RBSE Math Model Paper 10 (Solution Attached) No of Questions : 30 No of Pages : 4 Zm m H$ mü { H$ narjm, 2019 J{UV m S>b nona 10 g KÊQ>o nyumªh$

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1 RBSE Mth Model Pper 0 (Solution Attched) No of Questions : 0 No of Pges : 4 Zm m H$ mü { H$ nrjm, 09 J{UV m S>b non 0 g 4 KÊQ>o nyumªh$ 80 nrjm[w m Ho$ {be gm mý {ZX}e-. g^r àíz H$Zo A{Zdm h &. ^mj àíz g» m A H$ àë oh$ àíz A -0 ~ - g 6- X àíz H«$ m H$ 7 d 9 AmÝV[H$ {dh$ën h & 4. àíz H«$ m H$ 6 H$m boim{mì J«m $ non n ~ZmBE& ^mj-a. gyì EH$Ý yzoz nyd}u H$m à moj H$Vo hþe # H$m mz kmv H$s{OE-. gyì eyý gmå g wàm o Ûmm g rh$u- H$m hb kmv H$s{OE& x x- 6 x- + x g» m Ho$ A^mÁ JwUZIÊS>m H$s KmVm H$m moj $b {b{ie& 4. 7sec B 7tn B - H$m mz kmv H$s{OE&. {H$gr g n EH$ no S> H$s nn>mb H$s bå~mb no S> H$s bå~mb H$m JwZm h & Cg g gy H$m CÝZ Z H$moU {H$VZm hmojm? 6. Xr JB AmH ${V 4 PQRS EH$ MH«$s MVw^w O h Ohm±, + PQR 0c h & + PSR kmv H$mo& n îr> g» m

2 RBSE Mth Model Pper 0 (Solution Attched) 7. VrZ Ag oir {~ÝXþAm go JwOZo dmbo d Îmm H$s g» m {b{ie& 8. EH$ nmgo H$mo $H$m OmVm h Vmo VrZ go ~ S>r g» m àmá H$Zo H$s àm{ H$Vm kmv H$s{OE& 9. {X EH$ g S>H$ n mvm mv {g½zb EH$ Mm mho go H«$ e {ZåZ Xÿ[ m o n bjo h,8,,...vwm ApÝV {g½zb rq> n bjm h & Vmo h kmv H$mo {H$ 0dm± {g½zb {H$VZr Xÿr n bjm h? 0. nw{bg H$s PCR d Z gwjm H$s ÑpîQ> go N>moQ>r-N>moQ>r ~ÝXÿH o$ j {VO Ho$ gmw 4c H$m H$moU ~ZmVo hþe bjmb JB h & {X ~ÝXÿH$ Ûmm N>mo S>r JB Jmobr 9 rq> OmVr h Vmo Jmobr Ho$ ApÝV ñwmz H$s n Ïdr Vb go D±$MmB H$s JUZm H$s{OE& ^mj-~. ^mj {d{y go g» m 689 H$m KZ yb kmv H$s{O o&. Xem B o {H$ + EH$ An[ o g» m h &. EH$ d Îm Ho$ Mmn H$s bå~mb go r VWm {ÌÁ m 7 go r h & d Îm Ho$ bkw {ÌÁ IÊS> H$m joì $b kmv H$s{OE& 4. EH$ Jmobo H$m n îr>r joì $b 66 dj go r h Vmo Jmobo H$m Am VZ kmv H$s{OE&. EH$ gryo d rq> D±$Mo nmob Ho$ erf n EH$ CCTV H $ m bjm h Vm{H$ nmob Ho$ erf go rq> Xÿ ÑpîQ> oim Ho$ AmJo ^r mvm mv XoIm Om gho$& Bg pñw{v nmob Ho$ ~mx go dh Xÿr, {OgHo$ AmJo go mvm mv {XImB XoVm h, kmv H$s{OE& 6. x - x + x- H$mo x x ^mj-g - - go ^mj Xr{OE Am {d^moz EëJmo[Ï H$s gë Vm H$s Om±M H$s{OE& 7. EH$ g mýv lour Ho$ àw m nxm H$m moj $b 4m - m h & {X Bg lour H$m ndm± nx 07 h, Vmo n H$m mz kmv H$s{OE& Bg g mýv lour H$m dm± nx ^r kmv H$s{OE& 8. {H$gr Jbr O rz go m H$s D±$MmB n pñwv EH$ {I S>H$s go Jbr Ho$ Xÿgr Amo pñwv EH$ H$mZ Ho$ {ei VWm nmx Ho$ CÝZ Z VWm AdZ Z H$moU H«$ e 0c VWm 4c h & {XImBE {H$ H$mZ H$s$D±$MmB. 66 m h & ^. 7h 9. EH$ T ABC H$s mpü H$mE±, BE Am CF EH$ {~ÝXw G go JwOVr h & {X AG go r, BE go r Am FG go r hmo Vmo, GE Am GC kmv H$s{OE& 0. EH$ MVw^w O ABCD Ho$ {dh$u nñn {~ÝXþ O n Bg àh$m à{vàn>ox H$Vo h {H$ AO CO BO h, Vmo {gõ DO H$s{OE {H$ ABCD EH$ g bå~ MVw^w O h &. {gõ H$mo {H$ MH«$s MVw^w O Ho$ gå wi H$moU w½ gånyh$ m CZH$m moj 80c hmovm h &. ABC T H$s MZm H$s{OE {OgH$s ^wom BC 4 go r, B 40c + Ed A 90c + hmo& Bg {Ì^wO Ho$ n[jv d Îm H$s MZm H$s{OE Am n[ho$ýð H$s pñw{v H$s Om±Mo H$s{OE& n îr> g» m

