d¥Îm H$m joÌ’$b

kmV H$s{OE&

24. EH$ KZm^ H$s bå~mB©, Mm¡‹S>mB© Am¡a D±$MmB© H$m AZwnmV : :5 3 2 h¡& ¶{X KZm^ H$m gånyU© n¥îR>r¶ joÌ’$b 558

go‘r.2 h¡, Vmo CgH$s H$moam| H$s ‘mn kmV H$s{OE&

25. Xmo nmgm| H$mo EH$ gmW ’|$H$m OmVm h¡& {ZåZ KQ>ZmAm| H$s àm{¶H$Vm kmV H$s{OE…

1. àmá A§H$mo§ H$m ¶moJ EH$ g‘ g§»¶m&

2. àmá A§H$m| H$m JwUZ’$b EH$ g‘ g§»¶m&

3. àmá A§H$mo§ H$m ¶moJ EH$ A^mÁ¶ g§»¶m&

^mJ>-X

26. {ZåZ a¡{IH$ g‘rH$aU ¶w½‘ H$mo AmboIr¶ {d{Y go hb H$s{OE-

x y3 2 11+ - 0=

x y2 3 10- + 0=AV… BgH$s ghm¶Vm go g§~§Y x y k5 6+ = ‘| k H$m ‘mZ kmV H$s{OE&

27. {gÕ H$s{OE-

1. cot tanq q+ cosec secq q= ; 2. cossin

sincos

11

qq

qq

+ + + cosec2 q =

AWdm

27. 1. {gÕ H$s{OE, sin cossin cos 12 2

4 4

q qq q

-- =

2. ¶{X coscosBA m= VWm sin

cosBA n= hmo, Vmo {gÕ H$s{OE {H$ cosm n B n2 2 2 2+ =^ h .

28. 1. {~ÝXþ (1,2) Am¡a (6,7) H$mo {‘bmZo dmbo aoImIÊS> H$mo {~ÝXþ (3,4) {H$g AZwnmV ‘| {d^m{OV H$aVm

h¡?

2. Cg {~ÝXþ Ho$ {ZX}em§H$ kmV H$s{OE Omo {~ÝXþ (3,5) Am¡a (7,9) H$mo {‘bmZo dmbo aoImIÊS> H$mo 2…3 Ho$

AZwnmV ‘| AÝV… {d^m{OV H$aVm h¡&

29. {gÕ H$amo {H$ {Ì^wO H$s Xmo ^wOmAm| H$o dJm] H$m ¶moJ Vrgar ^wOm H$o ‘Ü¶ {~ÝXþ H$mo {‘bmZo dmbr ‘mpÜ¶H$m Ho$

dJ© Ed§ Vrgar ^wOm Ho$ AmYo Ho$ dJ© Ho$ ¶moJ Ho$ XþJwZo Ho$ ~am~a hmoVm h¡&

AWdm

29. {gÕ H$amo {H$ ¶[X MVw^w©O Ho$ gå‘wI H$moU gånyaH$ hm| Vmo dh EH$ MH«$s¶ MVw^w©O hmoVm h¡&

30. {ZåZ{b{IV ~maå~maVm ~§Q>Z {H$gr ‘mohëbo Ho$ 68 Cn^mo³VmAm| H$m {~Obr IM© ~VmVm h¡& BZ Am±H$‹S>m| go

‘mÜ¶H$, ‘mÜ¶ VWm ~hþbH$ kmV H$s{OE&

‘m{gH$ InV 65-85 85-105 105-125 125-145 145-165 165-185 185-200

Cn^mo³Vm 4 5 13 20 14 8 4

*******





No of Pages : 5

‘mÜ¶{‘H$ narjm, 2019-20

J{UV

‘m°S>b nona 2g‘¶ … 3 4




2.


A 1-10 1

~ 11-15 2

g 16-25 3

X 26-30 6



^mJ-A

1. gyÌ EH$m{YHo$Z nyd}U H$m à¶moJ H$aVo hþE 103 197# H$m ‘mZ kmV H$s{OE& (1)

2. gyÌ eyÝ¶ gmå¶ g‘wÀM¶m| Ûmam g‘rH$aU x x3 25

2 85 0+ + + = H$m hb kmV H$s{OE& (1)

3. {~Zm b§~r {d^mOZ à{H«$¶m {H$E ~VmBE {H$ 312513 n[a‘o¶ g§»¶m Ho$ Xe‘bd àgma gm§V h¢ ¶m Agm§V AmdVu

h¢? (1)

4. ¶{X cosA 52= , Vmo tan A4 4 2+ H$m ‘mZ kmV H$s{OE& (1)

5. {H$gr g‘¶ EH$ Iå^o H$s bå~mB© Am¡a CgH$s N>m¶m H$s bå~mB© H$m AZwnmV :1 3 h¡, Vmo Cg g‘¶ gy¶© H$m

CÞ¶Z H$moU {H$VZm hmoJm? (1)

6. VrZ Ag§aoIr¶ {~ÝXþ ,A B VWm C go hmoH$a OmZo dmbo d¥Îm Ho$ Ho$ÝÐ H$m {~ÝXþnW {ZYm©[aV H$s{O¶o& (1)

7. {XE JE {MÌ ‘| ¶{X PA d PB , Ho$ÝÐ O dmbo {H$gr d¥Îm na Xmo ñne© aoImE± Bg àH$ma h¢ {H$ APB 80c+ =

Vmo AOB+ H$m ‘mZ kmV H$s{OE& (1)




8. Xmo nmgm| H$mo ’|$H$Zo na A§H$m§o H$m ¶moJ 7 AmZo H$s àm{¶H$Vm kmV H$s{OE& (1)

9. àË¶oH$ {H$bmo‘rQ>a Ho$ ~mX H$m Q>¡³gr {H$am¶m O~{H$ àW‘ {H$bmo‘rQ>a Ho$ {bE {H$am¶m 10 ê$n¶o h¡ Am¡a àË¶oH$

A{V[a³V {H$bmo‘rQ>a Ho$ {bE {H$am¶m 6 ê$n¶o h¡& Cnamo³V pñW{V g‘mÝVa lo‹T>r h¡ ¶m Zht? (1)

10. {X¶o J¶o nmB© MmQ>© ‘| EH$ eha ‘| {d{^ÝZ dmhZm| Ûmam {H$¶m J¶m àXÿfU {d^mOZ H$mo Xem©¶m J¶m h¡&

¶{X Hw$b àXÿfU 720 BH$mB© ‘mZm J¶m h¡ Vmo H$mam| Ûmam CËnÞ àXÿfU H$s ‘mÌm ³¶m h¡? (1)

^mJ-~

11. ÛÝÛ ¶moJ {d{Y Ûmam g§»¶m 4312 H$m dJ© kmV H$s{OE& (2)

12. {gÕ H$s{OE {H$ 3 EH$ An[a‘o¶ g§»¶m h¡& (2)

13. EH$ d¥Îm H$s n[a{Y 44 ‘rQ>a h¡& d¥Îm H$m joÌ’$b kmV H$s{OE& (2)

14. EH$ ‘m{Mg H$s {S>ã~r H$s ‘mn 4 go‘r. # 2.5 go‘r. # 1.5 go‘r. h¡& Bg Vah H$s 12 {S>pã~¶m| Ho$ n¡{H$Q>

H$m Am¶VZ ³¶m hmoJm? (2)

15. ZrMo {X¶o J¶o J«m’$ ‘| Xmo àH$ma Ho$ dmhZm| A d B Ho$ N>… dfm] Ho$ àXÿfU H$m Am±H$‹S>m {X¶m J¶m h¡& A Kaoby

dmhZm| VWm B ì¶mdgm{¶H$ dmhZm| H$mo Xem©Vm h¡, Vmo J«m’$ H$m AÜ¶¶Z H$a ZrMo {X¶o J¶o àíZm| H$m CÎma Xr{OE&



1. ¶{X B H$m df© 2010 VWm 2011 ‘§o Hw$b àXÿfU 2.4 BH$mB© hmo Vmo df© 2008 d 2009 ‘| àXÿfU

{H$VZm ‘mnm J¶m?

2. {X¶o J¶o dfm] ‘| B H$m Am¡gV àXÿfU {H$VZm h¡? 1 1 2+ =

^mJ-g

16. ~hþnX f x x x4 3 5 2 32= + -^ h Ho$ eyÝ¶H$ kmV H$s{OE Am¡a eyÝ¶H$m| Ho$ ‘Ü¶ gå~ÝY gË¶m{nV

H$s{OE& (3)

17. ¶{X {H$gr A.P. Ho$ àW‘ 12 nXm| H$m ¶moJ 468 h¡ VWm BgH$m gmd©AÝVa 6 h¡ Vmo 10dm± nX kmV H$s{OE&

(3)

18. {H$gr AnyU© ‘rZma Ho$ AmYma go 120 ‘rQ>a Xÿa {H$gr {~ÝXþ go ‘rZma Ho$ {eIa H$m CÞ¶Z H$moU 30c h¡&

kmV H$s{OE {H$ ‘rZma H$mo Am¡a {H$VZm D±$Mm ~Zm¶m OmE {Oggo Cgr ñWmZ na CgH$m CÝZ¶Z H$moU 60c hmo

Om¶o? (3)

19. EH$ ABCT ‘|, ‘mpÜ¶H$mE± ,AD BE Am¡a CF {~ÝXþ G na à{VÀN>oX H$aVr h¢& {gÕ H$s{O¶o {H$

AD BE AB23>+ (g§Ho$V AG BG AB>+ ) (3)

20. Xr JB© AmH¥$[V ‘| aoImIÊS> XY , {Ì^wO ABC H$s ^wOm AC Ho$ g‘mÝVa h¡ VWm {Ì^wO H$mo Xmo g‘mZ ^mJm|

‘| ~m±Q>Vr h¡& AZwnmV ABAX kmV H$s{OE& (3)

21. AmH¥${V ‘§o, MH«$s¶ MVw^w©O ABCD Ho$ Mmam| H$moU kmV H$s{OE& (3)

22. 5 go‘r. {ÌÁ¶m H$m EH$ d¥Îm It{ME& Bg na Xmo ñne© aoImAm| H$m ¶w½‘ Bg àH$ma ~ZmBE {H$ CZHo$ ~rM ~Zm

H$moÊm 60c hmo& XmoZm| ñne© aoImAm| H$s bå~mB© ‘m{nE& (3)

23. EH$ d¥ÎmmH$ma IoV na <24 à{V ‘rQ>a H$s Xa go ~m‹S> bJmZo H$m ì¶¶ <5280 h¡& Bg joÌ H$s <0.50 à{VdJ©

‘rQ>a H$s Xa go OwVmB© H$amB© OmVr h¡& IoV H$s OwVmB© H$aZo H$m ì¶¶ kmV H$s{OE& (3)

24. EH$ bå~ d¥Îmr¶ ~obZ H$s D±$MmB© 7 go‘r. Am¡a AmYma H$s {ÌÁ¶m 3 go‘r. h¡& BgH$m dH«$n¥îR>r¶ joÌ’$b, gånyU©

n¥îR>r¶ joÌ’$b Am¡a Am¶VZ kmV H$s{OE& (3)




25. EH$ W¡bo ‘| 5 H$mbr, 7 bmb Am¡a 3 g’o$X J|X h¢& EH$ J|X ¶mÑÀN>¶m {ZH$mbr OmVr h¡& àm{¶H$Vm kmV H$s{OE

{H$ {ZH$mbr JB© J|X

1. bmb h¢

2. H$mbr ¶m g’o$X h¡

3. H$mbr Zht h¡& (3)

^mJ-X

26. {ZåZ a¡{IH$ g‘rH$aU ¶w½‘ H$mo AmboIr¶ {d{Y go hb H$s{OE-

x y2 3 8+ =

x y2 3- =-AV… BgH$s ghm¶Vm go g§~§Y x y Q9 10+ = ‘| Q H$m ‘mZ kmV H$s{OE&& (6)

27. {gÕ H$s{OE {H$-

1. cot cosecsin

cot cosecsin2q q

qq q

q+ = + - (3)

2. secsec

cossin

AA

AA1

1

2+ = - (3)

AWdm

27. 1. cot tan sin cossin1 2 2

q q q qq- = - (3)

2. ¶{X sec tan pq q+ = hmo, Vmo {gÕ H$s{OE {H$ sinpp

11

2

2

q +- = (3)

28. 1. EH$ aoIm H$m EH$ {gam (4,0) h¡ Am¡a ‘Ü¶ {~ÝXþ (4,1) h¡, Vmo aoIm Ho$ Xÿgao {gao Ho$ {ZX}em§H$ ³¶m

hm|Jo? (3)

2. Cg {~ÝXþ Ho$ {ZX}em§H$ kmV H$s{OE Omo {~ÝXþAm| ,5 2-^ h Am¡a ,1 421-^ h H$mo {‘bmZo dmbo aoImIÊS>

H$mo 7…9 ‘| ~mø {d^m{OV H$aVm h¡& (3)

29. 1. {gÕ H$amo {H$ EH$ A{YH$ H$moU {Ì^wO ABC {OgH$m B+ A{YH$ H$moU hmo Am¡a AD BC= h¡ Vmo

(3)

