amOñWmZ ~moS>© narjm 2019-20

10dt H$jm
J{UV
‘m°S>b nona 10
g‘¶ : 3 1 4 K§Q>o (nyUmªH$ : 80)

narjm[W©¶m| Ho$ {bE gm‘mݶ {ZX}e-

1. g^r àíZ H$aZo A{Zdm¶© h¢&
2.
^mJ àíZ g§»¶m A§H$ à˶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 = 2x - 10 ...(2)
XmoZm| g‘wÀM¶ g‘mZ hmoZo na gyÌmZwgma,
1. gyÌ EH$ݶyZoZ nyd}U H$m à¶moJ H$aVo hþE 46 # 99 H$m ‘mZ kmV 2x - 10 = 0 & 2x = 10
H$s{OE- 1
& x = 10 & x = 5
CÎma : 2

dm‘ nj = 46 - 1 = 45 3. 5005 g§»¶m Ho$ A^mÁ¶ JwUZIÊS>m| H$s KmVm| H$m ¶moJ’$b {b{IE&
X{jU nj = 99 - 45 = 54 1
46 # 99 = 46 - 1/99 - 45 CÎma :
5 5005
= 45/54 = 4554
7 1001
g§Ho$V- 11 143
1. JwUH$ A§H$ g§»¶m = Jwʶ A§H$ g§»¶m 13 13
2. JwUZ’$b = Jwʶ - 1/ JwUH$-dm‘nj 1
5005 = 5 # 7 # 11 # 3
2. gyÌ eyݶ gmå¶ g‘wÀM¶o Ûmam g‘rH$aU-
1 + 1 = 1 + 1 H$m hb kmV H$s{OE& AV… KmVm| H$m ¶moJ = 1 + 1 + 1 + 1 + 1 = 5 hmoJm&
x-4 x-6 x-2 x-8
1
CÎma : 4. 7 sec2 B - 7 tan2 B H$m ‘mZ kmV H$s{OE& 1
dm‘ nj Ho$ ham| H$m ¶moJ = x - 4 + x - 6 CÎma :
¶hm± na,
= 2x - 10 ...(1)
7 sec2 B - 7 tan2 B = 7 ^1 + tan2 B h - 7 tan2 B
X{jU nj Ho$ ham| H$m ¶moJ = x - 2 + x - 8
6a 1 + tan2 q = sec2 q@

g^r {dÚm{W©¶m| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona/S>oñH$ dH©$ àmßV H$aZo Ho$ {bE 9460377092 H$mo AnZr ³bmg Ho$
ìhmQ²>gEßn J«wn ‘| ES> H$a|& AmnH$s ³bmg Ho$ ìhmQ²>gEßn J«wn ‘| nona ^oO {XE OmE§Jo&
Page 2 www.rbse.online RBSE Math 10th Model Paper 10

= 7 + 7 tan2 B - 7 tan2 B 3 go ~‹S>r g§»¶m àmá H$aZo Ho$ n[aUm‘ 4,5,6

=7 ` AZwHy$b n[aUm‘m| H$s g§»¶m = 3
AV… A^rîQ> àm{¶H$Vm = 36 = 12
5. {H$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$VZm hmoJm? 1 9. ¶{X EH$ g‹S>H$ na ¶mVm¶mV {g½Zb EH$ Mm¡amho go H«$‘e… {ZåZ Xÿ[a¶m§o
CÎma : na bJo h¢… 3,8,13,.....VWm ApÝV‘ {g½Zb 253 ‘rQ>a na bJm h¡&
Vmo ¶h kmV H$amo {H$ 20dm± {g½Zb {H$VZr Xÿar na bJm h¡? 1
CÎma :
3,8,13, .......,253 (àíZ H$o AZwgma)
a a = 3, d = 5
a20 = l - ^n - 1h d (AÝV go n dm± nX)
= 253 - ^19h 5
= 253 - 95 = 158
‘mZm no‹S> AB H$s naN>mB© AC h¡& AV… 20dm± {g½Zb Mm¡amho go 159 ‘rQ>a Xÿa h¡&
‘mZm AB = x ‘rQ>a, V~, AC = 3 x ‘rQ>a
‘mZm +ACB = qc 10. nw{bg H$s PCR d¡Z ‘| gwajm H$s ÑpîQ> go N>moQ>r-N>moQ>r ~ÝXÿH§o$ j¡{VO
AB = tan q & tan q = x = 1 & q = 30c Ho$ gmW 45c H$m H$moU ~ZmVo hþE bJmB© JB© h¢& ¶{X ~ÝXÿH$ Ûmam N>mo‹S>r
AC 3x 3 JB© Jmobr 195 ‘rQ>a OmVr h¡ Vmo Jmobr Ho$ ApÝV‘ ñWmZ H$s n¥Ïdr
6. Xr JB© AmH¥${V ‘| 4PQRS EH$ MH«$s¶ MVw^w©O h¡ Ohm±, Vb go D±$MmB© H$s JUZm H$s{OE& 1
+PQR = 60c h¡& +PSR kmV H$amo& 1 CÎma :
h‘ OmZVo h¢-
sin q = bå~ = AC
H$U© AB
& AC = AB sin q