3 RBSE Mth Model Pper 0 (Solution Attched). Xr JB AmH ${V N>m m {H$V ^mj H$m joì $b kmv H$s{OE, Ohm± ABCD ^wom 4 go r. H$m EH$ dj h & 4. YmVw Ho$ VrZ KZ, {OZH$s H$moo 4 Ho$ AZwnmV h, H$mo {nkbmh$ EH$ KZ ~Zm m J m h {OgH$m {dh$u go r h & VrZm Kom H$s H$moo kmv H$s{OE&. Xmo {^ÝZ nmgm H$mo EH$ gmw $H$m OmVm h & àm{ H$Vm ³ m h {H$ XmoZm nmgm n àmá A H$m. H$m moj 9 h?. H$m moj 0 h?. H$m moj H$ -go-h$ 0 h?w 4. H$m moj h?. H$m moj m H$ h? 6. o EH$ nmgo n H$m JwUH$ Am Xÿgo n H$m JwUH$ h? ^mj-x 6. {ZåZ {IH$ g rh$um Ho$ w½ m H$mo AmboIr {d[y go hb H$s{OE VWm CZ {~ÝXþAm Ho$ {ZX}em H$ ^r kmv H$s{OE Ohm± BZHo$ Ûmm {Zê${nV oime± y-aj H$mo H$mQ>Vr h & 6 x- y+ 4 0 x+ y {gõ H$s{OE {H$- +6 () sin q- sin q tn q () cos q- cos q + sin q + cos q sec q cos q + sin q 7. () ^cosec sin ^sec cos AWdm A- Ah A- Ah tn A+ cot A () {X sec q cosec^q-6ch hm± q EH$ Ý yzh$mou h Vmo q H$m mz kmv H$s{OE& 8. () {X {~ÝXþ A^, h Am {~ÝXþ B H$mo { bmzo dmbo oimiês> H$m Ü {~ÝXþ P^-, h hmo, Vmo {~ÝXþ B Ho$ {ZX}em H$ kmv H$s{OE& () {~ÝXþAm P^- 4, h VWm Q^4, h H$mo Omo S>Zo dmbo oimiês> H$mo g {Ì^m{OV H$Zo dmbo {~ÝXþAm Ho$ {ZX} em H$ kmv H$s{OE& Xr JB AmH ${V ABC EH$ {Ì^wO h & {X AB, Vmo {gõ H$s{OE DE BC 6 n îr> g» m

4 RBSE Mth Model Pper 0 (Solution Attched) AWdm 9. AmH ${V, AB Am CD EH$ d Îm H$s Xmo OrdmE± h, Omo E n à{vàn>ox H$Vr h & {gõ H$s{OE {H$ C + (Mmn CXA Ûmm Ho$ÝÐ n AÝV[V H$moU + Mmn DYB Ûmm Ho$ÝÐ n AÝV[V H$moU) h & 6 0. {ZåZ ~må~mvm ~ Q>Z Ho$ mü d ~hþbh$ kmv H$s{OE- 6 àmám H$ N>mÌm H$s g» m n îr> g» m 4

5 moñwmz ~mos> nrjm 09 0dt H$jm J{UV m S>b non 0 g : 4 K Q>o (nyumªh$ : 80) nrjm[w m Ho$ {be gm mý {ZX}e-. g^r àíz H$Zo A{Zdm h &. ^mj àíz g» m A H$ àë oh$ àíz A -0 ~ - g 6- X àíz H«$ m H$ 7 d 9 AmÝV[H$ {dh$ën h & 4. àíz H«$ m H$ 6 H$m boim{mì J«m $ non n ~ZmBE& ^mj-a. gyì EH$Ý yzoz nyd}u H$m à moj H$Vo hþe 46 # 99 H$m mz kmv H$s{OE- dm nj 46 4 X{jU nj # / / 4 44 g Ho$V-. JwUH$ A H$ g» m JwÊ A H$ g» m. JwUZ $b JwÊ / JwUH$ dm nj. gyì eyý gmå g wàm o Ûmm g rh$u- x 4 x 6 x x 8 H$m hb kmv H$s{OE& dm nj Ho$ hm H$m moj x 4+ x 6 x 0...() X{jU nj Ho$ hm H$m moj x + x 8 x 0...() XmoZm g wàm g mz hmozo n gyìmzwgm, x 0 0 & x 0 x 0 & x g^r {dúm{w m go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non/s>oñh$ dh $ àmßv H$Zo Ho$ {be H$mo AnZr ³bmg Ho$ ìhmq²>geßn J«wn ES> H$ & AmnH$s ³bmg Ho$ ìhmq²>geßn J«wn non ^oo {XE OmE Jo& &. 00 g» m Ho$ A^mÁ JwUZIÊS>m H$s KmVm H$m moj $b {b{ie& # 7# # AV KmVm H$m moj hmojm& 4. 7sec B 7tn B H$m mz kmv H$s{OE& hm± n, 7sec B 7tn B 7 ^ + tn Bh 7tn B 6 + tn θ sec θ@