AC 2 AB BC BC BD22 2#= + +

2. ¶{X ABC3 EH$ Ý¶yZ H$moU {Ì^wO h¡ Am¡a AD BC= Vmo

AC 2 AB BC BC BD22 2#= + -



AWdm

29. {gÕ H$amo {H$ EH$ Mmn Ûmam d¥Îm Ho$ Ho$ÝX« na AÝV{aV H$moU d¥Îm Ho$ eof ^mJ Ho$ {H$gr {~ÝXþ na AÝV[aV H$moU

H$m XmoJwZm hmoVm h¡& (6)

30. J{UV H$s EH$ narjm ‘| 30 N>mÌm| Ûmam àmá {H$E JE A§H$m| H$m ~§Q>Z {ZåZ{b{IV h¡&

àmám§H$m| H$m dJ© AÝVamb 10-25 25-40 40-55 55-70 70-85 85-100

{dÚm{W©¶m| H$s g§»¶m 2 3 7 6 6 6

BZ Am±H$‹S>m§o go H$pënV ‘mÜ¶ {d{Y go ‘mÜ¶ kmV H$s{OE VWm ~hþbH$ ^r kmV H$s{OE& (6)

*******

AJbo gmb go H$moB© nmg~wH$ ¶m goånb nona

IarXZo H$s Oê$aV ZhtgÌ 2020-21 go amOñWmZ ‘| NCERT nmR²>¶H«$‘ bmJy

{H$¶m Om ahm h¡& Z¶o nmR²>¶H«$‘mZwgma g^r H$jmAm| Ho$ g^r

{df¶m| H$s Q>o³ñQ> ~wH$ Ed§ g^r àH$ma H$s ghm¶H$ AÜ¶¶Z

gm‘J«r O¡go- goånb nona/S>oñH$ dH©$ Am{X {dÚm[W©¶m| H$mo

‘mo~mBb na ìhmQ²>gEn Zå~a 9460443210 Ûmam Ed§

do~gmBQ> www.rbse.online na CnbãY H$adm¶r OmEJr&

BgHo$ {b¶o {dÚm{W©¶m| go {H$gr ^r àH$ma H$m H$moB© ewëH$ Zht

{b¶m OmEJm& BgHo$ {b¶o {dÚm{W©¶m| H$mo {H$gr ^r àH$ma H$m

H$moB© OTP Verification ¶m Email Ûmam Verification Zht XoZm hmoJm& Bg ~mao ‘| {H$gr ^r àH$ma H$s OmZH$mar

Ho$ {b¶o 9460443210 na ìhmQ²>gEn Ûmam ‘¡goO H$a|

¶m h‘mar do~gmBQ> www.rbse.online na {d{OQ> H$a|&







No of Pages : 4

‘mÜ¶{‘H$ narjm, 2019-20

J{UV

‘m°S>b nona 3g‘¶ … 3 4




2.


A 1-10 1

~ 11-15 2

g 16-25 3

X 26-30 6



^mJ-A

1. gyÌ EH$m{YHo$Z nyd}U H$m à¶moJ H$aVo hþE 1572 157

5# H$m ‘mZ kmV H$s{O¶o& (1)

2. gyÌ namdË¶© ¶moO¶oV² Ûmam g‘rH$aU x x2

5 35

2 1- = + H$m hb kmV H$s{OE& (1)

3. 312513 n[a‘o¶ g§»¶m Ho$ Xe‘bd àgmam| H$mo {b{IE& (1)

4. ¶{X secA 2= , Ohm± A EH$ Ý¶yZH$moU h¡, Vmo tanA H$m ‘mZ kmV H$s{OE& (1)

5. 50 ‘rQ>a D±$Mr ‘rZma Ho$ nmX go 50 3 ‘rQ>a Xÿar na pñWV {H$gr {~ÝXþ na ‘rZma H$m CÝZ¶Z H$moU {H$VZm

hmoJm& (1)

6. {H$gr {X¶o hþE AmYma Ho$ EH$ hr Amoa AÝV[aV hmoZo dmbo g‘H$moUm| Ho$ erfm] H$m {~ÝXþnW {b{I¶o& (1)

7. Xmo d¥Îm ~møV… ñne© H$aVo h¢& ¶{X XmoZm| d¥Îmm| H$s {ÌÁ¶mE± H«$‘e… 5 cm VWm 3 cm hmo§, Vmo CZHo$ Ho$ÝÐm| Ho$

~rM H$s Xÿar {b{IE& (1)

8. ~mah {Q>H$Q>m| na EH$-EH$ g§»¶m 1 go 12 VH$ {bIr JB© h¢& ¶{X CZ‘| go {H$gr EH$ {Q>H$Q> H$m ¶mÑpÀN>H$

M¶Z {H$¶m OmE Vmo Bg na {bIr hþB© g§»¶m Ho$ 2 ¶m 3 JwUO hmoZo H$s àm{¶H$Vm kmV H$s{OE& (1)




9. {H$gr g‹S>H$ na bJr ¶mVm¶mV bmBQ>m| H$mo {H$gr H$ma Ûmam nma H$aZo ‘o§ bJo g‘¶ (goH$ÊS> ‘|) H$mo t n2 1n = -

go àX{e©V {H$¶m OmE Vmo kmV H$s{OE {H$ dh H$ma Xmo H«$‘mJV g§Ho$Vm| H$mo {H$VZo g‘¶ ‘| nma H$aoJr? (1)

10. a‘oe H$mo AnZo Jm±d OmZo Ho$ {bE 10 {H$‘r. ~g go Ed§ 50 {H$‘r. aob go OmZm hmoVm h¡& ¶{X Cgo Hw$b 65

ê$n¶o {H$am¶m XoZm n‹S>m Vmo Bg g‘ñ¶m H$m ~rOJ{UVr¶ ê$n {b{IE& (1)

^mJ-~

11. gyÌ {Z{Ib‘² H$m à¶moJ H$aVo hþE 3994 97' H$m ‘mZ kmV H$s{OE& (2)

12. Xmo g§»¶mAm| H$m b.g. 78 Am¡a ‘.g. 2 h¡& ¶{X BZ g§»¶mAm| ‘| go nhbr g§»¶m x hmo, Vmo Xÿgar g§»¶m ³¶m

hmoJr? (2)

13. EH$ AY©d¥ÎmmH$ma ßbm°Q> H$s {ÌÁ¶m 21 ‘rQ>a h¡& BgH$m joÌ’$b VWm n[a‘mn kmV H$s{OE& (2)

14. ¶{X KZm^ H$s bå~mB© 12 ‘rQ>a, Mm¡‹S>mB© 9 ‘rQ>a VWm D±$MmB© 8 ‘rQ>a h¡, Vmo KZm^ Ho$ {dH$U© H$s bå~mB© kmV

H$s{OE& (2)

15. EH$ ‘moQ>a H$ma, A ñWmZ go B ñWmZ VH$ 175 {H$‘r. Xÿar 70 {H$‘r/KÊQ>m g‘mZ J{V go g^r 10 hao

¶mVm¶mV {g½Zbm| H$mo nma H$aVr h¡& ^mar ¶mVm¶mV Ho$ H$maU ¶h àW‘ {g½Zb na EH$ {‘ZQ>, Xygao {g½Zb

na 3 {‘ZQ>, Vrgao {g½Zb na 5 {‘ZQ> Ed§ Bgr àH$ma Xgd| {g½Zb na 19 {‘ZQ> ê$H$Vr h¡& ñWmZ B VH$

nhþ±MZo ‘| Bgo Hw$b {H$VZm g‘¶ bJoJm? Cn¶©w³V J{UVr¶ {d{Y go hb H$s{OE& (2)

^mJ-g

16. ¶{X {ÛKmV ~hþnX f x x x k82= - +^ h Ho$ eyÝ¶H$m| Ho$ dJm] H$m ¶moJ 40 hmo Vmo k H$m ‘mZ kmV H$s{OE& (3)

17. EH$ A.P. ‘| 50 nX h¢, {OgH$m Vrgam nX 12 h¡ Am¡a ApÝV‘ nX 106 h¡& BgH$m 29dm± nX kmV H$s{OE&

(3)

18. {H$gr ñVå^ H$s MmoQ>r H$m CÝZ¶Z H$moU g‘Vb na pñWV EH$ {~ÝXþ go 15c h¡¡& ñVå^ H$s Amoa 100 ‘rQ>a

MbZo na CÝZ¶Z H$moU 30c hmo OmVm h¡ Vmo ñVå^ H$s D±$MmB© kmV H$s{OE&

(Ohm± tan15 2 3c = - h¡&) (3)

19. {gÕ H$s{O¶o {H$ {Ì^wO H$s Xmo ‘mpÜ¶H$mAm| H$m ¶moJ Vrgar ‘mpÜ¶H$m go A{YH$ hmoVm h¡& (3)

20. AmH¥${V ‘| QA VWm ,PB AB na bå~ h¡ ¶{X AB 16= go‘r. OQ 5 13= go‘r Am¡a OP 3 13=

go‘r. h¡ Vmo AO Ed§ BO Ho$ ‘mZ kmV H$s{OE& (3)

21. MH«$s¶ MVw^w©O H$m gå‘wI H$moU kmV H$s{OE ¶{X Cg‘| go EH$ H$moU



1. Xÿgao H$m 72 hmo

2. Xÿgao H$m 411 hmo& (3)

22. 6 go‘r. ì¶mg H$m EH$ d¥Îm ~ZmBE& EH$ q~Xþ Q A§{H$V H$s{OE Omo {H$ BgHo$ Ho$ÝÐ go 8 go‘r. Xÿa h¡& ñne©

aoImAm| QA Am¡a QB H$s aMZm H$s{OE& CZH$s bå~mB© ‘m{nE& (3)

23. EH$ d¥ÎmmH$ma Kmg Ho$ ‘¡XmZ H$s {ÌÁ¶m 35 ‘rQ>a h¡& BgHo$ Mmam| Amoa 7 ‘rQ>a Mm¡‹S>m ‘mJ© ~Zm hþAm h¡& ‘mJ© H$m

joÌ’$b kmV H$s{OE& (3)

24. EH$ R>mog ~obZ H$m gånyU© n¥îR>r¶ joÌ’$b 462 dJ© go‘r. h¡& BgH$m dH«$ n¥îR>r¶ joÌ’$b, gånyU© n¥îR>r¶ joÌ’$b

H$m EH$-{VhmB© h¡& ~obZ H$m Am¶VZ kmV H$s{OE& (3)

25. EH$ H$jm ‘| 18 b‹S>{H$¶m± Am¡a 16 b‹S>Ho$ h¢& H$jm AÜ¶mnH$ H$mo H$jm Ho$ ‘m°ZrQ>a Ho$ {b¶o BZ‘o§ go EH$ H$m

M¶Z H$aZm h¡& dh àË¶oH$ H$m Zm‘ EH$ H$mS>© na {bIH$a BÝh| EH$ Q>moH$ar ‘| aIVr h¡ Am¡a {‘bm XoVr h¡& EH$

~ÀMo go Q>moH$ar go EH$ H$mS>© CR>mZo Ho$ {b¶o H$hm OmVm h¡& BgH$s ³¶m àm{¶H$Vm h¡ {H$ H$mS>© na…

1. EH$ b‹S>H$s H$m Zm‘ h¡?

2. EH$ b‹S>Ho$ H$m Zm‘ h¡?

3. H$jm Ho$ gd©loîR> N>mÌ H$m Zm‘ h¡?

4. {ed Hw$‘ma H$m Zm‘ Zht h¡, Omo Bg ñHy$b Ho$ àYmZmMm¶© H$m ~oQ>m h¡? (3)

^mJ-X

26. {ZåZ a¡{IH$ g‘rH$aU ¶wJ‘ H$mo AmboIr¶ {d{Y Ûmam hb H$s{OE-

x y2 + 6=

x y2 - 2=AV… BgH$s ghm¶Vm go gå~ÝY x y p2 3+ = ‘o p H$m ‘mZ kmV H$s{OE& (6)

27. {gÕ H$s{OE {H$-

1. tan sin sin1 1 1 12q q q+ + - =^ ^ ^h h h

2. cos sin sin1 24 4 2q q q- = - (3+3=6)

AWdm

27. 1. {gÕ H$s{OE {H$- cot

tan tan1

12

22

aa a

-- =

2. ¶{X cos sina b mq q+ = VWm sin cosa b nq q- = Vmo {gÕ H$s{OE…

m n a b2 2 2 2+ = + (3+3=6)

28. 1. {~ÝXþAm| (6,8) Am¡a (2,4) H$mo {‘bmZo dmbr aoImIÊS> Ho$ ‘Ü¶ {~ÝXþ go {~ÝXþ (1,2) H$s Xÿar kmV

H$s{OE& (3)

2. {gÕ H$s{OE {H$ ‘yb {~ÝXy O {~ÝXþAm| ,A 1 3-^ h Am¡a ,B 3 9-^ h H$mo {‘bmZo dmbo aoImIÊS> H$mo :1 3

Ho$ AZwnmV ‘| AÝV…{d^m{OV H$aVm h¡& ~mø {d^mOZ H$aZo dmbo {~ÝXþAm| Ho$ {ZX}em§H$ kmV H$s{OE& (3)




29. {gÕ H$amo {H$ {H$gr {Ì^wO H$s Xmo ^wOmAm| na ~Zo dJm] H$m ¶moJ CgH$s Vrgar ^wOm na ~Zo dJ© Ho$ ~am~a hmo