CÎma :
+PQR + +PSR = 180c
[MH«$s¶ MVw^w©O Ho$ gå‘wI H$moUm| H$m ¶moJ 180c hmoVm h¡&]
60c + +PSR = 180c ...$({X¶m h¡)
` +PSR = 120c ‘mZ aIZo na-
AC = 195 sin 45c
7. VrZ Ag§aoIr¶ {~ÝXþAm| go JwOaZo dmbo d¥Îmm| H$s g§»¶m {b{IE&
= 195 # 1
1 2
CÎma : = 195 = 137.91 ‘rQ>a
VrZ {~ÝXþ Omo EH$ gab aoIm ‘| Zht h¢, go hmoH$a OmZo dmbm EH$ hr 1.414
d¥Îm h¡& = 138 ‘rQ>a
AV… Jmobr Ho$ ApÝV‘ ñWmZ H$s n¥Ïdr Vb go D±$MmB© 138 ‘rQ>a
8. EH$ nmgo H$mo ’|$H$m OmVm h¡ Vmo VrZ go ~‹S>r g§»¶m àmá H$aZo H$s hmoJr&
àm{¶H$Vm kmV H$s{OE& 1
CÎma :
nmgo H$mo ’|$H$Zo na Hw$b gå^m{dV n[aUm‘ = 1, 2, 3, 4, 5, 6
AV… Hw$b gå^m{dV n[aUm‘m| H$s g§»¶m = 6

g^r Jwê$OZm| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona àmßV H$aZo Ho$ {bE 9460377092 na {g’©$ TEACHER eãX ìhmQ²>gEßn H$a|&
Amngo g§nH©$ H$a AmnH$mo {deof ê$n go ‘m°S>b nona ^oOo OmE|Jo&
RBSE Math 10th Model Paper 10 www.rbse.online Page 3

^mJ-~ 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$s{OE& 3
11. ^mJ {d{Y go g§»¶m 68921 H$m KZ‘yb kmV H$s{O¶o& 2 CÎma :
CÎma : {X¶m h¡-
^mJ {d{Y go- d¥Îm Ho$ Mmn H$s bå~mB©, ^L h = 12 go‘r
[H«$¶mnX . 41 VWm d¥Îm H$s {ÌÁ¶m, ^r h = 7 go‘r
- 43 068921 h‘ OmZVo h¢ {H$ ¶{X Mmn H$s bå~mB© ^Lh VWm d¥Îm H$s {ÌÁ¶m ^r h
- 64
h¡ V~ bKw {ÌÁ¶IÊS> H$m joÌ’$b
- 3 # 42 # 1 49
- 48 A = 1L #r
2
- 3 # 4 # 12 12
2 1
= # 12 # 7
# 1 - 12 2
- 13 01
= 6 # 7 = 42 dJ© go‘r
- 01
# AV… bKw {ÌÁ¶IÊS> H$m joÌ’$b = 42 dJ© go‘r
AV… 68921 H$m KZ‘yb = 41
g§Ho$V… 14. EH$ Jmobo H$m n¥îR>r¶ joÌ’$b 616 dJ© go‘r h¡ Vmo Jmobo H$m Am¶VZ
1. ApÝV‘ g‘yh 68 - 43 = 4 kmV H$s{OE& 2
2. KZ‘yb A§H$ 4 D$na {bIm& Z¶m ^mÁ¶ = 49 CÎma :
2
3. Z¶o ^mÁ¶ ‘| 3 # 4 # 1 = 48 H$m ^mJ {X¶m& ‘mZm Jmobo H$s {ÌÁ¶m = r go‘r
4. ^mJ’$b A§H$ 1 D$na {bIm& 3 # 42 # 1 KQ>m¶m& eof’$b
Jmobo H$m n¥îR>r¶ joÌ’$b = 616 dJ© go‘r
= 1, Z¶m ^mÁ¶ = 12
5. 12 - 3 # 4 # 12 = 12 , eof’$b = 0 4pr2 = 616
6. Z¶m ^mÁ¶ = 01 - 13 = 0 & 4 # 22 # r2 = 616
7
AV… KZ‘yb = 41 2 616 # 7
& r = = 49
4 # 22
12. Xem©B¶o {H$ 2 + 5 EH$ An[a‘o¶ g§»¶m h¡& 2 & r = 49 = 7 go‘r
CÎma :
Jmobo H$m Am¶VZ = 34 pr3
‘mZm {H$ 2 + 5 EH$ n[a‘o¶ g§»¶m h¡&
2+ 5 = a,b ! 0 ...(1) = 4 # 22 # 7 # 7 # 7
`
b 3 7
Ohm± a, b nyUmªH$ gh-A^mÁ¶ g§»¶mE± h¢& = # #7#7
4 22
3
g‘rH$aU (1) H$mo {ZåZ àH$ma {bI gH$Vo h¢, = 1437.33 KZ go‘r
5 =a- 2 AV… Jmobo H$m Am¶VZ = 1437.33 KZ go‘r
b
XmoZm| njm| H$m dJ© H$aZo na,
^ 5 h = aa - 2 k 15. EH$ grYo d 12 ‘rQ>a D±$Mo nmob Ho$ erf© na EH$ CCTV H¡$‘am bJm
2 2
b h¡ Vm{H$ nmob Ho$ erf© go 13 ‘rQ>a Xÿa ÑpîQ> aoIm Ho$ AmJo ^r ¶mVm¶mV
2
& 5 = a2 + 2 - 2 2 a XoIm Om gHo$& Bg pñW{V ‘| nmob Ho$ ~mX go dh Xÿar, {OgHo$ AmJo go
b b
¶mVm¶mV {XImB© XoVm h¡, kmV H$s{OE& 2
2
& 2 2 a = a2 - 3 CÎma :
b b
2 2
& 2 = a - 3b ...(2) {X¶m h¡, nmob H$s D±$MmB© = 12 ‘rQ>a
2ab
2 2
Xÿa ÑpîQ> aoIm H$s bå~mB© = 13 ‘rQ>a
My±{H$… a, b nyUmªH$ h¡, AV… a 2-ab3b EH$ n[a‘o¶ g§»¶m hmoJr& AV… ^BC h2 = ^AC h2 - ^AB h2
AV… g‘rH$aU (2) go 2 EH$ n[a‘o¶ g§»¶m h¡& O~{H$ h‘ OmZVo = ^13h - ^12h
2 2