6 Pge RBSE Mth 0th Model Pper tn B 7tn B 7. {H$gr g n EH$ no S> H$s nn>mb H$s bå~mb no S> H$s bå~mb H$m JwZm h & Cg g gy H$m CÝZ Z H$moU {H$VZm hmojm? mzm no S> AB H$s nn>mb h & mzm AB x rq>, V~, x rq> mzm + B θ c AB tn θ & tn θ x & θ 0c x 6. Xr JB AmH ${V 4 PQRS EH$ MH«$s MVw^w O h Ohm±, + PQR 60c h & + PSR kmv H$mo& go ~ S>r g» m àmá H$Zo Ho$ n[um 4,,6 ` AZwHy$b n[um m H$s g» m AV A^rîQ> àm{ H$Vm 6 9. {X EH$ g S>H$ n mvm mv {g½zb EH$ Mm mho go H«$ e {ZåZ Xÿ[ m o n bjo h,8,,...vwm ApÝV {g½zb rq> n bjm h & Vmo h kmv H$mo {H$ 0dm± {g½zb {H$VZr Xÿr n bjm h?,8,,..., (àíz H$o AZwgm), d 0 l ^n h d (AÝV go n dm± nx) ^9h 9 8 AV 0dm± {g½zb Mm mho go 9 rq> Xÿ h & 0. nw{bg H$s PCR d Z gwjm H$s ÑpîQ> go N>moQ>r-N>moQ>r ~ÝXÿH o$ j {VO Ho$ gmw 4c H$m H$moU ~ZmVo hþe bjmb JB h & {X ~ÝXÿH$ Ûmm N>mo S>r JB Jmobr 9 rq> OmVr h Vmo Jmobr Ho$ ApÝV ñwmz H$s n Ïdr Vb go D±$MmB H$s JUZm H$s{OE& h OmZVo h sin θ bå~ H$U AB & AB sin θ ` + PQR + + PSR 80c [MH«$s MVw^w O Ho$ gå wi H$moUm H$m moj 80c hmovm h &] 60c + +PSR 80c...$({X m h ) + PSR 0c 7. VrZ Ag oir {~ÝXþAm go JwOZo dmbo d Îmm H$s g» m {b{ie& VrZ {~ÝXþ Omo EH$ gb oim Zht h, go hmoh$ OmZo dmbm EH$ hr d Îm h & 8. EH$ nmgo H$mo $H$m OmVm h Vmo VrZ go ~ S>r g» m àmá H$Zo H$s àm{ H$Vm kmv H$s{OE& nmgo H$mo $H$Zo n Hw$b gå^m{dv n[um 46,,,,, AV Hw$b gå^m{dv n[um m H$s g» m 6 mz IZo n- 9 sin 4c 9 # rq> rq> AV Jmobr Ho$ ApÝV ñwmz H$s n Ïdr Vb go D±$MmB 8 rq> hmojr& g^r Jwê$OZm go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non àmßv H$Zo Ho$ {be n {g $ TEHER eãx ìhmq²>geßn H$ & Amngo g nh $ H$ AmnH$mo {deof ê$n go m S>b non ^ooo OmE Jo&

7 RBSE Mth 0th Model Pper 0 Pge ^mj-~. ^mj {d{y go g» m 689 H$m KZ yb kmv H$s{O o& ^mj {d{y go- [H«$ mnx # 4 # # 4# # 0 0 # AV 689 H$m KZ yb 4 g Ho$V. ApÝV g yh KZ yb A H$ 4 D$n {bim& Z m ^má 49. Z o ^má # 4 # 48 H$m ^mj {X m& 4. ^mj $b A H$ D$n {bim& # 4 # KQ>m m& eof $b, Z m ^má. # 4#, eof $b 0 6. Z m ^má 0 0 AV KZ yb 4. Xem B o {H$ + EH$ An[ o g» m h & mzm {H$ + EH$ n[ o g» m h & ` +, b! 0 b...() Ohm± b, nyumªh$ gh-a^má g» me± h & g rh$u () H$mo {ZåZ àh$m {bi gh$vo h, b XmoZm njm H$m dj H$Zo n, ^ h b k & + b b & b b & b b...