Vmo dh {Ì^wO g‘H$moU {Ì^wO hmoVm h¡& (6)

AWdm

29. AmH¥${V ‘|, ABCD EH$ MVw^w©O h¡, {Og‘| AD BC= Am¡a ADC BCD+ += h¡& {gÕ H$s{OE

ABCD EH$ MH«$s¶ MVw^w©O h¡& (6)

30. {ZåZ gmaUr {H$gr AñnVmb ‘o§ ^Vu amo{J¶m| H$s Am¶w Xem©Vr h¡-

Am¶w (dfm] ‘|) 5-15 15-25 25-35 35-45 45-55 55-65

n[admam|| H$s g§»¶m 6 11 21 23 14 5

Cnamo³V Am±H$‹S>m| go ~hþbH$ VWm ‘mÜ¶ kmV H$s{OE& XmoZm| Ho$ÝÐr¶ ‘mnm| H$s VwbZm H$s{OE Am¡a BZH$s ì¶m»¶m

H$s{OE& (6)

*******

AJbo gmb go H$moB© nmg~wH$ ¶m goånb nona IarXZo H$s Oê$aV Zht

gÌ 2020-21 go amOñWmZ ‘| NCERT nmR²>¶H«$‘ bmJy
















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A 1-10 1

~ 11-15 2

g 16-25 3

X 26-30 6



^mJ-A

1. gyÌ {Z{Ib‘² H$m à¶moJ H$aVo hþE 54 56# H$m ‘mZ kmV H$s{OE& (1)

2. g‘rH$aU xx

xx

2 12 4

2 42 1

++ = +

+ H$mo gab H$s{OE& (1)

3. 156 g§»¶m H$mo A^mÁ¶ JwUZI§S> Ho$ JwUZ’$b Ho$ ê$n ‘| ì¶³V H$s{OE& (1)

4. EH$ nV§J 20 ‘r. H$s D±$MmB© na C‹S> ahr h¡ VWm BgH$s S>moa ^y{‘ Ho$ gmW 30c H$m H$moU ~Zm ahr h¡& S>moa H$s

bå~mB© kmV H$s{OE& (1)

5. tan cos60 3 302 2c c+ H$m ‘mZ kmV H$s{OE& (1)

6. Xmo g‘mÝVa gab aoImAm| go g‘mZ Xÿar na ahZo dmbo {~ÝXþAm| H$m {~ÝXþnW {b{I¶o& (1)

7. {MÌ ‘| ¶{X TP Am¡a TQ Ho$ÝÐ O dmbo d¥Îm na Xmo ñne© aoImE± Bg àH$ma h¢ {H$ POQ 130c+ = Vmo

PTQ+ kmV H$s{OE& (1)




8. EH$ {g³Ho$ H$mo EH$ ~ma CN>mbm OmVm h¡& nQ> AmZo H$s àm{¶H$Vm kmV H$s{OE& (1)

9. ¶{X EH$ Q>¡³gr H$m {H$am¶m àW‘ {H$bmo‘rQ>a Ho$ {bE 12 ê$n¶o h¡ Am¡a BgHo$ ~mX AmZo dmbo à{V {H$bmo‘rQ>a

Ho$ {b¶o ¶h {H$am¶m 9 ê$n¶o hmo Vmo 15 {H$‘r. MbZo Ho$ {bE AmnH$mo ³¶m {H$am¶m MwH$mZm n‹‹S>oJm? (1)

10. Mm¡amho Ho$ {H$Zmao EH$ Iåô Ho$ emrf© na bJo CCTV H¡$‘ao go g‹S>H$ na {H$gr H$ma H$m CÝZ¶Z H$moU 45c h¡

Ed§ Iåô Ho$ AmYma go H$ma H$s Xÿar 10 ‘rQ>a h¡ Vmo Iåô H$s D±$MmB© kmV H$s{OE& (1)

^mJ-~

11. ÛÝÛ ¶moJ {d{Y Ûmam g§»¶m 2456 H$m dJ© kmV H$s{OE& (2)

12. {gÕ H$s{OE {H$ 3 2 5+ EH$ n[a‘o¶ g§»¶m h¡& (2)

13. 100 M³H$a ‘| EH$ ñHy$Q>a H$m n{h¶m 88 ‘rQ>a H$s Xÿar V¶ H$aVm h¡& Bg n{h¶o H$s {ÌÁ¶m kmV H$s{OE& (2)

14. EH$ KZm^ H$s ‘mn 15 go‘r. # 12 go‘r. # 6 go‘r. h¡& Bg KZm^ H$mo {nKbmH$a 3 go‘r. dmbo {H$VZo KZ

~Zm¶o Om gH$Vo h¢& (2)

15. EH$ ‘moQ>a H$ma A ñWmZ go B ñWmZ VH$ 175 {H$‘r. Xÿar 70 {H$‘r./KÊQ>m g‘mZ J{V go g^r 10 hao

¶mVm¶mV {g½Zbm| H$mo nma H$aVr h¡& ^mar ¶mVm¶mV Ho$ H$maU ¶h àW‘ {g½Zb na EH$ {‘ZQ>, Xygao {g½Zb

na 3 {‘ZQ>, Vrgao {g½Zb na 5 {‘ZQ> Ed§ Bgr àH$ma Xgd| {g½Zb na 19 {‘ZQ> ê$H$Vr h¡& ñWmZ B VH$

nhþ±MZo ‘| Bgo Hw$b {H$VZm g‘¶ bJoJm? Cn¶w³V J{UVr¶ {d{Y go hb H$s{OE& (2)

^mJ-g

16. ~hþnX f x x x x3 3 52 3= - - +^ h H$mo ~hþnX g x x x1 2= - -^ h Ûmam {d^mOZ EëJmo[aÏ‘ {d{Y go {d^m{OV

H$s{OE VWm ^mJ’$b Am¡a eof’$b kmV H$s{OE& (3)

17. ¶{X EH$ g‘mÝVa loUr H$m V¥Vr¶ nX 7 h¡ VWm gmVdm± nX, V¥Vr¶ nX Ho$ VrZ JwZm go Xmo A{YH$ h¡, Vmo CgHo$

àW‘ 20 nXm| H$m ¶moJ’$b kmV H$s{OE& (3)

18. g‘wÐ Vb go 60 ‘rQ>a D±$Mo bmBQ> hmD$g Ho$ {eIa go XoIZo na Xmo g‘wÐr OhmOm| Ho$ AdZ‘Z H$moU 30c d

45c h¢& ¶{X bmBQ> hmD$g Ho$ EH$ hr Amoa EH$ OhmO Xÿgao OhmO Ho$ R>rH$ nrN>o hmo, Vmo OhmOm| Ho$ ‘Ü¶ H$s

Xÿar kmV H$s{OE& (3)

19. EH$ ABCT ‘| ‘mpÜ¶H$mE± ,AD BE Am¡a CF {~ÝXþ G na à{VÀN>oX H$aVr h¢& {gÕ H$s{O¶o {H$- (3)

AD BE CF AB BC CA4 3>+ + + +^ ^h h



20. AmH¥${V ‘o§ CD Am¡a RS H«$‘e… ABCT Am¡a PQRT H$s ‘mpÜ¶H$mE± h¢& ¶{X ABC PQRT T+ hm|

Vmo {gÕ H$s{OE {H$

1. ADC PSRT T+

2. RSCD

PQAB= (3)

21. ¶{X MH«$s¶ MVw^w©O ABCD ‘o§ | |AD BC hm|, Vmo {gÕ H$s{OE {H$ A D+ += (3)

22. EH$ {Ì^wO ABC H$s aMZm H$s{OE {Og‘| AB 5= go‘r, BC 6= go‘r Am¡a ABC 60c+ = h¡& EH$

Xÿgam {Ì^wO ~ZmBE {OgH$s ^wOmE± ABCT H$s g§JV ^wOmAm| H$s 75 hmo& (3)

23. {ÌÁ¶m 21 go‘r. dmbo d¥Îm H$m EH$ Mmn Ho$ÝÐ na 60c H$m H$moU A§V[aV H$aVm h¡& kmV H$s{OE& (3)

1. Mmn H$s bå~mB©

2. Mmn Ûmam ~ZmE JE {ÌÁ¶I§S> H$m joÌ’$b

3. g§JV Ordm Ûmam ~ZmE JE d¥ÎmI§S> H$m joÌ’$b

24. EH$ ~obZ H$s D±$MmB© d {ÌÁ¶m H«$‘e… 7.5 go‘r. Am¡a 3.5 go‘r. h¡& BgHo$ gånyU© n¥îR> Ho$ joÌ’$b Am¡a dH«$

n¥îR> Ho$ joÌ’$b ‘| AZwnmV kmV H$s{OE& (3)

25. 52 Vme Ho$ nÎmm| H$s JS²>S>r go EH$ nÎmm ¶mÑÀN>¶m {ZH$mbm OmVm h¡& BgHo$ (1) B³H$m (2) hþ³‘ H$m ‘2’

(3) H$mbo a§J H$m ‘10’ hmoZo H$s n«m{¶H$Vm kmV H$s{OE& (3)

^mJ-X

26. a¡{IH$ g‘rH$aUm| x y 1 0- + = Am¡a x y3 2 12 0+ - = H$m J«m’$ It{M¶o& x-Aj Am¡a BZ aoImAm| go

~Zo {Ì^wO Ho$ erfm] Ho$ {ZX}em§H$ kmV H$s{O¶o Am¡a {Ì^wOmH$ma nQ>b H$mo N>m¶m§{H$V H$s{OE& (6)

27. {gÕ H$s{O¶o {H$- (3+3)

1. sec tan sin1q q q+ -^ ^h h cosq =

2. sin cos

cos sin1

1 2

q qq q+

+ -^ h

cotq =

AWdm

27. 1. {gÕ H$s{OE {H$ -

cottan

tancot tan cot1 1 1q

qq

q q q- + - = + + (3)

2. ¶{X tan sin mq q+ = VWm tan sin nq q- = Vmo {gÕ H$s{OE… m n mn42 2- = (3)

28. 1. {gÕ H$s{OE {H$ g‘H$moU {Ì^wO AOB ‘| H$U© H$m ‘Ü¶ {~ÝXþ C {Ì^wO Ho$ erfm] ,O A Am¡a B go




~am~a Xÿar na pñWV h¡& (3)

2. {~ÝXþAm| (15,5) Am¡a (9,20) H$mo {‘bmZo dmbo aoImIÊS> H$mo {~ÝXþ (11,15) {H$g AZwnmV ‘§o

{d^m{OV H$aVm h¡? (3)

29. {gÕ H$amo {H$ g‘H$moU {Ì^wO ‘|, H$U© na ~Zm H$moU eof ^wOmAm| na ~Zo dJm] Ho$ ¶moJ Ho$ ~am~a hmoVm h¡& (6)

AWdm

29. {gÕ H$s{OE {H$ d¥Îm H$s Xmo OrdmAm| ‘| go ~‹S>r Ordm Ho$ÝÐ Ho$ {ZH$Q> hmoVr h¡& (6)

30. {ZåZ{b{IV gmaUr 35 ZJam| H$s gmjaVm Xa (à{VeV ‘|) Xem©Vr h¡& ‘mÜ¶ gmjaVm Xa kmV H$s{OE& (6)

gmjaVm Xa (% ‘|) 45-55 55-65 65-75 75-85 85-90

ZJam| H$s g§»¶m 3 10 11 8 3

*******


















No of Pages : 4

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A 1-10 1

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g 16-25 3

X 26-30 6



^mJ-A

1. gyÌ EH$m{YHo$Z nyd}U H$m à¶moJ H$aVo hþE 1671 167

6# H$m ‘mZ kmV H$s{OE& (1)

2. gyÌ namdË¶© ¶moO¶oV² Ûmam x x x x5 1 3 2+ + = + +^ ^ ^ ^h h h h H$m hb kmV H$s{OE& (1)

3. {~Zm b§~r {d^mOZ à{H«$¶m {H$E ~VmBE {H$ 160015 n[a‘o¶ g§»¶m Ho$ Xe‘bd n«gma gm§V h¡ ¶m Agm§V AmdVu

h¢? (1)

4. gab H$s{OE… sec cosec

1 12 2q q

+ (1)

5. EH$ gr‹T>r, {OgH$s bå~mB© 45 ‘rQ>a h¡, {H$gr ‘rZma Ho$ erf© H$mo ñne© H$aVr h¡ VWm j¡{VO go 60c H$m H$moU

~ZmVr h¡& ‘rZma H$s D±$MmB© hmoJr- (1)

6. {Ì^wO Ho$ A§Xa Cg {~ÝXþ H$m {~ÝXþnW kmV H$s{OE Omo {H$ {Ì^wO H$s VrZm| ̂ wOmAm| go g‘mZ Xÿar na hm|& (1)

7. EH$ {~ÝXþ go d¥Îm na ItMr JB© ñne© aoIm H$s bå~mB© kmV H$s{OE, O~{H$ {~ÝXþ H$s d¥Îm Ho$ Ho$ÝÐ go Xÿar 13

go‘r. h¡ Am¡a d¥Îm H$s {ÌÁ¶m 5 go‘r. h¡& (1)

8. AÀN>r àH$ma go ’|$Q>r JB© 52 nÎmm| H$s EH$ JS²>S>r ‘| go EH$ nÎmm {ZH$mbm OmVm h¡& Bg nÎmo Ho$ ~mXemh hmoZo H$s

àm{¶H$Vm kmV H$s{OE& (1)