h¢ {H$ 2 EH$ An[a‘o¶ g§»¶m h¡& AV… ¶h n[aUm‘ {damoYm^mgr

= 169 - 144
h¡, Bg{bE h‘mar n[aH$ënZm {H$ 2 + 5 EH$ n[a‘o¶ g§»¶m h¡,
JbV h¡& ^BC h2 = 25
AV… 2 + 5 EH$ An[a‘o¶ g§»¶m h¡& B{V{gÕ‘
g^r {dÚm{W©¶m| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona/S>oñH$ dH©$ àmßV H$aZo Ho$ {bE 9460377092 H$mo AnZr ³bmg Ho$
ìhmQ²>gEßn J«wn ‘| ES> H$a|& AmnH$s ³bmg Ho$ ìhmQ²>gEßn J«wn ‘| nona ^oO {XE OmE§Jo&
Page 4 www.rbse.online RBSE Math 10th Model Paper 10

BC = 25 = 5 ‘rQ>a {X¶m h¡, g‘mÝVa loUr Ho$ àW‘ m nXm| H$m ¶moJ’$b
^Sm h = 4m2 - m
m = 1, 2, 3 aIZo na,
S1 = 4 # ^1 h2 - 1 = 3
S2 = 4 # ^2 h2 - 2 = 14
S3 = 4 # ^3 h2 - 3 = 33
a = a1 = 3 , a2 = S2 - S1
= 14 - 3 = 11
AV… nmob Ho$ nmX go dh Xÿar {OgHo$ AmJo go ¶mVm¶mV {XImB© XoJm
a3 = S3 - S2 = 33 - 14 = 19
= 5 ‘rQ>a hmoJr&
AV… g‘mÝVa loUr 3,11,19,... h¢&
¶hm±, a = 3 , d = 11 - 3 = 8
^mJ-g
an = 107 ({X¶m h¡)
16. x3 - 3x2 + 3x - 5 H$mo x - 1 - x2 go ^mJ Xr{OE Am¡a {d^mOZ & a + ^n - 1h # d = 107
EëJmo[aÏ‘ H$s g˶Vm H$s Om±M H$s{OE& 3 & 3 + ^n - 1h # 8 = 107
CÎma : & ^n - 1h # 8 = 107 - 3
‘mZm {H$
^n - 1h = 104
f ^x h = x3 - 3x2 + 3x - 5
&
8
n = 13 + 1 = 14
g ^x h = x - 1 - x2 = - x2 + x - 1
&
VWm
A~ f ^x h H$mo g ^x h go {d^m{OV H$a|Jo& a21 = 3 + ]21 - 1g # 8
= 3 + 20 # 8
= 3 + 160 = 163
AV… n = 14 VWm 21dm± nX = 163

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$mZ
AV… ^mJ’$b q ^x h = - x + 2 H$s$D±$MmB© 23.66 m h¡& ^ 3 = 1.732h 3
VWm eof’$b r ^x h = - 3 CÎma :
{d^mOZ EëJmo[aÏ‘ Ho$ à¶moJ go, ‘mZm {H$ O‘rZ go 15 m H$s D±$MmB© na EH$ {I‹S>H$s P h¡ VWm Jbr
^mÁ¶ = ^mOH$ # ^mJ’$b + eof’$b Ho$ Xÿgar Amoa EH$ ‘H$mZ CD Bg àH$ma h¡ {H$ {I‹S>H$s P go ‘H$mZ
Ho$ {eIa d nmX Ho$ CÝZ¶Z d AdZ‘Z H$moU H«$‘e… 30c VWm 45c
& x - 3x + 3x - 5 = ^- x2 + x - 1h^- x + 2h - 3
3 2
h¢& ‘mZm ‘H$mZ CD H$s D±$MmB© h m h¡&
& x3 - 3x2 + 3x - 5 = ^x3 - 2x2 - x2 + 2x + x - 2h
-3
& x3 - 3x2 + 3x - 5 = x3 - 3x2 + 3x - 2 - 3
& x3 - 3x2 + 3x - 5 = x3 - 3x2 + 3x - 5
My±{H$… ~m¶m± nj = Xm¶m± nj
AV… {d^mOZ EëJmo[aÏ‘ g˶m{nV hmoVm h¡&

17. EH$ g‘mÝVa loUr Ho$ àW‘ m nXm| H$m ¶moJ’$b 4m2 - m h¡& ¶{X
Bg loUr H$m n dm± nX 107 h¡, Vmo n H$m ‘mZ kmV H$s{OE& Bg
g‘mÝVa loUr H$m 21dm± nX ^r kmV H$s{OE& 3
CÎma :
g^r Jwê$OZm| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona àmßV H$aZo Ho$ {bE 9460377092 na {g’©$ TEACHER eãX ìhmQ²>gEßn H$a|&
Amngo g§nH©$ H$a AmnH$mo {deof ê$n go ‘m°S>b nona ^oOo OmE|Jo&
RBSE Math 10th Model Paper 10 www.rbse.online Page 5

