mwfl pRSn p`qr (gixq)

jmwq- d~svIN
ku`l AMk:80 smW: 3 ਘੰਟੇ
jrUrI not:-

Bwg-a iv`c pRSn 1 qoN 3 q`k hn [

pRSn 1 iv`c 16 pRSn bhu-ivklpI au~qr vwly 1-1 AMk vwly hn [
pRSn 2 iv`c 7 pRSn KwlI sQwn Brn vwly 1-1 AMk vwly hn [
pRSn 3 iv`c 7 pRSn shI / glq au~qrW vwly 1-1 AMk vwly hn [
Bwg-A iv`c pRSn 4 qoN 7 q`k 2 AMk vwly hn [
Bwg-e iv`c pRSn 8 qoN 13 q`k 4 AMk vwly hn [iehnW pRSnW iv`c iksy vI iqMn pRSnW iv~c
AMdrUnI Cot hovygI [ pRSn 12 dw Cot vwlw Bwg kys st~fI vwlw hY[
Bwg-s iv`c pRSn 14 qoN 16 q`k 6 AMk vwly hn, iehnW swry pRSnW iv~c AMdrUnI Cot
hovygI [

Bwg-a
hryk pRSn dw 1 AMk hY[

1. shI ivklp dI cOx kro:

(i) id~qy gey guxnKMf ru~K iv~c AigAwq sMiKAw kI hovygI?

3
81
3
27
3
?
3

(a) 6 (b) 3 (c) 9 (d) 18

𝑐
(ii) jykr 𝑝(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, ie~k do GwqI bhupd hY qW 𝑎
dw 𝑝(𝑥) dIAW isPrW nwl kI sMbMD

huMdw hY?
𝑐 𝑐
(a) 𝑎 isPrW dI GtwE hY (b) 𝑎
isPrW dI Bwg hY

𝑐 𝑐
(c) 𝑎
isPrW dw joVPl hY (d) 𝑎
isPrW dw guxnPl hY
(iii) id~qy ic~qr iv~c 𝑦 = 𝑝(𝑥) dy AwlyK leI isPrW dI igxqI ikMnI hovygI?

X’ X
O

Y’

(a) 2 (b) 6 (c) 4 (d) 3

(iv) smIkrxW 𝑥 − 𝑦 = 4 Aqy 𝑥 + 𝑦 = 14 ਦਾ ਹੱ ਲ ਹੈ।

(a) 𝑥 = 9, 𝑦 = 5 (b) 𝑥 = 5, 𝑦 = 9 (c) 𝑥 = −9, 𝑦 = 5 (d) 𝑥 = 9, 𝑦 = −5

(v) hyTW id~qIAW smIkrxW iv~coN ikhVI do GwqI smIkrx nhIN hY?

3 5 1
(a) 𝑥 − 𝑥 = 4 (b) 3𝑥 − 𝑥 = 𝑥 2 (c) 𝑥 + 𝑥 = 4 (d) 𝑥 2 − 3 = 4𝑥 2 − 4𝑥

(vi) jykr iksy AMk gixiqk lVI dy pihly 𝑛 pdW dw joVPl 𝑆𝑛 hovy qW ausdw 𝑛vW pd kI hovygw?

(a) 𝑆𝑛 + 𝑆𝑛−1 (b) 𝑆𝑛 − 𝑆𝑛−1 (c) 𝑆𝑛 + 𝑆𝑛+1 (d) 𝑆𝑛+1 − 𝑆𝑛

( vii) hyT id~qIAW AwikRqIAW iv~coN ikhVI AwikRqI c~kr dI sprS ryKw nUM drswauNdI hY?

(a) (b) (c) (d)

(viii) id~qy hoey ic~qr dw AiDAYn krky hyT iliKAW iv~coN shI kQn cu~xo:

A
R

7.6 sm 6√3 sm 3√3 sm 3.8 sm

6 12
sm sm
B C
12 sm
P Q

(a) ∠P=∠A (b) ∠P=∠B (c) ∠P=∠C (d) auprokq swry

(ix) cosec 0° dw mu~l kI hud

M w hY?

(a) 0 (b) √2 (c) pirBwiSq nhIN (d) 1

(x) 𝜃 dy iks mu~l leI sin𝜃= cos𝜃 hovygw?

(a) 300 (b) 450 (c) 600 (d) 900

(xi) jykr c~kr dy ArD ivAwsI KMf dw KyqrPl, c~kr dy KyqrPl dw 1⁄6 hovy qW kyNdrI kox dw

mwp kI hovygw?

(a) 900 (b) 600 (c) 450 (d) 300

(xii) ie~k 7 sm Bujw vwly Gx iv~coN sB qoN v~fI aucweI vwlw ie~k SMkU k~iFAw jWdw hY qW aus SMkU

dI aucweI kI hovygI?

7
(a) 2
sm (b) 14 sm (c) 7 sm (d) 21 sm

(xiii) smwn ArD ivAws Aqy smwn aucweI vwly byln Aqy SMkU dy Awieqn dw Anupwq kI huMdw hY?