9. {H$gr grYr g‹S>H$ na nhbm, Xÿgam, Vrgam ¶mVm¶mV {g½Zb H«$‘e… 3 {H$‘r., 5 {H$‘r., 7 {H$‘r., H$s Xÿar

na bJm h¡ Vmo 10d| {g½Zb H$s Xÿar kmV H$s{O¶o& (1)

10. EH$ ~g ‘| ~g ñQ>¡ÊS> go ñWmZ A Ho$ {bE 3 {Q>H$Q> Am¡a ñWmZ B Ho$ {bE 4 {Q>H$Q> <67 ‘| {‘bVo h¢, O~{H$

ñWmZ A Ho$ {bE 3 {Q>H$Q> Am¡a ñWmZ B Ho$ {bE 5 {Q>H$Q> <77 ‘| {‘bVo h¢ Vmo ~g ñQ>¡ÊS> go B VH$ H$m

{H$am¶m kmV H$s{OE& (1)

^mJ-~

11. gyÌ ÜdOm§H$ H$m à¶moJ H$aVo hþE 592837 119' H$m ‘mZ kmV H$s{OE& (2)

12. Xmo g§»¶mAm| H$m b.g. 39 Am¡a ‘.g. 1 h¡& ¶{X BZ g§»¶mAm| H$m ¶moJ’$b 16 hmo, Vmo ~‹S>r g§»¶m ~Vmd|& (2)

13. EH$ d¥ÎmmH$ma ßboQ> H$m joÌ’$b 154 dJ© go‘r. h¡& BgH$s n[a{Y kmV H$s{OE& (2)

14. EH$ KZ H$m Am¶VZ 512 KZ ‘rQ>a h¡, CgH$s ^wOm kmV H$s{OE& (2)

15. Cnamo³V XÊS> AmboI {H$gr eha ‘| {dJV dfm] ‘| ¶mVm¶mV XþK©Q>Zm ‘| ‘aZo dmbo ì¶p³V¶m| H$s g§»¶m H$mo ì¶³V

H$aVm h¡& (2)

1. df© 2001-2013 ‘§o ‘aZo dmbmo§ H$s d¥{Õ AWdm õmg Xa&

2. df© 2012-2014 ‘| ‘aZo dmbm| H$s d¥{Õ AWdm õmg Xa&

^mJ-g

16. {d^mOZ EoëJmo[aÏ‘ H$m à¶moJ H$a ~hþnX p x x x x3 4 54 2= - + +^ h H$mo g x x x12= + -^ h go ^mJ XoZo

na àmá ^mJ’$b Ed§ eof’$b kmV H$s{OE& (3)

17. ¶{X EH$ g‘mÝVa loUr H$m Xÿgam nX 2 VWm gmVdm± nX 22 h¡, Vmo CgHo$ 30 nXm| H$m ¶moJ’$b kmV

H$s{OE& (3)

18. 7 ‘rQ>a D±$Mo ^dZ Ho$ [eIa go EH$ Q>m°da Ho$ {eIa H$m CÞ¶Z H$moU 60c h¡ Am¡a BgHo$ nmX H$m AdZ‘Z H$moU

45c h¡& Q>m°da H$s D±$MmB© kmV H$s{OE& (3)

19. ABCT ‘| ‘mpÜ¶H$mE± ,AD BE Am¡a CF {~ÝXþ G go JwOaVr h¢& (3)

1. ¶{X GF 4= go‘r. hmo Vmo GC H$m ‘mZ kmV H$s{OE&

2. ¶{X .AD 7 5= go‘r. hmo Vmo GD H$m ‘mZ kmV H$s{OE&

20. ABCT ‘| B 90c+ = hmo Ed§ BD H$U© AC na bå~ hmo Vmo {gÕ H$s{OE& ADB BDCT T+ (3)



21. {gÕ H$s{O¶o {H$ Xmo g‘mÝVa OrdmAm| Ho$ ‘Ü¶ {~ÝXþAmo§ H$mo {‘bmZo dmbo aoImIÊS> d¥Îm Ho$ Ho$ÝÐ go hmoH$a OmVm

h¡& (3)

22. EH$ {Ì^wO ABC H$s aMZm H$s{OE {Og‘§o .BC 6 3= go‘r., .AB 5 2= go‘r. Am¡a ABC 60c+ = h¡&

EH$ Xÿgam {Ì^wO ~ZmBE {OgH$s ^wOmE± ABCT H$s g§JV ^wOmAm| H$s 34 JwZr hm|& (3)

23. 3.5 go‘r. {ÌÁ¶m Ho$ d¥Îm ‘| EH$ Ordm Ûmam Ho$ÝÐ na AÝV[aV H$moU 90c h¡& Bg Ordm Ûmam ~Zo bKw d¥ÎmIÊS>

H$m joÌ’$b kmV H$s{OE& 722p =b l (3)

24. 10 go‘r. {ÌÁ¶m Ho$ YmVw H$o Jmobo go g‘mZ {ÌÁ¶m Ho$ 8 Jmobo ~Zm¶o OmVo h¢& Bg àH$ma ~Zo àË¶oH$ Jmobo H$m

n¥îR>r¶ joÌ’$b kmV H$s{OE& (3)

25. {Q>H$Q>m| na 10 go 60 VH$ H$s g»¶mE± A§{H$V h¢& EH$ {Q>H$Q> ¶mÑÀN>¶m {ZH$mbm OmVm h¡& n«m{¶H$Vm kmV H$s{OE

{H$ {Q>H$Q> na- (3)

1. 22 go 38 VH$ H$s g§»¶m h¡&

2. EH$ A^mÁ¶ g§»¶m h¡&

3. 3 go {d^mÁ¶ g§»¶m h¡&

^mJ-X

26. {ZåZ g‘rH$aUm| H$m AmboI {d{Y go hb kmV H$s{OE- (6)

x y4 6+ 18=

x y2 3+ 9=

27. {gÕ H$s{O¶o& (3+3)

1. sin sin11

11

q q+ + - sec2 2q =

2. cottanAA

11

2

2

++

c m cottan tanAA A1

1 22= -

- =b l

AWdm

27. 1. {gÕ H$s{OE {H$- (3+3)

sin tan cos cot cosec sec1 1q q q q q q+ + + = +^ ^h h

2. ¶{X ,A B Am¡a C {Ì^wO ABC Ho$ AÝV…H$moU hm|, Vmo {XImBE {H$-

sinB C

2+^ h cosA2=

28. 1. Cg {Ì^wO H$s ‘mpÜ¶H$mAm| H$s bå~mB¶m± kmV H$s{OE, {OgHo$ erf© ,1 1-^ h, (0,4) VWm ,5 3-^ h h¢&

(3)

2. ¶{X {~ÝXþ ,P 3 5^ h {~ÝXþAm| ,A 2 3-^ h Am¡a B H$mo {‘bmZo dmbo aoImIÊS> H$mo 4…7 Ho$ AZwnmV ‘| AÝV…

{d^m{OV H$aVm h¡, Vmo B Ho$ {ZX}em§H$ kmV H$s{OE& (3)

29. {gÕ H$amo {H$ ¶{X Xmo {Ì^wOm| ‘| H$moB© g§JV Xmo ^wOmE± nañna g‘mZwnmVr hm| VWm CZHo$ ‘Ü¶ Ho$ H$moU ~am~a

hm| Vmo XmoZm| {Ì^wO g‘ê$n hmoVo h¢& (6)

AWdm




29. ¶{X Xmo d¥Îm, EH$-Xÿgao H$mo Xmo {~ÝXþAm| na à{VÀN>o{XV H$aVo hm|, Vmo {gÕ H$s{OE {H$ CZHo$ Ho$ÝÐm| H$mo {‘bmZo

dmbr aoIm CZH$s C^¶{ZîR> Ordm H$m bå~ g‘{Û^mOH$ hmoVr h¡& (6)

30. ¶{X ZrMo {X¶o J¶o ~§Q>Z H$m ‘mÜ¶ 50 hmo Vmo x d y Ho$ ‘mZ kmV H$a|- (6)

dJ©-AÝVamb 0-20 20-40 40-60 60-80 80-100 ¶moJ

~maå~maVm 17 x 32 y 19 120

*******


















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g 16-25 3

X 26-30 6



^mJ-A

1. gyÌ {Z{Ib‘² H$m à¶moJ H$aVo hþE 108 112# H$m ‘mZ kmV H$s{OE& (1)

2. gyÌ eyÝ¶ gmå¶ g‘wÀM¶| Ûmam g‘rH$aU xx

5 73 2

++ x

x3 1

1= -+ H$m hb kmV H$s{OE& (1)

3. 817 n[a‘o¶ g§»¶m Ho$ Xe‘bd àgmam| H$mo {b{IE& (1)

4. ¶{X cotA24 7= hmo, Vmo sinA H$m ‘mZ kmV H$s{OE& (1)

5. AB EH$ CÜdm©Ya Xrdma h¡, {OgH$m B ^mJ ^y{‘ Ho$ gånH©$ ‘| h¡& AC gr‹T>r O‘rZ go C {~ÝXþ na {Q>H$s h¡&

°ACB 45+ = Am¡a BC 5= ‘rQ>a, Vmo gr‹T>r H$s bå~mB© h¡- (1)

6. g‘mZ AmYma d g‘mZ joÌ’$b dmbo {Ì^wOm| Ho$ erf© H$m {~ÝXþnW {b{I¶o& (1)

7. ¶{X Xmo d¥Îm {OZH$s {ÌÁ¶mE± H«$‘e… 9 go‘r. VWm 4 go‘r. h¡ Am¡a do EH$-Xÿgao H$mo A§V…ñne© H$aVo h¢ Vmo CZH$o

Ho$ÝÐm| Ho$ ~rM H$s Xÿar kmV H$amo& (1)

8. EH$ nmgo H$mo EH$ ~ma CN>mbm OmVm h¡& 5 go N>moQ>r ¶m CgHo$ ~am~a g§»¶m àmá hmoZo H$s àm{¶H$Vm ³¶m h¡? (1)

9. ¶{X Amn nhbr, Xÿgar, Vrgar d Mm¡Wr {g½Zb bmBQ> H$mo H«$‘e… 3, 9, 15, 21 goH$ÊS> ‘| nma H$aVo hm| Vmo




69 goH$ÊS> ‘o§ H$m¡Z-gr {g½Zb bmBQ> nma H$a MwHo$ hm|Jo? (1)

10. EH$ Mm¡amho na ‘Ü¶ ‘| EH$ AB D$Üdm©Ya nmob J‹S>m hþAm h¡ Am¡a Cg na H¡$‘am bJm h¡, {OgH$m B ^mJ ^y{‘

Ho$ gånH©$ ‘| h¡& H¡$‘ao H$m ’$moH$g {~ÝXÿ ^y{‘ na {~ÝXw C na h¡ Omo {H$ B go 4 ‘rQ>a Xÿar na h¡, Vmo H¡$‘ao d

{~ÝXþ C Ho$ ~rM j¡{VO Xÿar kmV H$amo {Og‘§o {X¶m h¡ ACB 60c+ =^ h (1)

^mJ-~

11. ÛÝÛ ¶moJ {d{Y Ûmam g§»¶m 4225 H$m dJ©‘yb kmV H$s{OE& (2)

12. {gÕ H$s{OE {H$ 7 5 EH$ An[a‘o¶ g§»¶m h¡& (2)

13. Cg d¥Îm H$s {ÌÁ¶m kmV H$s{OE {OgH$m joÌ’$b 616 dJ© go‘r h¡& (2)

14. EH$ ~obZ H$m ì¶mg 14 go‘r VWm D±$MmB© 15 go‘r h¡& ~obZ H$m gånyU© n¥îR>r¶ joÌ’$b kmV H$s{OE& (2)

15. {MÌ ‘§o {X¶m J¶m d¥Îm MmQ>© ‘B©-OyZ 2013 Ho$ Xm¡amZ dmhZm| H$m Ho$ÝÐr¶ gaH$ma Ûmam Mbm¶o J¶o A{^¶mZ ‘| H$Q>o

hþE MmbmZm| H$s g§»¶m H$mo {S>J«r c^ h ‘| Xem©Vm h¡& Bgo Ü¶mZnyd©H$ n{‹T>¶o d {ZåZ àíZm§o Ho$ CÎma Xr{OE- (2)

1. ¶{X Hw$b dmhZ 72 bmI h¢ Vmo ‘Ü¶ àXoe ‘| H$Q>o MmbmZm| H$s g§»¶m amOñWmZ Ho$ H$Q>o MmbmZm| H$s

g§»¶m go {H$VZm A{YH$ h¡?