TPQC ‘|, QD = CD - CQ = CD - AP
= ^h - 15h m
QC
tan 45c =
PQ
& 15
1 = PQ
& PQ = 15 m
QD
TPOD ‘|, tan 30c =
PQ
& 1 = h - 15 AO = CO
3 15 BO DO
& h - 15 = 15 & h - 15 = 5 3 {gÕ H$aZm h¡- ABCD EH$ g‘bå~ MVw^w©O h¡, BgHo$ {bE h‘|
3
AB = CD {gÕ H$aZm hmoJm&
& h = 15 + 5 # 1.732 = 23.66 m
aMZm-O go OE | | AB ItMr&
AV… ‘H$mZ H$s D±$MmB© = 23.66 m AO = CO
Cnn{Îm- BO DO
({X¶m hþAm h¡)
19. EH$ TABC H$s ‘mpܶH$mE± AD, BE Am¡a CF EH$ {~ÝXw G go ¶m AO = BO ...(1)
JwOaVr h¢& ¶{X AG = 5 go‘r, BE = 12 go‘r Am¡a FG = 3 CO DO
go‘r hmo Vmo AD, GE Am¡a GC kmV H$s{OE& 3 TABC ‘|, OE || AB
CO = CE
CÎma : `
OA EB
{MÌ ‘| TABC H$s ‘mpܶH$m¶| AD, BE Am¡a CF h¢ Omo EH$ (AmYma^yV g‘mZwnm{VH$Vm à‘o¶ Ûmam)
{~ÝXþ G go JwOaVr h¢& OA
¶m = EB ...(2)
h‘ OmZVo h¢ {H$ {~ÝXþ G ‘mpܶH$mAm| H$mo 2…1 ‘§o AÝV… {d^m{OV CO CE
H$aVm h¡& (1) d (2) go, BO = EB
DO CE
¶m BO = BE
DO EC
& OE || CD (TBCD Ԥo AmYma^yV
AmZwnm{VH$ à‘o¶ Ho$ {dbmo‘ go) ...(3)
a OE || AB (aMZm go) ...(4)
(3) d (4) go, AB || CD
AWm©V² ABCD EH$ g‘bå~ MVw^w©O h¡& B{V{gÕ‘²

21. {gÕ H$amo {H$ MH«$s¶ MVw^w©O Ho$ gå‘wI H$moU ¶w½‘ gånyaH$ ¶m CZH$m
Bg{bE, AD = 3 AG
2 ¶moJ 180c hmoVm h¡& 3
= 3#5 CÎma :
2
{X¶m hþAm h¡- ABCD EH$ MH«$s¶ MVw^w©O h¡&
= 15 = 7.5 go‘r
2 {gÕ H$aZm- +A + +C = 180c
GE = 1 BE +B + +D 180c
3
= 1 # 12 = 4 go‘r aMZm- O H$mo B d D go {‘bm¶m&
3
VWm GC = 2FG = 2 # 3 = 6 go‘r
Cnn{Îm- Mmn DAB Ûmam Ho$ÝÐ na AÝV[aV H$moU xc Am¡a d¥Îm Ho$
eof ^mJ na AÝV[aV H$moU +C h¡&
20. EH$ MVw^w©O ABCD Ho$ {dH$U© nañna {~ÝXþ O na Bg àH$ma AV…, +C = 1 xc ...(1)
2
BO = DO h¡, Vmo {gÕ H$s{OE {H$ ABCD
à{VÀN>oX H$aVo h¢ {H$ AO CO

EH$ g‘bå~ MVw^w©O h¡& 3 Bgr n«H$ma Mmn DCB Ûmam Ho$ÝÐ na AÝV[aV H$moU yc Am¡a d¥Îm Ho$
CÎma : eof ^mJ na AÝV[aV H$moU +A h¡&
{X¶m h¡-MVw^w©O ABCD ‘| AmH¥${V Ho$ AZwgma,

g^r {dÚm{W©¶m| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona/S>oñH$ dH©$ àmßV H$aZo Ho$ {bE 9460377092 H$mo AnZr ³bmg Ho$
ìhmQ²>gEßn J«wn ‘| ES> H$a|& AmnH$s ³bmg Ho$ ìhmQ²>gEßn J«wn ‘| nona ^oO {XE OmE§Jo&
Page 6 www.rbse.online RBSE Math 10th Model Paper 10

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

AV… +A = 1 yc ...(2)
2 CÎma :
g‘rH$aU (1) d (2) H$mo Omo‹S>Zo na,
dJ© ABCD H$m joÌ’$b = 14 # 14 cm2
+C + +A = 1 ^xc + ych
2 = 196 cm2
¶m +C + +A = 1 # 360c = 180c ...(3) à˶oH$ d¥Îm H$m ì¶mg 14 cm = 7 cm
2 2
My±{H$ MVw^w©O Ho$ Mmam| H$moU H$m ¶moJ 360c hmoVm h¡ Bg{bE à˶oH$ d¥Îm H$s {ÌÁ¶m = 72 cm
AV… +B + +D = 360c - ^+A + +C h AV… EH$ d¥Îm H$m joÌ’$b = pr2
¶m +B + +D = 360c - 180c = 180c ...(3) = 22 # 7 # 7 cm2
7 2 2
B{V{gÕ‘²
= 154 cm = 77 cm2
4 2
22. TABC H$s aMZm H$s{OE {OgH$s ^wOm BC = 4 go‘r, 22 2
+B = 40c Ed§ +A = 90c hmo& Bg {Ì^wO Ho$ n[aJV d¥Îm H$s
Bg{bE Mmam| d¥Îm H$m joÌ’$b = 4 # 7 cm
aMZm H$s{OE Am¡a n[aHo$ÝÐ H$s pñW{V H$s Om±Mo H$s{OE& 3 = 154 cm2
CÎma : AV… N>m¶m§{H$V joÌ H$m joÌ’$b = ^196 - 154hcm2
aMZm Ho$ MaU-
= 42 cm2