() My±{H$ b, nyumªh$ h, AV b EH$ n[ o g» m hmojr& b AV g rh$u () go EH$ n[ o g» m h & O~{H$ h OmZVo h {H$ EH$ An[ o g» m h & AV h n[um {dmoym^mgr h, Bg{bE h mr n[h$ënzm {H$ + EH$ n[ o g» m h, JbV h & AV + EH$ An[ o g» m h & B{V{gÕ. EH$ d Îm Ho$ Mmn H$s bå~mb go r VWm {ÌÁ m 7 go r h & d Îm Ho$ bkw {ÌÁ IÊS> H$m joì $b kmv H$s{OE& {X m h - d Îm Ho$ Mmn H$s bå~mb, ^Lh go r VWm d Îm H$s {ÌÁ m, ^r h 7 go r h OmZVo h {H$ {X Mmn H$s bå~mb ^Lh VWm d Îm H$s {ÌÁ m ^r h h V~ bkw {ÌÁ IÊS> H$m joì $b A L r # 7 # # 6# 7 4 dj go r AV bkw {ÌÁ IÊS> H$m joì $b 4 dj go r 4. EH$ Jmobo H$m n îr>r joì $b 66 dj go r h Vmo Jmobo H$m Am VZ kmv H$s{OE& mzm Jmobo H$s {ÌÁ m r go r Jmobo H$m n îr>r joì $b 66 dj go r 4π r 66 & 4 # r 7 # 66 & r 66 # # & r 49 7 go r Jmobo H$m Am VZ r 4 π 4 # # # # 4# # 7# KZ go r AV Jmobo H$m Am VZ 47. KZ go r. EH$ gryo d rq> D±$Mo nmob Ho$ erf n EH$ CCTV H $ m bjm h Vm{H$ nmob Ho$ erf go rq> Xÿ ÑpîQ> oim Ho$ AmJo ^r mvm mv XoIm Om gho$& Bg pñw{v nmob Ho$ ~mx go dh Xÿr, {OgHo$ AmJo go mvm mv {XImB XoVm h, kmv H$s{OE& {X m h, nmob H$s D±$MmB rq> Xÿ ÑpîQ> oim H$s bå~mb rq> AV ^BC h ^ h ^ABh ^BC h ^h ^h g^r {dúm{w m go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non/s>oñh$ dh $ àmßv H$Zo Ho$ {be H$mo AnZr ³bmg Ho$ ìhmq²>geßn J«wn ES> H$ & AmnH$s ³bmg Ho$ ìhmq²>geßn J«wn non ^oo {XE OmE Jo&

8 Pge 4 RBSE Mth 0th Model Pper 0 BC rq> AV nmob Ho$ nmx go dh Xÿr {OgHo$ AmJo go mvm mv {XImB XoJm rq> hmojr& ^mj-g 6. x x + x H$mo x x go ^mj Xr{OE Am {d^moz EëJmo[Ï H$s gë Vm H$s Om±M H$s{OE& mzm {H$ fx ^ h x x + x VWm gx ^ h x x x + x A~ fx ^ h H$mo g^xh go {d^m{ov H$ Jo& AV ^mj $b q^xh x + VWm eof $b r^xh {d^moz EëJmo[Ï Ho$ à moj go, ^má ^moh$ # ^mj $b + eof $b & x x + x ^ x + x h^ x+ h & x x + x ^x x x + x+ x h & x x + x x x + x & x x + x x x + x My±{H$ ~m m± nj Xm m± nj AV {d^moz EëJmo[Ï gë m{nv hmovm h & {X m h, g mýv lour Ho$ àw m nxm H$m moj $b m,, IZo n, ^S m h 4m m S 4# ^h S 4# ^h 4 S 4# ^h, S S 4 S S 4 9 AV g mýv lour,,9,... h & hm±,, d 8 n 07 ({X m h ) & + ^n h # d 07 & + ^n h # 8 07 & ^n h # 8 07 & ^n h 04 8 & n ] g# 8 + 0# AV n 4 VWm dm± nx 6 8. {H$gr Jbr O rz go m H$s D±$MmB n pñwv EH$ {I S>H$s go Jbr Ho$ Xÿgr Amo pñwv EH$ H$mZ Ho$ {ei VWm nmx Ho$ CÝZ Z VWm AdZ Z H$moU H«$ e 0c VWm 4c h & {XImBE {H$ H$mZ H$s$D±$MmB. 66 m h & ^. 7h mzm {H$ O rz go m H$s D±$MmB n EH$ {I S>H$s P h VWm Jbr Ho$ Xÿgr Amo EH$ H$mZ CD Bg àh$m h {H$ {I S>H$s P go H$mZ Ho$ {ei d nmx Ho$ CÝZ Z d AdZ Z H$moU H«$ e 0c VWm 4c h & mzm H$mZ CD H$s D±$MmB h m h & 7. EH$ g mýv lour Ho$ àw m nxm H$m moj $b 4m m h & {X Bg lour H$m ndm± nx 07 h, Vmo n H$m mz kmv H$s{OE& Bg g mýv lour H$m dm± nx ^r kmv H$s{OE& g^r Jwê$OZm go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non àmßv H$Zo Ho$ {be n {g $ TEHER eãx ìhmq²>geßn H$ & Amngo g nh $ H$ AmnH$mo {deof ê$n go m S>b non ^ooo OmE Jo&