2. h[a¶mUm ‘| H$Q>o MmbmZm| H$s g§»¶m kmV H$s{OE&

^mJ-g

16. {ÛKmV g‘rH$aU x x4 4 3 3 02 + + = H$mo nyU© dJ© ~ZmH$a hb H$s{OE& (3)

17. 0 Am¡a 50 Ho$ ~rM H$s {df‘ g§»¶mAm| H$m ¶moJ kmV H$s{OE& (3)

18. EH$ nd©V Ho$ {eIa go nyd© H$s Amoa pñWV Xmo {~ÝXþAm| go {eIa Ho$ AdZ‘Z H$moU 30c d 45c h¢& ¶{X {~ÝXþAm|

Ho$ ~rM H$s Xÿar 1 {H$‘r. hmo Vmo nd©V H$s D±$MmB© kmV H$s{OE& (3)

19. ABCT g‘{Û~mhþ {Ì^wO h¡ {Og‘| AB AC= , BC H$m ‘Ü¶ {~ÝXþ D h¡& {gÕ H$s{OE {H$ n[aHo$ÝÐ, A§V…

Ho$ÝÐ, bå~ Ho$ÝX VWm Ho$ÝÐH$ g^r AD aoIm na pñWV h¢& (3)

20. {H$gr ABCT Ho$ erf© A go ^wOm BC na S>mbm J¶m bå~ BC H$mo {~ÝXþ D na Bg àH$ma à{VÀN>o{XV

H$aVm h¡ {H$ DB CD3= h¡& {gÕ H$s{OE {H$- AB2 2 AC BC2 2 2= + h¡& (3)



21. AB Am¡a CD d¥Îm H$s Xmo OrdmE± Bg àH$ma h¢ {H$ AB 10= go‘r., CD 24= go‘r. Am¡a | |AB CD h¡&

AB Ed§ CD Ho$ ~rM H$s Xÿar 17 go‘r. h¡& d¥V H$s {ÌÁ¶m kmV H$s{OE& (3)

22. 3 go‘r. {ÌÁ¶m H$m EH$ d¥Îm It{ME& BgH$o ~‹T>mE hþE EH$ ì¶mg Ho$ XmoZm| Amoa Xmo q~Xþ P Am¡a Q br{OE Omo

H|$Ð go H«$‘e… 8 go‘r. Am¡a 5 go‘r. H$s Xÿar na hm|& {~ÝXþAm| P Am¡a Q go d¥Îm na ñne© aoImE± It{ME& aMZm

Ho$ MaU {b{IE (3)

23. EH$ K‹S>r Ho$ KÊQ>o H$s gwB© 5 go‘r. bå~r h¡& 70 {‘ZQ> ‘§o Bg gwB© Ûmam ~ZmE JE {ÌÁ¶IÊS> H$m joÌ’$b kmV

H$s{OE& (3)

24. EH$ bå~ d¥Îmr¶ ~obZmH$ma S´>‘ Ho$ AmYma Am¡a {eIa XmoZm| AÕ©d¥ÎmmH$ma h¢& ~obZmH$ma ^mJ H$m ì¶mg 14 go‘r.

Am¡a Hw$b D±$MmB© 30 go‘r. h¡& S´>‘ H$m gånyU© n¥îR> kmV H$s{OE& (3)

25. EH$ gÝXÿH$ ‘| 90 {S>ñH$ h¢, {OZ na 1 go 90 VH$ H$s g§»¶mE± {bIr h¢& EH$ {S>ñH$ ¶mÑÀN>¶m {ZH$mbr OmVr

h¡& àm{¶H$Vm kmV H$s{OE {H$ Bg na

1. Xmo A§H$m| H$s g§»¶m h¡&

2. 5 go {d^m{OV EH$ g§»¶m h¡& (3)

^mJ-X

26. AmboIr¶ {d[Y Ûmam {ZåZ g‘rH$aU {ZH$m¶ H$m hb kmV H$s{OE- (6)

x y2 4+ 10=

x y3 6+ 12=

27. {gÕ H$s{OE- (3+3=6)

(1) sin cossin cos 12 2

4 4

q qq q

-- =

(2) sin cossin cos

sin cossin cos

cos cos1 22

2 12

2 2q qq q

q qq q

q q-+ + +

- =-

=-

AWdm

27. {gÕ H$s{O¶o (3+3=6)




(1) cottan

tancot sec cosec1 1 1q

qq

q q q- + - = +

(2) cot coseccot cosec

sincos

A AA A

AA

11 1

- ++ - = +

28. 1. {gÕ H$s{OE {H$ {~ÝXþAm| (5,7) Am¡a (3,9) H$mo {‘bmZo dmbo aoImIÊS> H$m ‘Ü¶ {~ÝXþ dhr h¡ Omo

{~ÝXþAm| (8,6) VWm (0,10) H$mo {‘bmZo dmbo aoImIÊS> H$m ‘Ü¶ {~ÝXþ h¡& (2)

2. {~ÝXþAm| (11,9) Am¡a (1,2) H$mo {‘bmZo dmbr aoIm H$mo g‘{Ì^m{OV H$aZo dmbo {~ÝXþAm| Ho$ {ZX}em§H$

kmV H$s{OE& (4)

29. {gÕ H$amo {H$ ¶{X Xmo {Ì^wOm| ‘| g§JV ^wOmAm| H$m AZwnmV ~am~a hm|, Vmo XmoZmo§ {Ì^wO nañna g‘ê$n hmoVo h¢&

AWdm

29. {gÕ H$s{OE {H$ d¥Îm Ho$ AÝXa {H$gr {~ÝXþ go hmoH$a OmZo dmbr g^r OrdmAm| ‘| go dh Ordm g~go N>moQ>r hmoVr

h¡, Omo Cg {~ÝXþ go hmoH$a OmZo dmbo ì¶mg na bå~ hmoVr h¡& (6)

30. EH$ OrdZ ~r‘m EO|Q> 100 nm°{bgr YmaH$m| H$s Am¶w Ho$ ~§Q>Z Ho$ {ZåZ{b{IV Am±H$‹S>o kmV H$aVm h¡& ‘mÜ¶H$

Am¶w n[aH${bV H$s{OE, ¶{X nm°{bgr Ho$db CÝht ì¶p³V¶m| H$mo Xr OmVr h¡, {OZH$s Am¶w 18 df© ¶m Cggo

A{YH$ hmo naÝVw 60 df© go H$‘ hmo& (6)

Am¶w dfm] ‘§o nm°{bgr YmaH$m| H$s g§»¶m

20 go H$‘ 2

25 go H$‘ 6

30 go H$‘ 24

35 go H$‘ 45

40 go H$‘ 78

45 go H$‘ 89

50 go H$‘ 92

55 go H$‘ 98

60 go H$‘ 100

*******

AJbo gmb go H$moB© nmg~wH$ ¶m goånb nona IarXZo H$s Oê$aV ZhtgÌ 2020-21 go amOñWmZ ‘| NCERT nmR²>¶H«$‘ bmJy {H$¶m Om ahm h¡& Z¶o

nmR²>¶H«$‘mZwgma g^r H$jmAm| Ho$ g^r {df¶m| H$s Q>o³ñQ> ~wH$ Ed§ g^r àH$ma H$s ghm¶H$

AÜ¶¶Z gm‘J«r O¡go- goånb nona/S>oñH$ dH©$ Am{X {dÚm[W©¶m| H$mo ‘mo~mBb na ìhmQ²>gEn Zå~a

9460443210 Ûmam Ed§ do~gmBQ> www.rbse.online na CnbãY H$adm¶r OmEJr& BgHo$

{b¶o {dÚm{W©¶m| go {H$gr ^r àH$ma H$m H$moB© ewëH$ Zht {b¶m OmEJm& BgHo$ {b¶o {dÚm{W©¶m|

H$mo {H$gr ^r àH$ma H$m H$moB© OTP Verification ¶m Email Ûmam Verification Zht XoZm hmoJm& Bg ~mao ‘| {H$gr ^r àH$ma H$s OmZH$mar Ho$ {b¶o 9460443210 na

ìhmQ²>gEn Ûmam ‘¡goO H$a| ¶m h‘mar do~gmBQ> www.rbse.online na {d{OQ> H$a|&






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^mJ-A


5# H$m ‘mZ kmV H$s{OE& 1

2. gyÌ namdË¶© ¶moO¶oV² Ûmam g‘rH$aU x x11

12 0+ - - = H$m hb kmV H$s{OE& 1

3. 3825 g§»¶m Ho$ A^mÁ¶ JwUZIÊS>m| H$s KmVm| H$m ¶moJ’$b {b{IE& 1

4. ¶{X tan cotA B= , Vmo {gÕ H$s{OE {H$ A B 90c+ = h¡& 1

5. EH$ nmob {OVZm D±$Mm h¡ CVZr hr CgHo$ à{V{~å~ H$s bå~mB© h¡& à{V{~å~ Ho$ {gao H$m CÝZ¶Z H$moU h¡- 1

6. Xmo {~ÝXþAm| ‘| go hmoH$a JwOaZo dmbo d¥Îmm| Ho$ Ho$ÝÐm| H$m {~ÝXþnW {b{I¶o& 1

7. ¶{X ì¶mg 10 go‘r. VWm ì¶mg 8 go‘r. dmbo Xmo d¥Îm EH$-Xÿgao H$mo ~mh²¶ñne© H$aVo h¢, Vmo CZHo$ Ho$ÝÐm| Ho$

~rM H$s Xÿar kmV H$amo& 1

8. EH$ W¡bo ‘| EH$ g’o$X J|X, EH$ H$mbr J|X VWm EH$ bmb J|X EH$ hr AmH$ma H$s h¢& g{dVm {~Zm W¡bo Ho$ AÝXa

Pm±Ho$, Bg‘| go EH$ J|X {ZH$mbVr h¡& BgH$s ³¶m àm{¶H$Vm hmoJr {H$ dh bmb J|X hmoJr? 1

9. ¶mVm¶mV g§Ho$Vm| ‘| bmb ~Îmr H$s H¡$gr Á¶m{‘Vr AmH¥${V hmoVr h¡? 1




10. {H$gr ZJa ‘| Q>¡³gr H$m {H$am¶m nhbo {H$bmo‘rQ>a H$m 9 ê$n¶o, CgHo$ ~mX Ho$ {bE 6 ê$n¶o h¡& ¶{X V¶ H$s

JB© Xÿar x {H$‘r. Am¡a {H$am¶m y ê$n¶o h¡ Vmo Bgo g‘rH$aU Ho$ ê$n ‘| ì¶³V H$s{OE& 1

^mJ-~

11. ^mJ {d{Y go g§»¶m 59049 H$m dJ©‘yb kmV H$s{OE& 2

12. Xmo g§»¶mAm| H$m b.g. 42 Am¡a ‘.g. 7 h¡& ¶{X BZ g§»¶mAm| H$m AÝVa 7 hmo, Vmo N>moQ>r g§»¶m ~Vmd|& 2

13. Cg d¥Îm H$s {ÌÁ¶m kmV H$s{OE {OgH$m joÌ’$b 616 dJ© go‘r. h¡& 2

14. EH$ ~obZ H$m Am¶VZ go‘r.30 3p h¡ VWm AmYma H$m joÌ’$b go‘r.6 2p h¡& ~obZ H$s D±$MmB© kmV H$s{OE& 2

15. {X¶o J¶o nmB© MmQ>© (d¥Îm {MÌ) ‘| df© 2014 ‘| {H$gr eha ‘| g‹S>H$ ‘| g‹S>H$ XþK©Q>Zm ‘| {d{^Þ H$maUm| go ‘aZo

dmbo ì¶p³V¶m| H$s g§»¶m H$mo {S>J«r ‘| ì¶³V {H$¶m J¶m h¡& ¶{X Cg df© Hw$b 10800 ì¶p³V¶m| H$s g‹S>H$

XþK©Q>Zm ‘| ‘¥Ë¶w hþB© hmo Vmo {ZåZ àíZm| H$m CÎma Xr{O¶o&

1. EëH$mohm°b godZ Ho$ H$maU ‘aZo dmbo ì¶p³V¶m| H$s g§»¶m {H$VZr h¡?

2. VoO J{V go dmhZ MbmZo go ‘aZo dmbo ì¶p³V¶m| H$s g§»¶m {H$VZr h¡? (1+1=2)

^mJ-g

16. EH$ {^ÝZ H$m A§e CgHo$ ha go 3 H$‘ h¡& ¶{X {^Þ Ho$ ha ‘| EH$ Omo‹S> {X¶m OmE, Vmo {^Þ H$m ‘mZ 151 H$‘

hmo OmVm h¡& {^ÝZ kmV H$s{OE& 3

17. EH$ g‘mÝVa loUr ‘| àW‘ nX 8 h¡, ndm± nX 33 h¡ VWm nhbo n nXm| H$m ¶moJ 123 h¡ Vmo n VWm gmd©AÝVa

d H$mo kmV H$s{OE& 3

18. ‘rZma Ho$ AmYma go Am¡a EH$ gab aoIm ‘| 4 ‘rQ>a VWm 9 ‘rQ>a H$s Xÿar na pñWV Xmo {~ÝXþAm| go ‘rZma Ho$

{eIa Ho$ CÝZ¶Z H$moU nyaH$ H$moU h¢& {gÕ H$s{OE {H$ ‘rZma H$s D±$MmB© 6 ‘rQ>a h¡& 3