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$s{OE& 3
CÎma :
H$moam| H$m AZwnmV = 3 : 4 : 5
‘mZm H$moa 3x, 4x Am¡a 5x h¡&
` BZ KZm| H$m Am¶VZ H«$‘e… 27x3, 64x3 Am¡a 125x3 go‘r3 hm|J|&
A~ VrZm| KZm| Ho$ Am¶VZm| H$m ¶moJ = 27x3 + 64x3 + 125x3
1. My±{H$ {Ì^wO ‘| +A + +B + +C = 180c (^wOm BC Ho$ = 216x3 go‘r3
C na pñWV H$moU kmV H$aZo Ho$ {bE)
‘mZm Z¶o KZ H$s ^wOm = a go‘r
AV… +C = 180 - ]+A + +B g
` Z¶o KZ H$m {dH$U© = a 3 go‘r.
¶m +C = 180 - ^90 + 40h = 50c
a 3 = 12 3 & a = 12
2. TABC H$s BC = 4 go‘r., +B = 40c d +C = 50c
H$m Cn¶moJ H$a aMZm H$s& Bg aMZm go +A = 90c ñdV… ` Z¶o KZ H$m Am¶VZ = ^12h3 = 1728 go‘r3
àmá hmoJm& A~, 216x3 = 1728
3. AB Ed§ AC Ho$ bå~ g‘{Û^mO ItMH$a n[aHo$ÝÐ O àmá
& x3 = 8
{H$¶m&
4. n[aHo$ÝÐ go EH$ erf© A VH$ {ÌÁ¶m boH$a EH$ d¥Îm H$s aMZm H$s & x =2
Omo TABC Ho$ g^r erfm] go JwOaVm h¡& ` KZ I H$s H$moa = 3 # 2 = 6 go‘r
¶hr TABC H$m A^rîQ> n[ad¥Îm (n[aJV) d¥Îm h¡& TABC EH$
KZ II H$s H$moa = 4 # 2 = 8 go‘r
g‘H$moU {Ì^wO h¡, {OgH$m n[aHo$ÝÐ {Ì^wO Ho$ H$U© BC na pñWV h¡&
KZ III H$s H$moa = 5 # 2 = 10 go‘r
g^r Jwê$OZm| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona àmßV H$aZo Ho$ {bE 9460377092 na {g’©$ TEACHER eãX ìhmQ²>gEßn H$a|&
Amngo g§nH©$ H$a AmnH$mo {deof ê$n go ‘m°S>b nona ^oOo OmE|Jo&
RBSE Math 10th Model Paper 10 www.rbse.online Page 7

25. Xmo {^ÝZ nmgm| H$mo EH$ gmW ’|$H$m OmVm h¡& àm{¶H$Vm ³¶m h¡ {H$ XmoZm| CÎma :
nmgm| na àmá A§H$m|… 3 {X¶m J¶m a¡{IH$ g‘rH$aU ¶w½‘ h¡-
1. H$m ¶moJ 9 h¡? 2x - 5y + 4 = 0
2. H$m ¶moJ 10 h¡? 2x + y - 8 = 0
3. H$m ¶moJ H$‘-go-H$‘ 10 h¡? 2x - 5y + 4 = 0 Ho$ J«m’$ Ho$ {bE h‘| àmá h¡-
4. H$m ¶moJ 13 h¡?
5. H$m ¶moJ 12 ¶m H$‘ h¡? 5y = 2x + 4
6. ‘§o EH$ nmgo na 2 H$m JwUH$ Am¡a Xÿgao na 3 H$m JwUH$ h¡? ¶m y = 2x + 4
5
CÎma :
O~ Xmo {^ÝZ nmgm| H$mo ’|$H$m OmVm h¡, Vmo g^r g‘ gå^mdr n[aUm‘m§o ¶{X x = 3 hmo, Vmo y = # 3 + 4 = 6 + 4 = 10 = 2
2
5 5 5
H$s g§»¶m = 36 1
2# +4
1. XmoZm| g§»¶mAmo§ H$m ¶moJ 9 AmZo H$s {d{Y¶m± (6,3), (5,4), VWm ¶{X x = 12 Vmo y = 2 = 1+4 = 5 = 1
5 5 5
(4,5) Am¡a (3,6) AWm©V² 4 h¡&
A~ ¶h Vm{bH$m àmá h‘| àmá hþB©-
` P (¶moJ 9) = 4 = 1
36 9
x 3 0.5
2. XmoZm| g§»¶mAm| H$m ¶moJ 10 AmZo H$s {d{Y¶m± (6,4), (5,5) Am¡a
y 2 1
(4,6) h¡ AWm©V² 3 h¡&
` P (¶moJ 10) = 3 = 1
36 12
3. ¶moJ H$‘-go-H$‘ 10 H$m AW© h¡ 10,11 ¶m 12; AV… KQ>Zm
¶moJ ݶyZV‘ 10 AmZo H$s {d{Y¶m± (6,4), (5,5), (4,6),
(6,5), (5,6), (6,6) AWm©V² 6 h¢&
` P (¶moJ H$‘-go-H$‘ 10) = 6 = 1
36 6
4. Xmo nmgmo§ H$s ’|$H$ ‘| ¶moJ 13 H$ämr àmá Zht hmoVm h¡& AV… KQ>Zm
XmoZm| g§»¶mAm| H$m ¶moJ 13 AmZo Ho$ H$moB© AZwHy$b n[aUm‘ Zht
h¢&
` P (¶moJ 13) = 0 = 0
36
5. Xmo nmgm| H$s ’|$H$ ‘| ¶moJ 12 ¶m 12 go H$‘ AmZo H$s gå^mdZm¶|
g^r 36 n[aUm‘ h¢&
` P (¶moJ 12 ¶m 12 go H$‘) = 36 = 1
36