9 RBSE Mth 0th Model Pper 0 Pge T PQC, QD CD CQ CD AP ^h hm QC tn 4c PQ & PQ & PQ m QD T POD, tn 0c PQ & h & h & h & h + # m AV H$mZ H$s D±$MmB. 66 m 9. EH$ T ABC H$s mpü H$mE±, BE Am CF EH$ {~ÝXw G go JwOVr h & {X AG go r, BE go r Am FG go r hmo Vmo, GE Am GC kmv H$s{OE& {MÌ T ABC H$s mpü H$m, BE Am CF h Omo EH$ {~ÝXþ G go JwOVr h & h OmZVo h {H$ {~ÝXþ G mpü H$mAm H$mo o AÝV {d^m{ov H$Vm h & Bg{bE, AG # 7. go r GE BE # 4 go r VWm GC FG # 6 go r 0. EH$ MVw^w O ABCD Ho$ {dh$u nñn {~ÝXþ O n Bg àh$m AO CO à{vàn>ox H$Vo h {H$ BO DO h, Vmo {gõ H$s{OE {H$ ABCD EH$ g bå~ MVw^w O h & {X m h -MVw^w O ABCD AmH ${V Ho$ AZwgm, AO CO BO DO {gõ H$Zm h -ABCD EH$ g bå~ MVw^w O h, BgHo$ {be h AB CD {gõ H$Zm hmojm& MZm-O go OE AB ItMr& Cnn{Îm- m AO BO AO CO T ABC, OE AB ` m CO OA OA CO BO CO ({X m hþam h ) DO BO...() DO CE EB (AmYm^yV g mzwnm{vh$vm à o Ûmm) EB...() CE EB () d () go, DO CE m BO BE DO EC & OE CD ( T BCD o AmYm^yV AmZwnm{VH$ à o Ho$ {dbmo go)...() OE AB (MZm go)...(4) () d (4) go, AB CD AWm V² ABCD EH$ g bå~ MVw^w O h & B{V{gÕ ². {gõ H$mo {H$ MH«$s MVw^w O Ho$ gå wi H$moU w½ gånyh$ m CZH$m moj 80c hmovm h & {X m hþam h - ABCD EH$ MH«$s MVw^w O h & {gõ H$Zm- + A+ + C 80c + B+ + D 80c MZm- O H$mo B d D go { bm m& Cnn{Îm- Mmn DAB Ûmm Ho$ÝÐ n AÝV[V H$moU xc Am d Îm Ho$ eof ^mj n AÝV[V H$moU + C h & AV, + C x c...() Bgr n«h$m Mmn DCB Ûmm Ho$ÝÐ n AÝV[V H$moU yc Am d Îm Ho$ eof ^mj n AÝV[V H$moU + A h & g^r {dúm{w m go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non/s>oñh$ dh $ àmßv H$Zo Ho$ {be H$mo AnZr ³bmg Ho$ ìhmq²>geßn J«wn ES> H$ & AmnH$s ³bmg Ho$ ìhmq²>geßn J«wn non ^oo {XE OmE Jo&

10 Pge 6 RBSE Mth 0th Model Pper 0. Xr JB AmH ${V N>m m {H$V ^mj H$m joì $b kmv H$s{OE, Ohm± ABCD ^wom 4 go r. H$m EH$ dj h & AV + A y c...() g rh$u () d () H$mo Omo S>Zo n, + C+ + A x c + y c ^ h m + C+ + A 60 # c 80c...() My±{H$ MVw^w O Ho$ Mmm H$moU H$m moj 60c hmovm h AV + B+ + D 60c ^+ A+ + Ch m + B+ + D 60c 80c 80c...() B{V{gÕ ². T ABC H$s MZm H$s{OE {OgH$s ^wom BC 4 go r, + B 40c Ed + A 90c hmo& Bg {Ì^wO Ho$ n[jv d Îm H$s MZm H$s{OE Am n[ho$ýð H$s pñw{v H$s Om±Mo H$s{OE& MZm Ho$ MU- dj ABCD H$m joì $b 4 # 4 cm 96 cm àë oh$ d Îm H$m ì mg 4 cm 7 cm Bg{bE àë oh$ d Îm H$s {ÌÁ m 7 cm AV EH$ d Îm H$m joì $b π r 7 cm 7 # # 7 4 cm 77 cm 4 Bg{bE Mmm d Îm H$m joì $b 4 # cm 7 4 cm AV N>m m {H$V joì H$m joì $b ^96 4hcm 4 cm. My±{H$ {Ì^wO + A+ + B+ + C 