19. {Ì^wO H$s VrZm| ^wOmAm| Ho$ bå~ g‘{Û^mOH$ EH$ hr {~ÝXþ go hmoH$a OmVo h¢& 3

20. Xr JB© AmH¥${V ‘| aoImIÊS> XY , {Ì^wO ABC H$s ^wOm AC Ho$ g‘mÝVa h¡ VWm {Ì^wO H$mo Xmo g‘mZ ^mJm|

‘| ~m±Q>Vr h¡& AZwnmV ABAX kmV H$s{OE& 3



21. EH$ d¥Îm H$s Xmo OrdmE± AB Am¡a AC ~am~a h¢& {gÕ H$s{OE {H$ d¥Îm H$m Ho$ÝÐ BAC+ Ho$ g‘{Û^mOH$ na

pñWV hmoJm& 3

22. EH$ g‘H$moU {Ì^wO ABC ~ZmBE {Og‘| AB 6= go‘r, BC 8= go‘r Am¡a B 90c+ = h¡& B go AC na

b§~ BD ~ZmBE Am¡a q~XþAm| ,B C Am¡a D go JwOaVm EH$ d¥Îm ~ZmBE& A go Bg d¥Îm na EH$ ñne© aoImAm|

H$s aMZm H$s{OE& 3

23. EH$ d¥ÎmmH$ma nmH©$ H$s {ÌÁ¶m 3.5 ‘rQ>a h¡& nmH©$ Ho$ Mmam| Amoa 1.4 ‘rQ>a Mm¡‹S>m ’w$Q>nmW ~Zm hþAm h¡& ’w$Q>nmW

H$m joÌ’$b kmV H$s{OE& 3

24. EH$ R>mog YmVw Ho$ Jmobo H$mo {nKbmH$a g‘mZ {ÌÁ¶m Ho$ N>moQ>o Jmobo ~Zm¶o OmVo h¢& Bg {d{Y ‘| Jmobo Ho$ Am¶VZ

H$s 10% hm{Z hmo OmVr h¡& N>moQ>o Jmobo H$s {ÌÁ¶m ~‹S>o Jmobo H$s 91 h¡& ¶{X ~‹S>o Jmobo H$mo a§JZo Ho$ {b¶o 10 brQ>a

a§J H$s Amdí¶H$Vm hmoVr h¡, Vmo N>moQ>o gämr Jmobm| H$mo a§JZo Ho$ {b¶o {H$VZo a§J H$s Amdí¶H$Vm hmoJr? 3

25. 52 Vme Ho$ nÎmm| H$s JS²>S>r go {M‹S>r Ho$ ~mXemh, ~oJ‘ Am¡a Jwbm‘ AbJ H$a {X¶o J¶o h¢ VWm eof H$mo AÀN>r

àH$ma go {‘bm {X¶m J¶m h¡& eof ‘| go EH$ nÎmm ¶mÑÀN>¶m {ZH$mbm OmVm h¡& àm{¶H$Vm kmV H$s{OE {H$ dh-

1. EH$ nmZ

2. EH$ ~mXemh

3. EH$ {M‹S>r

4. nmZ H$m 10, h¡& 3

^mJ-X

26. AmboIr¶ {d{Y Ûmam {ZåZ{b{IV g‘rH$aU {ZH$m¶ H$m hb kmV H$s{OE- (3+3=6)

x y2 3+ 13=

x y5 2- 4=

27. {gÕ H$s{O¶o- (3+3=6)

(1) coscos cosec cot1

1qq q q-

+ = +

(2) sinsin sec tan1

1qq q q+

- = -

AWdm

27. (1) {gÕ H$s{O¶o {H$- 3

secsec cot cosec1

1qq q q-

+ = +




(2) ¶{X sin cos pq q+ = Am¡a sec cosec qq q+ = hmo, Vmo {gÕ H$s{OE {H$ q p p1 22 - =^ h 3

28. (1) ¶{X {~ÝXþ ,K 2^ h VWm (3,4) Ho$ ~rM H$s Xÿar 8 hmo, Vmo K H$m ‘mZ {b{IE& 3

(2) {~ÝXþAm| ,4 0-^ h Am¡a ,0 6^ h H$mo {‘bmZo dmbo dmbo aoImIÊS> H$mo 4 ~am~a ^mJm| ‘| ~m±Q>Zo dmbo {~ÝXþAm|

Ho$ {ZX}em§H$ kmV H$s{OE& 3

29. {gÕ H$amo {H$ {Ì^wO H$s EH$ ^wOm H$mo ~‹T>mZo na ~ZZo dmbo ~{hîH$moU H$m g‘{Û^mOH$ H$moU H$s gå‘wI ^wOm

~mø {d^mOZ {Ì^wO H$s eof XmoZm| ^wOmAm| Ho$ AZwnmV ‘| H$aVm h¡& 6

AWdm

29. AmH¥${V ‘|, O d¥Îm H$m Ho$ÝÐ h¡& BD OD= Am¡a CD AB= h¡& CAB+ kmV H$s{OE& 6

30. J{UV H$s EH$ narjm ‘| 30 {dÚm{W©¶m| Ûmam àmßV {H$E JE A§H$m| H$m ~§Q>Z {ZåZ{b{IV h¡- 6

àmßVm§H$m| H$m dJ©-AÝVamb 10-25 25-40 40-55 55-70 70-85 85-100

{dÚm{W©¶m| H$s g§»¶m 2 3 7 6 6 6

BZ Am±H$‹S>m| go H$pënV ‘mÜ¶ {d{Y go ‘mÜ¶ kmV H$s{OE Ed§ ~hþbH$ ^r kmV H$s{OE&

*******

AJbo gmb go H$moB© nmg~wH$ ¶m goånb nona IarXZo H$s Oê$aV ZhtgÌ 2020-21 go amOñWmZ ‘| NCERT nmR²>¶H«$‘ bmJy {H$¶m Om ahm h¡& Z¶o

nmR²>¶H«$‘mZwgma g^r H$jmAm| Ho$ g^r {df¶m| H$s Q>o³ñQ> ~wH$ Ed§ g^r àH$ma H$s ghm¶H$

AÜ¶¶Z gm‘J«r O¡go- goånb nona/S>oñH$ dH©$ Am{X {dÚm[W©¶m| H$mo ‘mo~mBb na ìhmQ²>gEn Zå~a

9460443210 Ûmam Ed§ do~gmBQ> www.rbse.online na CnbãY H$adm¶r OmEJr& BgHo$

{b¶o {dÚm{W©¶m| go {H$gr ^r àH$ma H$m H$moB© ewëH$ Zht {b¶m OmEJm& BgHo$ {b¶o {dÚm{W©¶m|

H$mo {H$gr ^r àH$ma H$m H$moB© OTP Verification ¶m Email Ûmam Verification Zht XoZm hmoJm& Bg ~mao ‘| {H$gr ^r àH$ma H$s OmZH$mar Ho$ {b¶o 9460443210 na

ìhmQ²>gEn Ûmam ‘¡goO H$a| ¶m h‘mar do~gmBQ> www.rbse.online na {d{OQ> H$a|&






No of Pages : 4

‘mÜ¶{‘H$ narjm, 2019-20J{UV

‘m°S>b nona 8

g‘¶ … 3 41 KÊQ>o nyUmªH$ … 80



2.


A 1-10 1

~ 11-15 2

g 16-25 3

X 26-30 6



^mJ-A

1. gyÌ {Z{Ib‘² H$m à¶moJ H$aVo hþE 137 9999# H$m ‘mZ kmV H$s{OE& 1

2. gyÌ eyÝ¶ gmå¶ g‘wÀM¶o Ûmam g‘rH$aU x x x x21

61

11

71

+ + + = + + + H$m hb kmV H$s{OE& 1

3. {~Zm b§~r {d^mOZ à{H«$¶m {H$E ~VmBE {H$ 34329 n[a‘o¶ g§»¶m Ho$ Xe‘bd àgma gm§V h¢ ¶m Agm§V AmdVu

h¢? 1

4. tan tan tan55 45 35$ $c c c H$m ‘mZ kmV H$s{OE& 1

5. 9 ‘rQ>a D±$Mo EH$ D$Üdm©Ya Iåô H$s N>m¶m H$s bå~mB© {H$VZr hmoJr, ¶{X Cg g‘¶, gy¶© H$m CÝZ¶Z H$moU

°30 hmo? 1

6. {Og {Ì^wO ‘| bå~Ho$ÝÐ, n[aHo$ÝÐ Am¡a AÝV…Ho$ÝÐ EH$ hr hm|, Cg {Ì^wO H$m Zm‘ {b{IE& 1

7. EH$ {g³Ho$ H$mo Xmo ~ma CN>mbm OmVm h¡& H$‘-go-H$‘ EH$ {MV AmZo H$s àm{¶H$Vm kmV H$s{OE? 1

8. ¶{X EH$ Q>¡³gr H$m {H$am¶m àW‘ {H$bmo‘rQ>a Ho$ {bE <15 VWm BgHo$ ~mX à{V [H$‘r. Ho$ {bE <8 h¡ Vmo

12 {H$‘r. MbZo Ho$ {bE ³¶m {H$am¶m XmoJo? 1

9. EH$ ~g ñQ>¡ÊS> na EH$ Iåô H$o AmYma go 30 ‘rQ>a Xÿar na pñWV ßboQ>’$m°‘© Ho$ EH$ {~ÝXþ go Iåô Ho$ erf©

na bJo CCTV H¡$‘ao H$m CÝZ¶Z H$moU 60c h¡ Vmo Iåô H$s D±$MmB© kmV H$s{OE& 1




10. Xr JB© AmH¥${V ‘|, ¶{X m (Mmn PMQ) 100c= , Vmo PQS+ H$m ‘mn kmV H$amo& 1

^mJ-~

11. ÛÝÛ ¶moJ {d{Y Ûmam g§»¶m 125316 H$m dJ©‘yb kmV H$s{OE&afd 2

12. {gÕ H$s{OE {H$ 3 2 5+ EH$ An[a‘o¶ g§»¶m h¡& 2

13. EH$ d¥Îm H$s {ÌÁ¶m 7 go‘r h¡ VWm Ho$ÝÐ na AÝV[aV H$moU 60c h¡& Mmn H$s bå~mB© kmV H$s{OE& 2

14. ¶{X EH$ e§Hw$ H$m dH«$n¥îR> 2035 dJ© go‘r VWm AmYma H$m ì¶mg 35 go‘r hmo Vmo e§Hw$ H$s {V¶©H$ D±$MmB© kmV

H$s{OE& 2

15. g‘wÐ Ho$ {H$Zmao gwajm H$s ÑpîQ> go EH$ Iå^o na EH$ CCTV H¡$‘am bJm¶m J¶m h¡& ¶{X Bg H¡$‘ao Ho$ Ûmam

1.5 ‘rQ>a bå~m ì¶p³V 33.5 ‘rQ>a H$s Xÿar na ñnîQ> XoIm Om gH$Vm h¡ O~{H$ H¡$‘am 35 ‘rQ>a H$s D±$MmB©

na bJm h¡, Vmo H¡$‘ao H$m AdZ‘Z H$moU kmV H$s{OE& 2

^mJ-g

16. ~hþnX x x x6 11 63 2- + - Ho$ g^r eyÝ¶H$ kmV H$s{OE O~{H$ BgHo$ Xmo eyÝ¶H$ 1 VWm 2 h¡& 3

17. gwã~mamd Zo 1995 ‘| <5000 Ho$ ‘m{gH$ doVZ na H$m¶© Amaå^ {H$¶m Am¡a àË¶oH$ df© <200 H$s doVZ d¥{Õ

àmá H$s& {H$g df© ‘| CgH$m doVZ <7000 hmo J¶m? 3

18. ¶{X gy¶© H$m CÝZ¶Z H$moU 30c go 60c ‘| n[ad{V©V hmo OmVm h¡& Vmo BZ XmoZm| CÝZ¶Z H$moUm| na 15 ‘rQ>a

D±$Mo Iå~o H$s N>m¶m H$s bå~mB© ‘| AÝVa kmV H$s{OE& 3

19. EH$ ABCT ‘| ‘mpÜ¶H$mE± ,AD BE Am¡a CF EH$ {~ÝXþ G go JwOaVr h¢& ¶{X AG 6= go‘r. Am¡a

.BE 12 6= go‘r. Am¡a FG 3= go‘r. hmo, Vmo ,AD GE Am¡a GC kmV H$s{OE& 3



20. ¶{X Xmo {Ì^wOm| ‘| H$moB© g§JV Xmo ̂ wOmE± nañna g‘mZwnmVr hmo VWm CZHo$ ‘Ü¶ Ho$ H$moU ~am~a hmo Vmo XmoZmo§ {Ì^wO

g‘ê$n hmoVo h¢& 3

21. EH$ MVw^w©O ABCD ‘| AB AC AD= = hm|, Vmo {gÕ H$s{OE {H$- BAD BDC CBD2+ + += +^ h

3

22. ABCT H$s aMZm H$s{OE {Og‘| AB 6= go‘r, BC 4= go‘r Am¡a B 120c+ = hmo, {Ì^wO Ho$ AÝVJ©V

d¥Îm H$s aMZm H$s{OE& 3

23. AmH¥${V ‘| N>m¶m§{H$V joÌ’$b kmV H$s{OE, ¶{X AB 5= go‘r., AC 12= go‘r. Am¡a O d¥Îm H$m Ho$ÝÐ h¡& 3

24. 12 go‘r ì¶mg Ho$ ~obZmH$ma ~V©Z ‘| Hw$N> nmZr ^am h¡& EH$ 4 go‘r {ÌÁ¶m H$m R>mog YmVw H$m Jmobm Bg‘o§ S>mbm

OmVm h¡& nmZr H$s gVh H$s D±$MmB© ‘| {H$VZr d¥{Õ hmoJr ¶{X Jmobm nmZr ‘| nyU©V¶m Sy>~ OmVm h¡? 3