6. nhbo nmgo na 2 H$m JwUH$ Am¡a Xÿgao nmgo na 3 H$m JwUH$

AmZo H$s {d{Y¶m± (2,3),(2,6),(4,3),(4,6),(6,3)(6,6),
(3,2),(3,4),(3,6),(6,2),(6,4) h¢&
A~, J«m’$ 2x + y - 8 = 0 Ho$ {bE h‘| àmá h¡-
` KQ>Zm Ho$ AZwHy$b Adgam| H$s g§»¶m = 11
2x + y = 8 ¶m y = 8 - 2x
` A^rîQ> àm[¶H$Vm = 11
36 A~ ¶{X x = 2 , V~ y = 8 - 2 # 2 = 8 - 4 = 4
A~ ¶{X x = 3 , V~ y = 8 - 2 # 3 = 8 - 6 = 2
^mJ-X A~ ¶h Vm{bH$m àmá hþB©-

26. {ZåZ a¡{IH$ g‘rH$aUm| Ho$ ¶w½‘m| H$mo AmboIr¶ {d[Y go hb H$s{OE x 2 3
VWm CZ {~ÝXþAm| Ho$ {ZX}em§H$ ^r kmV H$s{OE Ohm± BZHo$ Ûmam y 4 2
{Zê${nV aoImE± y -Aj H$mo H$mQ>Vr h¢& 6 {~ÝXþAm| A ^3, 2h VWm B ^0.5, 1h H$mo J«m’$ nona na Ambo{IV {H$¶m
2x - 5y + 4 = 0
J¶m VWm BÝh| {‘bmH$a 2x - 5y + 4 = 0 H$m J«m’$ àmá {H$¶m
J¶m& A~ C ^2, 4h VWm A ^3, 2h H$mo Bgr J«m’$ na Ambo{IV H$a
2x + y - 8 = 0 Am¡a BZH$mo {‘bmH$a 2x + y - 8 = 0 H$m J«m’$ n«má {H$¶m J¶m& ¶o
XmoZmo§ a§oIm¶| {~ÝXþ (3,2) na à{VÀN>oX H$aVr h¢& AV… x = 3 VWm
g^r {dÚm{W©¶m| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona/S>oñH$ dH©$ àmßV H$aZo Ho$ {bE 9460377092 H$mo AnZr ³bmg Ho$
ìhmQ²>gEßn J«wn ‘| ES> H$a|& AmnH$s ³bmg Ho$ ìhmQ²>gEßn J«wn ‘| nona ^oO {XE OmE§Jo&
Page 8 www.rbse.online RBSE Math 10th Model Paper 10

y = 2 hr BZH$m hb h¡ Am¡a XmoZm| gab aoIm¶| y -Aj H$mo {ZX}em§H$ = 1 = 1

^0, 0.8h Am¡a (0.8) na H$mQ>Vr h¢& sin2 A + cos2 A sin2 A + cos2 A
sin A cos A sin A cos A
= 1
27. {gÕ H$s{OE {H$- 3+3=6 sin2 A + cos2 A
3
sin A cos A sin A cos A
(1) sin q 3- 2 sin q = tan q
2 cos q - cos q 1 1
= =
sin q + cos q = 2 sec q sin A + cos A tan A + cot A
(2) 1 +
cos q 1 + sin q cos A sin A
CÎma : = R.H.S.
3
(1) L.H.S. = sin q 3- 2 sin q (2) {X¶m h¡-
2 cos q - cos q
sin q ^1 - 2 sin2 qh sec 5q = cosec ^q - 36ch
=
cos q ^2 cos2 q - 1h & cosec ^90c - 5qh = cosec ^q - 36ch
2 2 2
= sin q = sin 2q + cos q2 - 2 sin 2 q G 7a cosec ^90c - qh = sec qA
cos q 2 cos q - ^sin q + cos qh