80c (^wom BC Ho$ C n pñwv H$moU kmv H$Zo Ho$ {be) AV + C 80 ] + A+ + Bg m + C 80 ^ h 0c. T ABC H$s BC 4 go r., + B 40c d + C 0c H$m Cn moj H$ MZm H$s& Bg MZm go + A 90c ñdv àmá hmojm&. AB Ed Ho$ bå~ g {Û^mO ItMH$ n[ho$ýð O àmá {H$ m& 4. n[ho$ýð go EH$ erf A VH$ {ÌÁ m boh$ EH$ d Îm H$s MZm H$s Omo T ABC Ho$ g^r erfm] go JwOVm h & hr T ABC H$m A^rîQ> n[d Îm (n[jv) d Îm h & T ABC EH$ g H$moU {Ì^wO h, {OgH$m n[ho$ýð {Ì^wO Ho$ H$U BC n pñwv h & 4. YmVw Ho$ VrZ KZ, {OZH$s H$moo 4 Ho$ AZwnmV h, H$mo {nkbmh$ EH$ KZ ~Zm m J m h {OgH$m {dh$u go r h & VrZm Kom H$s H$moo kmv H$s{OE& H$mom H$m AZwnmV : 4: mzm H$mo x, 4 x Am x h & ` BZ KZm H$m Am VZ H«$ e 7x, 64x Am x go r hm J & A~ VrZm KZm Ho$ Am VZm H$m moj 7x + 64x + x mzm Z o KZ H$s ^wom 6x go r go r ` Z o KZ H$m {dh$u go r. & ` Z o KZ H$m Am VZ ^h 78 go r g^r Jwê$OZm go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non àmßv H$Zo Ho$ {be n {g $ TEHER eãx ìhmq²>geßn H$ & Amngo g nh $ H$ AmnH$mo {deof ê$n go m S>b non ^ooo OmE Jo& A~, 6x 78 & x 8 & x ` KZ I H$s H$mo # 6 go r KZ II H$s H$mo 4# 8 go r KZ III H$s H$mo # 0 go r

11 RBSE Mth 0th Model Pper 0 Pge 7. Xmo {^ÝZ nmgm H$mo EH$ gmw $H$m OmVm h & àm{ H$Vm ³ m h {H$ XmoZm nmgm n àmá A H$m. H$m moj 9 h?. H$m moj 0 h?. H$m moj H$ -go-h$ 0 h? 4. H$m moj h?. H$m moj m H$ h? 6. o EH$ nmgo n H$m JwUH$ Am Xÿgo n H$m JwUH$ h? O~ Xmo {^ÝZ nmgm H$mo $H$m OmVm h, Vmo g^r g gå^mdr n[um m o H$s g» m 6. XmoZm g» mamo H$m moj 9 AmZo H$s {d{y m± (6,), (,4), (4,) Am (,6) AWm V² 4 h & ` P ( moj 9) XmoZm g» mam H$m moj 0 AmZo H$s {d{y m± (6,4), (,) Am (4,6) h AWm V² h & ` P ( moj 0) 6. moj H$ -go-h$ 0 H$m AW h 0, m ; AV KQ>Zm moj Ý yzv 0 AmZo H$s {d{y m± (6,4), (,), (4,6), (6,), (,6), (6,6) AWm V² 6 h & ` P ( moj H$ -go-h$ 0) Xmo nmgmo H$s $H$ moj H$ämr àmá Zht hmovm h & AV KQ>Zm XmoZm g» mam H$m moj AmZo Ho$ H$moB AZwHy$b n[um Zht h & ` P ( moj ) Xmo nmgm H$s $H$ moj m go H$ AmZo H$s gå^mdzm g^r 6 n[um h & ` P ( moj m go H$ ) nhbo nmgo n H$m JwUH$ Am Xÿgo nmgo n H$m JwUH$ AmZo H$s {d{y m± (,),(,6),(4,),(4,6),(6,)(6,6), (,),(,4),(,6),(6,),(6,4) h & ` KQ>Zm Ho$ AZwHy$b Adgm H$s g» m ` A^rîQ> àm[ H$Vm ^mj-x 6 {X m J m {IH$ g rh$u w½ h - x y+ 4 0 x+ y 8 0 x y+ 4 0 Ho$ J«m $ Ho$ {be h àmá h - y x + 4 m y x + 4 {X x hmo, Vmo y # + 4 VWm {X x # + 4 Vmo y A~ h Vm{bH$m àmá h àmá hþb x 0. y A~, J«m $ x+ y 8 0 Ho$ {be h àmá h - x+ y 8 m y 8 x A~ {X x, V~ y 8 # {ZåZ {IH$ g rh$um Ho$ w½ m H$mo AmboIr {d[y go hb H$s{OE VWm CZ {~ÝXþAm Ho$ {ZX}em H$ ^r kmv H$s{OE Ohm± BZHo$ Ûmm {Zê${nV oime± y-aj H$mo H$mQ>Vr h & 6 x y+ 4 0 x+ y 8 0 A~ {X x, V~ y 8 # 8 6 A~ h Vm{bH$m àmá hþb x y 4 {~ÝXþAm A^, h VWm B^0., h H$mo J«m $ non n Ambo{IV {H$ m J m VWm BÝh { bmh$ x y+ 4 0 H$m J«m $ àmá {H$ m J m& A~ C^4, h VWm A^, h H$mo Bgr J«m $ n Ambo{IV H$ Am BZH$mo { bmh$ x+ y 8 0 H$m J«m $ n«má {H$ m J m& o XmoZmo oim {~ÝXþ (,) n à{vàn>ox H$Vr h & AV x VWm g^r {dúm{w m go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non/s>oñh$ dh $ àmßv H$Zo Ho$ {be H$mo AnZr ³bmg Ho$ ìhmq²>geßn J«wn ES> H$ & AmnH$s ³bmg Ho$ ìhmq²>geßn J«wn non ^oo {XE OmE Jo&

12 Pge 8 RBSE Mth 0th Model Pper 0 y hr BZH$m hb h Am XmoZm gb oim y-aj H$mo {ZX}em H$ ^008,. h Am ( 08.) n H$mQ>Vr h & 7. {gõ H$s{OE {H$- +6 () sin θ sin θ tn θ cos θ cos θ () + sin θ + cos θ sec θ cos θ + sin θ () L.H.S. sin θ sin θ cos θ cos θ sin θ^ sin θh cos θ^cos θ h sin θ sin cos sin cos θ θ+ θ θ cos θ ^sin θ+ cos θh G 6 sin θ+ cos sin θ < cos θ sin θ F cos θ cos θ sin θ cos θ sin θ < cos θ sin θ F cos θ cos θ sin θ sin θ tn θ RHS... B{V{gÕ ² cos θ () L.H.S. + sin θ + cos θ cos θ + sin θ ^ + sin θh + cos θ (LCM bozo n) cos θ^ + sin θh + sin θ+ sin θ+ cos θ cos θ^ + sin θh 6 sin θ+ cos + + sin θ ^ + sin θh cos θ^ + sin θh cos θ^ + sin θh sec θ RHS... cos θ AWdm 7. () ^cosec A sin Ah^sec A cos Ah tn A+ cot A () {X sec θ cosec^θ 6ch hm± θ EH$ Ý yzh$mou h Vmo θ H$m mz kmv H$s{OE& () L.H.S. ^cosec A sin Ah^sec A cos Ah sin A c mc cos Am sin A cos A c sin A mc cos A m sin A cos A cos A c sin A m sin Acos A sin A cos A sin Acos A 6 sin A+ cos A@ sin A+ cos A () {X m h - sin A+ cos A sin A+ cos A sin Acos A sin Acos A sin A + cos A sin Acos A sin Acos A sin A + cos A tn A+ cot A cos A sin A RHS... sec θ cosec^θ 6ch & cosec^90c θ h cosec^θ 6ch & 90c θ θ 6c & θ+ θ 90c+ 6c & 6θ 6c & θ 6 c 6 AV θ c 7 cosec^90c θh sec θa 8. () {X {~ÝXþ A^, h Am {~ÝXþ B H$mo { bmzo dmbo oimiês> H$m Ü {~ÝXþ P^, h hmo, Vmo {~ÝXþ B Ho$ {ZX}em H$ kmv H$s{OE& () {~ÝXþAm P^ 4, h VWm Q^4, h H$mo Omo S>Zo dmbo oimiês> H$mo g {Ì^m{OV H$Zo dmbo {~ÝXþAm Ho$ {ZX}em H$ kmv H$s{OE& +6 () mzm {~ÝXþ Bx ^, yh h Am {X m J m {~ÝXþ P Ü {~ÝXþ h & àízmzwgm, x + + x ` x 4 g^r Jwê$OZm go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non àmßv H$Zo Ho$ {be n {g $ TEHER eãx ìhmq²>geßn H$ & Amngo g nh $ H$ AmnH$mo {deof ê$n go m S>b non ^ooo OmE Jo& y Bgr Vh go, y ` y AV {~ÝXþ B^ 4, h () mzm {H$ Ax ^, yh Am B^x, yh A^rîQ> {~ÝXþ h Omo {~ÝXþAm P^ 4, h Am Q^4, h H$mo Omo S>Zo dmbo oimiês> H$mo g {Ì^m{OV H$Vo h & mzm {H$, PA AB QB x