25. 52 Vme Ho$ nÎmm| H$s JS²>S>r go EH$ H$mbm Jwbm‘, EH$ bmb ~oJ‘ Am¡a Xmo H$mbo ~mXemh AbJ H$a {X¶o OmVo h¢&

eof nÎmm| ‘o§ go EH$ nVm ¶mÑÀN>¶m {ZH$mbm OmVm h¡& àm{¶H$Vm kmV H$s{OE {H$ dh-

1. EH$ H$mbm nÎmm h¡&

2. EH$ ~mXemh h¡

3. EH$ bmb ~oJ‘ h¡& 3

^mJ-X

26. {ZåZ a¡{IH$ g‘rH$aU ¶w½‘ H$mo Ambo{IH$ {d{Y go hb H$s{OE VWm CZ {~ÝXþAm| Ho$ {ZX}em§H$ kmV H$s{OE Ohm±

BZHo$ Ûmam {Zê${nV aoImE± y-Aj H$mo H$mQ>Vr h¢& (6)

x y3 2+ 12= VWm x y5 2- 4=

27. {gÕ H$s{OE {H$- (3+3=6)

(1) sec cos sinsin

112q q q

q- = +-

^ h

(2) sec cosec tan cot2 2q q q q+ = +

AWdm

27. (1) sec cosec

cot tan sin cossin cos

13 3

2 2

q qq q q q

q q-

+ + -=

^ ^h h 3

(2) ¶{X sin cosx r A C= , sin siny r A C= VWm cosz r A= V~ {gÕ H$s{OE x y z r2 2 2 2+ + = 3




28. (1) {~ÝXþ ,x 5^ h VWm (4, 2) Ho$ ‘Ü¶ Xÿar 3 go‘r. hmo Vmo x H$m ‘mZ kmV H$s{OE& 3

(2) kmV H$s{OE {H$ aoIm x y3 9+ = {~ÝXþAm| (1, 3) VWm (2,7) H$mo {‘bmZo dmbo aoImIÊS> H$mo {H$g

AZwnmV ‘| {d^m{OV H$aVr h¡? 3

29. {gÕ H$r{OE {H$ ¶{X H$moB© EH$ aoIm {H$gr {Ì^wO Ho$ EH$ AmÝV[aH$ H$moU H$m g‘{Û^mOZ H$ao Vmo dh

g‘{Û^mOH$ aoIm Cg H$moU H$s gå‘wI ^wOm H$mo {Ì^wO H$s eof ^wOmAm| H$s bå~mB¶m| Ho$ AZwnmV ‘| {d^m{OV

H$aVr h¡& 6

AWdm

29. AmH¥${V ‘o§, O d¥Îm H$m Ho$ÝÐ h¡ Am¡a BCO 30c+ = h¡& x Am¡a y kmV H$s{OE& 6

30. {ZåZ{b{IV Am±H$‹S>m§o H$s ‘mpÜ¶H$m 525 h¡& ¶{X ~maå~maVmAm| H$m ¶moJ 100 h¡, Vmo x d y H$m ‘mZ kmV

H$s{OE- 6

dJ©-AÝVamb ~maå~maVm0-100 2

100-200 5

200-300 x300-400 12

400-500 17

500-600 20

600-700 y700-800 9

800-900 7

900-1000 4

*******

AJbo gmb go H$moB© nmg~wH$ ¶m goånb nona

IarXZo H$s Oê$aV ZhtgÌ 2020-21 go amOñWmZ ‘| NCERT nmR²>¶H«$‘ bmJy
















No of Pages : 4

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g‘¶ … 3 41 KÊQ>o nyUmªH$ … 80



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A 1-10 1

~ 11-15 2

g 16-25 3

X 26-30 6



^mJ-A


5# H$m ‘mZ kmV H$s{OE& 1

2. gyÌ namdË¶© ¶moO¶oV² Ûmam g‘rH$aU x x2 15

3 29 0- - - = H$m hb kmV H$s{OE& 1

3. 160015 n[a‘o¶ g§»¶m Ho$ Xe‘bd àgmam| H$mo {b{IE& 1

4. {gÕ H$s{OE {H$ cos cosec35 55 1$c c = 1

5. gå‘wI {MÌ ‘| BC EH$ d¥j h¡& {H$gr g‘¶ CgH$s naN>mB© AB , 8 3 ‘rQ>a Wr& ¶{X Cg g‘¶ d¥j H$s

MmoQ>r H$m CÝZ¶Z H$moU °30 H$m ahm hmo, Vmo d¥j H$s D±$MmB© kmV H$s{OE& 1

6. EH$ K‹S>r ‘| goH$ÊS> H$s gwB© Ho$ {gao H$m {~ÝXþnW {b{IE& 1




7. Xr JB© AmH¥${V ‘|, PQRS4 EH$ MH«$s¶ MVw^w©O h¡ Ohm±, PQR 50c+ = h¡& PSR+ kmV H$amo& 1

8. {H$gr à¶moJ H$s g^r àmapå^H$ KQ>ZmAm| H$s àm{¶H$Vm H$m ¶moJ {b{IE& 1

9. ¶{X amOy nhbr, Xÿgar, Vrgar d Mm¡Wr {g½Zb bmBQ> H$mo H«$‘e… 3, 8, 13, 18, goH$ÊS> nma H$aVm h¡ Vmo

78 goH$ÊS> ‘| H$m¡Z gr {g½Zb bmBQ> nma H$a MwH$m hmoJm& 1

10. EH$ ~g ñQ>¡ÊS> na EH$ Iåô Ho$ AmYma go 40 ‘rQ>a Xÿar na pñWV ßboQ>’$m‘© Ho$ EH$ {~ÝXþ go Iåô H$s MmoQ>r

na bJo hþE H¡$‘ao H$m CÝZ¶Z H$moU 60c h¡ Vmo Iåô H$s D±$MmB© kmV H$s{OE& 1

^mJ-~

11. ÛÝÛ ¶moJ {d{Y Ûmam g§»¶m 1522756 H$m dJ©‘yb kmV H$s{OE& 2

12. Xmo g§»¶mAm| H$m b.g. CZHo$ ‘.g. H$m 15 JwZm h¡ VWm bKwÎm‘ g‘mndË¶© Am¡a ‘hÎm‘ g‘mndV©H$ H$m ¶moJ’$b

912 h¡& ¶{X BZ‘| go EH$ g§»¶m 171 h¡, Vmo Xÿgar g§»¶m H$m ‘mZ ~Vmd|& 2

13. EH$ d¥Îm H$s {ÌÁ¶m 10.5 go‘r Am¡a {ÌÁ¶IÊS> H$m H$moU 45c h¡& bKw {ÌÁ¶IÊS> H$m joÌ’$b kmV H$s{OE&

722p =_ i 2

14. EH$ AÕ© Jmobo H$s {ÌÁ¶m 4.5 go‘r. h¡& BgH$m n¥îR>r¶ joÌ’$b kmV H$s{OE& 2

15. EH$ grYo d 8 ‘rQ>a D±$Mo nmob na ¶mVm¶mV {Z¶ÝÌU Ho$ {bE CCTV H¡$‘am bJm h¡& Omo nmob H$o erf© go 17

‘rQ>a Xÿa ÑpîQ> aoIm VH$ ¶mVm¶mV XoI gH$Vm h¡& nmob Ho$ Mmamo§ Amoa ¶h H¡$‘am {H$VZm joÌ’$b ¶mVm¶mV XoI

gH$Vm h¡? 2

^mJ-g

16. {ÛKmV ~hþnX x x 22 + - Ho$ eyÝ¶H$ kmV H$s{OE Am¡a eyÝ¶H$m| VWm JwUm§H$m| Ho$ ~rM Ho$ gå~ÝY H$s gË¶Vm

Om±M H$s{OE& 3

17. 500 Am¡a 900 Ho$ ~rM pñWV 7 Ho$ gämr JwUOm| H$m ¶moJ’$b kmV H$s{OE& 3

18. {H$gr ‘rZma Ho$ AmYma go a Am¡a b Xÿar na EH$ hr aoIm na pñWV Xmo {~ÝXþ H«$‘e… C d D go XoIZo na

‘rZma Ho$ {eIa Ho$ CÝZ¶Z H$moU EH$-Xÿgao Ho$ nyaH$ h¢& {gÕ H$s{OE {H$ ‘rZma H$s D±$MmB©& 3

19. EH$ {Ì^wO H$s Xmo ‘mpÜ¶H$mE± g‘mZ ‘mn H$s hm| Vmo dh {Ì^wO g‘{Û~mhþ {Ì^wO hmoVm h¡& 3



20. ABCD EH$ g‘bå~ MVw^w©O h¡ {Og‘| | |AB DC h¡ VWm BgHo$ {dH$U© nañna {~ÝXþ O na à{VÀN>oX H$aVo

h¢& Xem©BE {H$ BOAO

DOCO= h¡& 3

21. AmH¥${V ‘| ABCD EH$ MH«$s¶ MVw^w©O h¡& a Am¡a b H$m ‘mZ kmV H$s{OE& 3

22. EH$ 4 go‘r. {ÌÁ¶m H$m d¥Îm It{ME& Cg na Xmo ñne© aoImE± Bg àH$ma It{ME {H$ do nañna 70c H$m H$moU

~ZmVr hm|& 3

23. 4 go‘r. {ÌÁ¶m dmbo EH$ d¥Îm Ho$ Cg {ÌÁ¶IÊS> H$m joÌ’$b kmV H$s{OE, {OgH$m H$moU 60c h¡& gmW hr g§JV

XrK© {ÌÁ¶IÊS> H$m joÌ’$b ^r kmV H$s{OE& ( .3 14p = H$m à¶moJ H$a|) 3

24. 22 go‘r # 12 go‘r Ho$ Am¶VmH$ma H$mJO H$mo Xmo AbJ-AbJ {d{Y¶m| go ‘mo‹S>H$a Xmo ~obZ ~Zm¶o Om gH$Vo

h¢& 3

1. XmoZm| ~obZm| Ho$ Am¶VZm| H$m AZwnmV kmV H$s{OE&

2. XmoZm§o ~obZm| Ho$ Am¶VZm| H$m AÝVa kmV H$s{OE&

25. 52 Vme Ho$ nÎmm| go gämr nÎmo, {OZH$s g§»¶mE± 3 Ho$ JwUH$ h¢, hQ>m {X¶o OmVo h¢& A~ EH$ nÎmm ¶mÑÀN>¶m

{ZH$mbm OmVm h¡& àm{¶H$Vm kmV H$s{OE {H$ ¶h nÎmm…

1. EH$ Vñdra (~mXemh, ~oJ‘ ¶m Jwbm‘) dmbm nÎmm h¡&

2. EH$ bmb, g‘ g§»¶m dmbm nÎmm h¡& 3




^mJ-X

26. {ZåZ a¡{IH$ g‘rH$aUm| Ho$ ¶w½‘ H$mo AmboIr¶ {d{Y go hb H$s{OE VWm BgH$s ghm¶Vm go a H$m ‘mZ kmV

H$s{OE O~{H$ x y a4 3+ = h¡& x y3 6+ = ; x y2 3 12- = 6

27. (1) ¶{X tan baq = Vmo {gÕ H$s{OE {H$- (3+3=6)

sin cossin cosa ba b

a ba b

2 2

2 2

q qq q

+- =

+-

(2) cot cottan tan

a ba b

++ tan tana b=

AWdm 27. (1) tan

coscot

sin sin cosAA

AA A A1 1- + - = + 3

(2) ¶{X q EH$ Ý¶yZH$moU h¡ VWm cosec5 7q = Vmo sin cos 12q q+ - H$m ‘mZ kmV H$s{OE& 3

28. (1) ¶{X ,A B Am¡a C Ho$ {ZX}em§H$ H«$‘e… , , ,6 1 1 3-^ ^h h VWm ,x 8^ h h¢ Vmo x H$m ‘mZ kmV H$s{O¶o

O~{H$ AB BC= hmo& 3

(2) dh AZwnmV kmV H$s{OE O~{H$ {~ÝXþ ,p3-^ h {~ÝXþAm| ,5 4- -^ h Am¡a ,2 3-^ h H$mo AÝV…{d^m{OV

H$aVm h¡& p H$m ‘mZ ^r kmV H$s{OE& 3

29. {gÕ H$amo {H$ {H$gr {Ì^wO H$s EH$ ̂ wOm Ho$ g‘mÝVa ItMr JB© EH$ aoIm {Ì^wO H$s eof Omo ̂ wOmAm| H$mo à{VÀN>oX

H$ao Vmo ¶h XmoZm| ^wOmAm| H$mo g‘mZ AZwnmV ‘| {d^m{OV H$aVr h¡& 6

AWdm 29. AB Am¡a AC {ÌÁ¶m r dmbo EH$ d¥Îm H$s Xmo OrdmE± Bg àH$ma h¢ {H$ AB AC2= h¡& ¶{X p Am¡a q H«$‘e…

Ho$ÝÐ go AB Am¡a AC H$s Xÿ[a¶m± h¢, Vmo {gÕ H$s{OE {H$ q p r4 32 2 2= + h¡& 6

30. {ZåZ ~maå~maVm ~§Q>Z Ho$ ‘mÜ¶ d ‘mpÜ¶H$m kmV H$s{OE& 6

dJ© 0-8 8-16 16-24 24-32 32-40 40-48

fi 42 30 50 22 8 5

*******

AJbo gmb go H$moB© nmg~wH$ ¶m goånb nona IarXZo H$s Oê$aV ZhtgÌ 2020-21 go amOñWmZ ‘| NCERT nmR²>¶H«$‘ bmJy {H$¶m Om ahm h¡& Z¶o nmR²>¶H«$‘mZwgma g^r H$jmAm| Ho$ g^r

{df¶m| H$s Q>o³ñQ> ~wH$ Ed§ g^r àH$ma H$s ghm¶H$ AÜ¶¶Z gm‘J«r O¡go- goånb nona/S>oñH$ dH©$ Am{X {dÚm[W©¶m| H$mo

‘mo~mBb na ìhmQ²>gEn Zå~a 9460443210 Ûmam Ed§ do~gmBQ> www.rbse.online na CnbãY H$adm¶r OmEJr&

BgHo$ {b¶o {dÚm{W©¶m| go {H$gr ̂ r àH$ma H$m H$moB© ewëH$ Zht {b¶m OmEJm& BgHo$ {b¶o {dÚm{W©¶m| H$mo {H$gr ̂ r àH$ma H$m

H$moB© OTP Verification ¶m Email Ûmam Verification Zht XoZm hmoJm& Bg ~mao ‘| {H$gr ̂ r àH$ma H$s OmZH$mar

Ho$ {b¶o 9460443210 na ìhmQ²>gEn Ûmam ‘¡goO H$a| ¶m h‘mar do~gmBQ> www.rbse.online na {d{OQ> H$a|&



n¥îR> g§»¶m 1 www.rbse.online

RBSE Math Model Paper 10 (Solution Attached)


No of Pages : 4

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J{UV

‘m°S>b nona 10

g‘¶ … 3 41 KÊQ>o nyUmªH$ … 80



2.