(a) 1:3 (b) 1:1 (c) 3:1 (d) 2:3

(xiv) AMkiVAW 4,6,5,0,2,1,3,2,3,2 dw bhulk kI hovygw?

(a) 4 (b) 6 (c) 2 (d) 3

(xv) hyTW id~qIAW sMiKAwvW iv~coN ikhVI sMiKAw iksy Gtnw dI sMBwvnw nhIN ho skdI?

2 3
(a) 1 (b) (c) (c) 0
3 2

(xvi) AsMBv Gtnw dI sMBwvnw kI huMdI hY?

1
(a) 2
(b) 1 (c) 0 (d) -1

2. shI/glq au~qr dI cOx kro:

(i) √3 ie~k pirmyX sMiKAw nhIN hY[ (shI/glq)

𝑎1 𝑏 𝑐
(ii) jykr iksy smIkrn pRxwlI iv~c 𝑎2
= 𝑏1 ≠ 𝑐1 hovy qW smIkrn pRxwlI dw
2 2

iv~lKx h~l huMdw hY[ (shI/glq)

(iii) jykr smIkrn 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 dy mUl smwn hovy qW 𝐷 ≥ 0 huMdw hY[ (shI/glq)

(iv) c~kr dy AMdUrnI ibMdU qoN c~kr nUM do sprS ryKwvW iK~cIAW jw skdIAW hn[ (shI/glq)

(v) ibMdU 𝑃(3,4) dI mUl ibMdU qoN dUrI 5 iekweI hY[ (shI/glq)

3
(vi) kox 𝐴 dy iksy mu~l dy leI sin 𝐴 = 5 ho skdw hY[ (shI/glq)

(vii) m~Dmwn, m~iDkw Aqy bhulk iv~c sMbMD 3 bhulk = m~iDkw +2 m~Dmwn huMdw hY[ (shI/glq)
3. KwlI sQwn Bro:

(i) ਜੇਕਰ (6,k) ਦਦੱ ਤੀ ਗਈ ਸਮੀਕਰਨ 𝟑𝒙 − 𝒚 = 𝟐𝟐 ਦਾ ਇੱ ਕ ਹੱ ਲ ਹੈ ਤਾਂ k ਦਾ ਮੱ ਲ

_______ਹੋਵੇਗਾ।

(ii) AMk gixiqk lVI 2,7,12 dw Aglw pd________ hY[

(iii) ic~qr iv~c, jykr LM QR hovy qW PM=_________ hovygI[

L M

Q R

(iv) jykr ryKwKMf RS dw m~D ibMdU M hY qW RM Aqy SM dw Anupwq ________ hovygw[

(v) ie~k c~krI KMf dw KyqrPl = sMgq ArDivAwsI KMf dw KyqrPl – sMgq ______ dw KyqrPl

huMdw hY[

(vi) goly dI ku~l sqHw dw KyqrPl ________ huMdw hY[

(vii) jykr iksy mYc iv~c ie~k iKfwrI dy ij~qx dI sMBwvnw 0.62 hovy qW dUsry (ivroDI) iKfwrI dy

hwrn dI sMBwvnw ________ hovygI[

Bwg-A
hryk pRSn dy 2 AMk hn[

4. jykr m.s.v. (360,657)=9 id~qw hY qW l.s.v. (360,657) pqw kro[

5. do GwqI bhupd pqw kro ijsdy isPrW dw joVPl Aqy guxnPl kRmvwr 0 Aqy √5 hovy[

6. ArD ivAws 21 sm vwly c~kr dI ie~k cwp kyNdr ’qy 60° dw kox bxwauNdI hY, qW cwp duAwrw

bxwey gey ArD ivAwsI KMf dw KyqrPl pqw kro[

7. 52 p~iqAW dI cMgI qrWH PYNtI geI qwS dI gu~tI iv~coN ie~k p~qw bwhr k~iFAw jWdw hY qW hyT

iliKAW nUM pRwpq krn dI sMBwvnw pqw kro:-

(a) lwl rMg dw bwdSwh (A) hu~km dw p~qw

 Bwg-e
hryk pRSn dy 4 AMk hn[

8. do GwqI smIkrx 3𝑥 2 − 4√3𝑥 + 4 = 0 dy mUlW dI pRwikRqI dw pqw kro Aqy jykr mUl sMBv hn

qW auhnW nUM pqw kro[

9. AMk gixiqk lVI 3,15,27,39,……… dw ikMnvW pd ausdy 54vyN pd qoN 132 v~D hovygw?

jW

jykr iksy AMk gixiqk lVI dy pihly 7 pdW dw joVPl 49 hY Aqy pihly 17 pdW dw joVPl 289

hY, qW iesdy pihly 𝑛 pdW dw joVPl pqw kro[

10. ibMdUAW (4,-1) Aqy (-2,-3) nUM imlwaux vwly ryKwKMf nUM iqMn smwn BwgW iv~c vMfx vwly ibMdUAW

dy inrdyS AMk pqw kro[

11. ∆OPQ iv~c, ijsdw kox P smkox hY, OP = 7cm Aqy OQ − PQ = 1 cm hY qW 𝑠𝑖𝑛𝑄 Aqy 𝑐𝑜𝑠𝑄