13 RBSE Mth 0th Model Pper 0 Pge 9 AQ x+ x x PB x+ x x PA x : AQ x Am PB BQ x x : AV {~ÝXþ APQ, H$mo Ho$ AZwnmV VWm {~ÝXþ BPQ, H$mo Ho$ AZwnmV {d^m{ov H$Vr h {~ÝXþ Ho$ {be, x # ^4h+ # ^ h + # ^h + # ^4h y + ` A Ho$ {ZX}em H$ b, l {~ÝXþ B Ho$ {be, 4 ^ h+ ^ h x + y ^ h+ 4 ^ h ` B Ho$ {ZX}em H$ b, 4 l AV A VWm B Ho$ {ZX}em H$ H«$ e b,,, l b 4 l h & 9. Xr JB AmH ${V ABC EH$ {Ì^wO h & {X AB, Vmo {gõ H$s{OE DE BC 6 {X m h, AB AB m XmoZm njm KQ>mZo n, m AB AB BD BD EC EC AV EH$ {Ì^wO H$s ^womam AB Ed H$mo DE g mz AZwnmV {d^m{ov H$Vr h & {gõ H$Zm h - DE BC MZm-D go OmZo dmbr EH$ AÝ oim DF ItMr& Cnn{Îm- mzm {H$ oim DE ^wom BC Ho$ g mýv Zht h VWm D go hmoh$ OmZo dmbr EH$ AÝ oim DF ^wom BC Ho$ g mýv h & AWm V² DF BC AV AmYm^yV AmZwnm{VH$Vm à o go, bo{h$z {X m hþam h DB AF...() FC...() DB EC g r. () VWm () H$mo ~m~ H$Zo n, AF FC XmoZm njm Omo S>Zo n, AF FC + EC + EC AF + FC + EC FC EC FC EC FC EC h V~ hr gå^d h O~ F Ed E XmoZm {~ÝXþ gånmvr hm, AWm V² DF Ed DE gånmvr oime± h & AV DE BC B{V{gÕ ² AWdm 9. AmH ${V, AB Am CD EH$ d Îm H$s Xmo OrdmE± h, Omo E n à{vàn>ox H$Vr h & {gõ H$s{OE {H$ + C (Mmn CXA Ûmm Ho$ÝÐ n AÝV[V H$moU + Mmn DYB Ûmm Ho$ÝÐ n AÝV[V H$moU) h & 6 g^r {dúm{w m go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non/s>oñh$ dh $ àmßv H$Zo Ho$ {be H$mo AnZr ³bmg Ho$ ìhmq²>geßn J«wn ES> H$ & AmnH$s ³bmg Ho$ ìhmq²>geßn J«wn non ^oo {XE OmE Jo&

14 Pge 0 RBSE Mth 0th Model Pper 0 {X m h -AB Ed CD EH$ d Îm H$s Xmo OrdmE± h, Omo E n à{vàn>ox H$Vr h & {gõ H$Zm h -+ C (Mmn CXA Ûmm Ho$ÝÐ n AÝV[V H$moU + Mmn DYB Ûmm Ho$ÝÐ n AÝV[V H$moU) MZm-, BC Ed BD H$mo { bmvo h & Cnn{Îm-AB Ed CD d Îm H$s Xmo OrdmE± h & Omo E n à{vàn>ox H$Vr h & h OmZVo h {H$ EH$ Mmn Ûmm d Îm Ho$ Ho$ÝÐ n AÝV[V H$moU, d Îm Ho$ eof ^mj Ho$ {H$gr {~ÝXþ n AÝV[V H$moU H$m XmoJwZm hmovm h & Mmn CXA, Ho$ÝÐ n + AOC Ed eof ^mj n + ABC AÝV[V H$Vm h & ` + AOC + ABC...() Bgr àh$m, + BOD + BCD...() g rh$u () d () H$mo Omo S>Zo n, + AOC + + BOD ^+ ABC + + BCDh...() {Ì^wO H$m ~{hh$m ou, AmÝV[H$ {dnrv H$moUm Ho$ moj Ho$ ~m~ hmovm h & Bg{bE {Ì^wO CEB, + C + ABC + + BCD...(4) g rh$u () d (4) go, + AOC + + BOD + C & + C ] + AOC + + BOD g AV C + (Mmn CXA Ûmm Ho$ÝÐ n AmÝV[H$ H$moU + Mmn DYB Ûmm Ho$ÝÐ n AÝV[V H$moU 0. {ZåZ ~må~mvm ~ Q>Z Ho$ mü d ~hþbh$ kmv H$s{OE- 6 àmám H$ N>mÌm H$s g» m àmám H$ N>mÌm H$s g» m f ^ h Ü mz x f$ x / f 00 / fx 4460 / fx mü X A H$ / f 00 hm± g~go A{YH$ ~må~mvm 4 g yh (40-0) H$s h AV l 40, f 4, f 0, h 0, f0 8 f f0 gyì ~hþbh$ l + f f f 0 # h # 0 4 ^ h # # ~hþbh$ AV A^rîQ> ~hþbh$ A H$ g^r Jwê$OZm go {ZdoXZ h {H$ RBSE Ho$ gm ëds> m S>b non àmßv H$Zo Ho$ {be n {g $ TEHER eãx ìhmq²>geßn H$ & Amngo g nh $ H$ AmnH$mo {deof ê$n go m S>b non ^ooo OmE Jo&