6a sin2 q + cos2 q = 1@ & 90c - 5q = q - 36c

cos2 q - sin2 q & 5q + q = 90c + 36c

= sin q < F
cos q 2 cos q - sin2 q - cos2 q
2
& 6q = 126c
2 2
= sin q < cos2 q - sin2 q F & q = 126 = 21c
cos q cos q - sin q 6
AV… q = 21c
= sin q = tan q = R.H.S. B{V{gÕ‘²
cos q
28. (1) ¶{X {~ÝXþ A ^2, 5h Am¡a {~ÝXþ B H$mo {‘bmZo dmbo aoImIÊS>
(2) L.H.S. = 1 + sin q + cos q H$m ‘ܶ {~ÝXþ P ^- 1, 2h hmo, Vmo {~ÝXþ B Ho$ {ZX}em§H$ kmV
cos q 1 + sin q
H$s{OE&
^1 + sin qh2 + cos2 q
=
cos q ^1 + sin qh
(LCM boZo na) (2) {~ÝXþAm| P ^- 3, 4h VWm Q ^4, 5h H$mo Omo‹S>Zo dmbo aoImIÊS> H$mo
2 2
g‘{Ì^m{OV H$aZo dmbo {~ÝXþAm| Ho$ {ZX}em§H$ kmV H$s{OE&
= 1 + sin q + 2 sin q + cos q
cos q ^1 + sin qh
3+3=6
CÎma :
6a sin2 q + cos2 q = 1@
(1) ‘mZm {~ÝXþ B ^x1, y1h h¡ Am¡a {X¶m J¶m {~ÝXþ P ‘ܶ {~ÝXþ h¡&
2 ^1 + sin qh
= 1 + 1 + 2 sin q =
cos q ^1 + sin qh cos q ^1 + sin qh
= 2 = 2 sec q = R.H.S.
cos q

AWdm àíZmZwgma, - 1 = 2 + x1
2
- 2 = 2 + x1 ` x1 = - 4
27. (1) ^cosec A - sin Ah^sec A - cos Ah = tan A +
1
cot A 5 + y1
Bgr Vah go, 2 =
3 2
(2) ¶{X sec 5q = cosec ^q - 36ch ¶hm± 5q EH$ ݶyZH$moU h¡ Vmo 4 = 5 + y1 ` y1 = - 1
q H$m ‘mZ kmV H$s{OE& 3 AV… {~ÝXþ B ^- 4, - 1h
CÎma :
(1) L.H.S. = ^cosec A - sin Ah^sec A - cos Ah (2) ‘mZm {H$ A ^x1, y1h Am¡a B ^x2, y2h A^rîQ> {~ÝXþ h¢ Omo {~ÝXþAm|
P ^- 3, 4h Am¡a Q ^4, 5h H$mo Omo‹S>Zo dmbo aoImIÊS> H$mo g‘{Ì^m{OV
= c 1 - sin A mc 1 - cos A m
sin A cos A H$aVo h¢&
2
=c 1 - sin A mc 1 - cos2 A m
sin A cos A
2 2
= cos A c sin A m = sin A cos A
sin A cos A 1
= sin A cos A 6a 1 = sin2 A + cos2 A@
sin2 A + cos2 A ‘mZm {H$, PA = AB = QB = x
g^r Jwê$OZm| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona àmßV H$aZo Ho$ {bE 9460377092 na {g’©$ TEACHER eãX ìhmQ²>gEßn H$a|&
Amngo g§nH©$ H$a AmnH$mo {deof ê$n go ‘m°S>b nona ^oOo OmE|Jo&
RBSE Math 10th Model Paper 10 www.rbse.online Page 9

AQ = x + x = 2x
PB = x + x = 2x
PA = x = 1 = 1 : 2
AQ 2x 2
Am¡a PB = 2x = 2 = 2 : 1
BQ x 1
AV… {~ÝXþ A, PQ H$mo 1…2 Ho$ AZwnmV ‘| VWm {~ÝXþ B, PQ H$mo
2…1 Ho$ AZwnmV ‘| {d^m{OV H$aVr h¡ {~ÝXþ Ho$ {bE,
1 ^4 h + 2 # ^- 3h AV… EH$ {Ì^wO H$s ^wOmAm| AB Ed§ AC H$mo DE g‘mZ AZwnmV
x1 = # = 4 - 6 = -2
1+2 3 3 ‘| {d^m{OV H$aVr h¡&
1 # ^5 h + 2 # ^4 h {gÕ H$aZm h¡- DE | | BC
y1 = = 5 + 8 = 13
2+1 3 3 aMZm- D go OmZo dmbr EH$ Aݶ aoIm DF ItMr&
` A Ho$ {ZX}em§H$ b- , l
2 13 Cnn{Îm-‘mZm {H$ aoIm DE ^wOm BC Ho$ g‘mÝVa Zht h¡ VWm D
3 3
{~ÝXþ B Ho$ {bE, go hmoH$a OmZo dmbr EH$ Aݶ aoIm DF ^wOm BC Ho$ g‘mÝVa h¡&
2 ^4 h + 1 ^- 3h AWm©V² DF || BC
x2 = = 8-3 = 5
2+1 3 3 AV… AmYma^yV AmZwnm{VH$Vm à‘o¶ go,
2 ^5 h + 1 ^4 h
y2 = = 10 + 4 = 14 AD = AF ...(1)
2+1 3 3 DB FC
bo{H$Z {X¶m hþAm h¡
` B Ho$ {ZX}em§H$ b 5 , 14 l AD = AE
3 3 ...(2)
DB EC
AV… A VWm B Ho$ {ZX}em§H$ H«$‘e… b- 32 , 13
3 l b3 3 l
, 5 , 14 h¢&
g‘r. (1) VWm (2) H$mo ~am~a H$aZo na,
AF = AE
29. Xr JB© AmH¥${V ‘| ABC EH$ {Ì^wO h¡& ¶{X AD
AB
= AE , Vmo {gÕ
AC FC EC
H$s{OE DE | | BC 6 XmoZm| njm| ‘| 1 Omo‹S>Zo na,
AF + 1 = AE + 1
FC EC
AF + FC = AE + EC
FC EC
AC = AC
FC EC
FC = EC
¶h V~ hr gå^d h¡ O~ F Ed§ E XmoZm| {~ÝXþ gånmVr hm|, AWm©V²
DF Ed§ DE gånmVr aoImE± h¢& AV… DE | | BC B{V{gÕ‘²
CÎma :
AD = AE AWdm
{X¶m h¡, AB AC
¶m AB = AC 29. AmH¥${V ‘|, AB Am¡a CD EH$ d¥Îm H$s Xmo OrdmE± h¢, Omo E na
AD AE à{VÀN>oX H$aVr h¢& {gÕ H$s{OE {H$ +AEC = 12 (Mmn CXA
XmoZm| njm| ‘| 1 KQ>mZo na, Ûmam Ho$ÝÐ na AÝV[aV H$moU + Mmn DYB Ûmam Ho$ÝÐ na AÝV[aV
¶m AB - 1 = AC - 1 H$moU) h¡& 6
AD AE
AB - AD = AC - AE
AD AE
BD = EC
AD AE
AD = AE
BD EC