dy mu~l pqw kro[

Q

P O
7cm
jW

𝑠𝑖𝑛 𝜃−𝑐𝑜𝑠𝜃+1 1
is~D kro ik =
𝑠𝑖𝑛 𝜃+𝑐𝑜𝑠𝜃−1 𝑠𝑒𝑐𝜃−𝑡𝑎𝑛𝜃

12. jmIn dy ie~k ibMdU qoN, ie~k 20 mItr au~cI iemwrq dy isKr ’qy l~gy sMcwr mInwr dy ql Aqy

isKr dy aucwx kox kRmvwr 45° Aqy 60° hn[ sMcwr mInwr dI aucweI pqw kro[

jW

ie~k ipMf iv~c ie~k ibjlI dw KMbw jo ik 5 mItr lMbw hY, iv~c KrwbI Aw jWdI hY[aus KrwbI nMU

dUr krn leI ie~k ielYktRISIAn nUM bulwieAw jWdw hY[ielYktRISIAn v~loN d~isAw jWdw hY ik

KMby au~pr qwrW nUM TIk krn leI mYnUM zmIn nwl 60° dw kox bxwauNdy hoey ie~k pOVI lgwauxI

pvygI jo ik KMby dy auprly isry qoN 1.3 mItr hyTW q~k phuMcy[
 1. ijs ibMdU q~k pOVI lgweI jwxI hY, auh zmIn qoN ikMnw au~pr hY?

2. pOVI dI lMbweI ikMnI hovygI ?

13. l~kVI dy ie~k Tos bylx dy hryk isry ’qy ie~k ArD golw Kod ky k~Fdy hoey, ie~k vsqU bxweI

geI hY,ijvyN ik ic~qr iv~c ivKwieAw igAw hY[jykr bylx dI au~cweI 10 sm hY Aqy AwDwr dw

ArD ivAws 3.5 sm hY qW ies vsqU dI ku~l sqwH dw KyqrPl pqw kro[
 Bwg-s
hryk pRSn dy 6 AMk hn[

14. ਪੜਤਾਲ ਕਰੋ ਦਕ ਹੇਠਾਂ ਦਦੱ ਤਾ ਸਮੀਕਰਨਾਂ ਦਾ ਜੋੜਾ ਸੰ ਗਤ ਹੈ ਜਾਂ ਅਸੰ ਗਤ?

𝒙 + 𝟑𝒚 = 𝟔

𝟐𝒙 − 𝟑𝒚 = 𝟏𝟐
ਜੇਕਰ ਇਹ ਸੰ ਗਤ ਹੈ ਤਾਂ ਇਸਦਾ ਦਕਹੜਾ ਹੱ ਲ ਹੋਵੇਗਾ ਅਤੇ ਉਹ ਹੱ ਲ ਪਤਾ ਕਰੋ।
jW

pMj swl pihlW nUrI dI aumr sonMU dI aumr dw iqMn guxw sI[ds swl bwd nUrI dI aumr sonUM dI

aumr dw do guxw ho jwvygI[nUrI Aqy sonUM dI vrqmwn aumr ikMnI hY?

15. is~D kro ik jykr iksy iqRBuj dI ie~k Bujw dy smWqr bwkI do BujwvW nUM iBMn iBMn ibMdUAW ’qy

k~tdI hoeI ie~k ryKw iK~cI jwvy, qW bwkI do BujwvW ie~k hI Anupwq iv~c vMfIAW jWdIAW hn[

jW

id~qy hoey ic~qr iv~c, 𝑋𝑌 Aqy 𝑋′𝑌′, kyNdr 𝑂 vwly iksy c~kr ’qy do smWqr sprS ryKwvW hn

Aqy sprS ibMdU 𝐶 ’qy sprS ryKw 𝐴𝐵, 𝑋𝑌 nMU 𝐴 Aqy 𝑋′𝑌′ nUM 𝐵 ’qy k~tdI hY[is~D kro ik

∠ 𝐴0𝐵 = 90° hY[

16. id~qy pOdy dIAW 40 p~qIAW dI lMbweI lgBg imlImItr iv~c mwpI jWdI hY Aqy pRwpq AMikVAW

nUM hyTW id~qI swrxI dy rUp iv~c drswieAw jWdw hY:

lMbweI p~qIAW dI
(imlImItr iv~c) sMiKAw
118 – 126 3
127 - 135 5
136 - 144 9
145 - 153 12
154 - 162 5
163 - 171 4
171 - 180 2

p~qIAW dI m~iDkw lMbweI pqw kro[

jW

hyT id~qI swrxI iksy mu~hly dy 25 pirvwrW dy Bojn aup`r hox vwly rozwnw Krc nUM drswauNdI hY:

rozwnw Krc (ru iv~c) 100 – 150 150 – 200 200 – 250 250 – 300 300 – 350

pirvwrW dI sMiKAW 4 5 12 2 2

Bojn aupr hoey Krc dw m~Dmwn pqw kro[