A 1-10 1

~ 11-15 2

g 16-25 3

X 26-30 6



^mJ-A

1. gyÌ EH$Ý¶yZoZ nyd}U H$m à¶moJ H$aVo hþE 46 99# H$m ‘mZ kmV H$s{OE- 1

2. gyÌ eyÝ¶ gmå¶ g‘wÀM¶o Ûmam g‘rH$aU-

x x x x41

61

21

81

- + - = - + - H$m hb kmV H$s{OE& 1

3. 5005 g§»¶m Ho$ A^mÁ¶ JwUZIÊS>m| H$s KmVm| H$m ¶moJ’$b {b{IE& 1

4. sec tanB B7 72 2- H$m ‘mZ kmV H$s{OE& 1

5. {H$gr g‘¶ na EH$ no‹S> H$s naN>mB© H$s bå~mB© no‹S> H$s bå~mB© H$m 3 JwZm h¡& Cg g‘¶ gy¶© H$m CÝZ¶Z

H$moU {H$VZm hmoJm? 1

6. Xr JB© AmH¥${V ‘| PQRS4 EH$ MH«$s¶ MVw^w©O h¡ Ohm±, PQR 50c+ = h¡& PSR+ kmV H$amo& 1


n¥îR> g§»¶m 2www.rbse.online


7. VrZ Ag§aoIr¶ {~ÝXþAm| go JwOaZo dmbo d¥Îmm| H$s g§»¶m {b{IE& 1

8. EH$ nmgo H$mo ’|$H$m OmVm h¡ Vmo VrZ go ~‹S>r g§»¶m àmá H$aZo H$s àm{¶H$Vm kmV H$s{OE& 1

9. ¶{X EH$ g‹S>H$ na ¶mVm¶mV {g½Zb EH$ Mm¡amho go H«$‘e… {ZåZ Xÿ[a¶m§o na bJo h¢… 3,8,13,.....VWm ApÝV‘

{g½Zb 253 ‘rQ>a na bJm h¡& Vmo ¶h kmV H$amo {H$ 20dm± {g½Zb {H$VZr Xÿar na bJm h¡? 1

10. nw{bg H$s PCR d¡Z ‘| gwajm H$s ÑpîQ> go N>moQ>r-N>moQ>r ~ÝXÿH§o$ j¡{VO Ho$ gmW 45c H$m H$moU ~ZmVo hþE bJmB©

JB© h¢& ¶{X ~ÝXÿH$ Ûmam N>mo‹S>r JB© Jmobr 195 ‘rQ>a OmVr h¡ Vmo Jmobr Ho$ ApÝV‘ ñWmZ H$s n¥Ïdr Vb go D±$MmB©

H$s JUZm H$s{OE& 1

^mJ-~

11. ^mJ {d{Y go g§»¶m 68921 H$m KZ‘yb kmV H$s{O¶o& 2

12. Xem©B¶o {H$ 2 5+ EH$ An[a‘o¶ g§»¶m h¡& 2

13. EH$ d¥Îm Ho$ Mmn H$s bå~mB© 12 go‘r VWm {ÌÁ¶m 7 go‘r h¡& d¥Îm Ho$ bKw {ÌÁ¶IÊS> H$m joÌ’$b kmV

H$s{OE& 3

14. EH$ Jmobo H$m n¥îR>r¶ joÌ’$b 616 dJ© go‘r h¡ Vmo Jmobo H$m Am¶VZ kmV H$s{OE& 2

15. EH$ grYo d 12 ‘rQ>a D±$Mo nmob Ho$ erf© na EH$ CCTV H¡$‘am bJm h¡ Vm{H$ nmob Ho$ erf© go 13 ‘rQ>a Xÿa

ÑpîQ> aoIm Ho$ AmJo ^r ¶mVm¶mV XoIm Om gHo$& Bg pñW{V ‘| nmob Ho$ ~mX go dh Xÿar, {OgHo$ AmJo go ¶mVm¶mV

{XImB© XoVm h¡, kmV H$s{OE& 2

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16. x x x3 3 53 2- + - H$mo x x1 2- - go ^mJ Xr{OE Am¡a {d^mOZ EëJmo[aÏ‘ H$s gË¶Vm H$s Om±M H$s{OE& 3

17. EH$ g‘mÝVa loUr Ho$ àW‘ m nXm| H$m ¶moJ’$b m m4 2 - h¡& ¶{X Bg loUr H$m ndm± nX 107 h¡, Vmo n H$m

‘mZ kmV H$s{OE& Bg g‘mÝVa loUr H$m 21dm± nX ^r kmV H$s{OE& 3

18. {H$gr Jbr ‘| O‘rZ go 15 m H$s D±$MmB© na pñWV EH$ {I‹S>H$s go Jbr Ho$ Xÿgar Amoa pñWV EH$ ‘H$mZ

Ho$ {eIa VWm nmX Ho$ CÝZ¶Z VWm AdZ‘Z H$moU H«$‘e… 30c VWm 45c h¢& {XImBE {H$ ‘H$mZ H$s$D±$MmB©

. m23 66 h¡& .3 1 732=^ h 3

19. EH$ ABCT H$s ‘mpÜ¶H$mE± ,AD BE Am¡a CF EH$ {~ÝXw G go JwOaVr h¢& ¶{X AG 5= go‘r, BE 12=

go‘r Am¡a FG 3= go‘r hmo Vmo ,AD GE Am¡a GC kmV H$s{OE& 3

20. EH$ MVw^w©O ABCD Ho$ {dH$U© nañna {~ÝXþ O na Bg àH$ma à{VÀN>oX H$aVo h¢ {H$ BOAO

DOCO= h¡, Vmo {gÕ

H$s{OE {H$ ABCD EH$ g‘bå~ MVw^w©O h¡& 3

21. {gÕ H$amo {H$ MH«$s¶ MVw^w©O Ho$ gå‘wI H$moU ¶w½‘ gånyaH$ ¶m CZH$m ¶moJ 180c hmoVm h¡& 3

22. ABCT H$s aMZm H$s{OE {OgH$s ^wOm BC 4= go‘r, B 40c+ = Ed§ A 90c+ = hmo& Bg {Ì^wO Ho$

n[aJV d¥Îm H$s aMZm H$s{OE Am¡a n[aHo$ÝÐ H$s pñW{V H$s Om±Mo H$s{OE& 3


n¥îR> g§»¶m 3 www.rbse.online


23. Xr JB© AmH¥${V ‘| N>m¶m§{H$V ^mJ H$m joÌ’$b kmV H$s{OE, Ohm± ABCD ^wOm 14 go‘r. H$m EH$ dJ© h¡& 3

24. YmVw Ho$ VrZ KZ, {OZH$s H$moao 3…4…5 Ho$ AZwnmV ‘| h¡, H$mo {nKbmH$a EH$ KZ ~Zm¶m J¶m h¡ {OgH$m {dH$U©

12 3 go‘r h¡& VrZm| Koam| H$s H$moao kmV H$s{OE& 3

25. Xmo {^ÝZ nmgm| H$mo EH$ gmW ’|$H$m OmVm h¡& àm{¶H$Vm ³¶m h¡ {H$ XmoZm| nmgm| na àmá A§H$m|… 3

1. H$m ¶moJ 9 h¡?

2. H$m ¶moJ 10 h¡?

3. H$m ¶moJ H$‘-go-H$‘ 10 h¡?w

4. H$m ¶moJ 13 h¡?

5. H$m ¶moJ 12 ¶m H$‘ h¡?

6. ‘§o EH$ nmgo na 2 H$m JwUH$ Am¡a Xÿgao na 3 H$m JwUH$ h¡?

^mJ-X

26. {ZåZ a¡{IH$ g‘rH$aUm| Ho$ ¶w½‘m| H$mo AmboIr¶ {d[Y go hb H$s{OE VWm CZ {~ÝXþAm| Ho$ {ZX}em§H$ ^r kmV

H$s{OE Ohm± BZHo$ Ûmam {Zê${nV aoImE± y-Aj H$mo H$mQ>Vr h¢& 6

x y2 5 4- + 0=

x y2 8+ - 0=

27. {gÕ H$s{OE {H$- 3+3=6

(1) cos cos

sin sin tan2

23

3

q qq q q

-- =

(2) cossin

sincos sec1

1 2qq

qq q+ + + =

AWdm 27. (1) cosec sin sec cos

tan cotA A A A

A A1- - = +

^ ^h h 3

(2) ¶{X sec cosec5 36cq q= -^ h ¶hm± 5q EH$ Ý¶yZH$moU h¡ Vmo q H$m ‘mZ kmV H$s{OE& 3

28. (1) ¶{X {~ÝXþ ,A 2 5^ h Am¡a {~ÝXþ B H$mo {‘bmZo dmbo aoImIÊS> H$m ‘Ü¶ {~ÝXþ ,P 1 2-^ h hmo, Vmo {~ÝXþ B

Ho$ {ZX}em§H$ kmV H$s{OE&

(2) {~ÝXþAm| ,P 3 4-^ h VWm ,Q 4 5^ h H$mo Omo‹S>Zo dmbo aoImIÊS> H$mo g‘{Ì^m{OV H$aZo dmbo {~ÝXþAm| Ho$ {ZX}

em§H$ kmV H$s{OE& 3+3=6

29. Xr JB© AmH¥${V ‘| ABC EH$ {Ì^wO h¡& ¶{X ABAD

ACAE= , Vmo {gÕ H$s{OE | |DE BC 6


n¥îR> g§»¶m 4www.rbse.online


AWdm 29. AmH¥${V ‘|, AB Am¡a CD EH$ d¥Îm H$s Xmo OrdmE± h¢, Omo E na à{VÀN>oX H$aVr h¢& {gÕ H$s{OE {H$

AEC 21+ = (Mmn CXA Ûmam Ho$ÝÐ na AÝV[aV H$moU + Mmn DYB Ûmam Ho$ÝÐ na AÝV[aV H$moU) h¡& 6

30. {ZåZ ~maå~maVm ~§Q>Z Ho$ ‘mÜ¶ d ~hþbH$ kmV H$s{OE- 6

àmám§H$ 20-30 30-40 40-50 50-60 60-70

N>mÌm| H$s g§»¶m 4 28 42 20 6

*******

gÌ 2020-21 go Z¶o nmR²>¶H«$‘mZwgma g^r H$jmAm| Ho$ g^r {df¶m| H$s Q>o³ñQ> ~wH$ Ed§ g^r àH$ma H$s ghm¶H$ AÜ¶¶Z gm‘J«r {dÚm[W©¶m| H$mo ‘mo~mBb na ìhmQ²>gEn Ûmam Ed§ do~gmBQ> www.rbse.online na CnbãY H$adm¶r OmEJr& BgHo$ {b¶o {dÚm{W©¶m| go {H$gr ^r àH$ma H$m H$moB© ewëH$ Zht {b¶m OmEJm& BgHo$ {b¶o {dÚm{W©¶m| H$mo {H$gr ^r àH$ma H$m H$moB© OTP Verification ¶m Email Ûmam Verification Zht XoZm hmoJm& h‘mam ìhmQ²>gEn Zå~a OmZZo ¶m AÝ¶ {H$gr ^r àH$ma H$s OmZH$mar Ho$ {b¶o do~gmBQ> www.rbse.online na {d{OQ> H$a|&




‘mÜ¶{‘h$ narjm, 2019-20 j{uv ‘m°s>b nona 1€¦ · rbse math model paper 1 n¥îr>...

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