g^r {dÚm{W©¶m| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona/S>oñH$ dH©$ àmßV H$aZo Ho$ {bE 9460377092 H$mo AnZr ³bmg Ho$
ìhmQ²>gEßn J«wn ‘| ES> H$a|& AmnH$s ³bmg Ho$ ìhmQ²>gEßn J«wn ‘| nona ^oO {XE OmE§Jo&
Page 10 www.rbse.online RBSE Math 10th Model Paper 10

CÎma : AV… +AEC = 12 (Mmn CXA Ûmam Ho$ÝÐ na AmÝV[aH$ H$moU

{X¶m h¡- AB Ed§ CD EH$ d¥Îm H$s Xmo OrdmE± h¢, Omo E na à{VÀN>oX + Mmn DYB Ûmam Ho$ÝÐ na AÝV[aV H$moU
H$aVr h¢&
{gÕ H$aZm h¡-+AEC = 12 (Mmn CXA Ûmam Ho$ÝÐ na AÝV[aV 30. {ZåZ ~maå~maVm ~§Q>Z Ho$ ‘mܶ d ~hþbH$ kmV H$s{OE- 6
H$moU + Mmn DYB Ûmam Ho$ÝÐ na AÝV[aV H$moU)
àmám§H$ 20-30 30-40 40-50 50-60 60-70
aMZm- AC, BC Ed§ BD H$mo {‘bmVo h¢& N>mÌm| H$s 4 28 42 20 6
Cnn{Îm- AB Ed§ CD d¥Îm H$s Xmo OrdmE± h¢& Omo E na à{VÀN>oX g§»¶m
H$aVr h¢& CÎma :
àmám§H$ N>mÌm| H$s g§»¶m ‘ܶ‘mZ x f$x
^f h
20-30 4 25 100
30-40 28 35 980
40-50 42 45 1890
50-60 20 55 1100
60-70 6 65 390

h‘ OmZVo h¢ {H$ EH$ Mmn Ûmam d¥Îm Ho$ Ho$ÝÐ na AÝV[aV H$moU, d¥Îm /f = 100 /fx = 4460
Ho$ eof ^mJ Ho$ {H$gr {~ÝXþ na AÝV[aV H$moU H$m XmoJwZm hmoVm h¡& /fx
‘mܶ X = = 4460 = 44.60 A§H$
Mmn CXA , Ho$ÝÐ na +AOC Ed§ eof ^mJ na +ABC AÝV[aV /f 100
H$aVm h¡& ¶hm± g~go A{YH$ ~maå~maVm 42 g‘yh (40-50) H$s h¡
` +AOC = 2+ABC ...(1) AV… l = 40 , f1 = 42 , f2 = 20 , h = 10 , f0 = 28
1 - f0
Bgr àH$ma, +BOD = 2+BCD ...(2) gyÌ ~hþbH$ = l + 2f f- f0 - f2 #
h
1
g‘rH$aU (1) d (2) H$mo Omo‹S>Zo na,
= 40 + 42 - 28
+AOC + +BOD = 2 ^+ABC + +BCD h # 10
....(3) 2 ^42h - 28 - 20
{Ì^wO H$m ~{hH$m©oU, AmÝV[aH$ {dnarV H$moUm| Ho$ ¶moJ Ho$ ~am~a hmoVm
= 40 + 14 10
h¡& 84 - 48 #
Bg{bE {Ì^wO CEB ‘|,
= 40 + 14 # 10
+AEC = +ABC + +BCD ...(4) 36
g‘rH$aU (3) d (4) go, = 40 + 140 = 40 + 3.89
36
+AOC + +BOD = 2+AEC ~hþbH$ = 43.89
& +AEC = 1 ]+AOC + +BODg AV… A^rîQ> ~hþbH$ = 43.89 A§H$
2

*******

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g^r Jwê$OZm| go {ZdoXZ h¡ {H$ RBSE Ho$ gm°ëdS> ‘m°S>b nona àmßV H$aZo Ho$ {bE 9460377092 na {g’©$ TEACHER eãX ìhmQ²>gEßn H$a|&
Amngo g§nH©$ H$a AmnH$mo {deof ê$n go ‘m°S>b nona ^oOo OmE|Jo&