Rajasthan Board 10th Model Paper 2022 Maths

iz’u&i= dh ;kstuk

d{kk & 10th
fo"k; &xf.kr
vof/k & 2 ?k.Vs 45 feuV iw.kkZad & 80
1- mn~ns'; gsrq vadHkkj &
Ø-l-a mn~ns'; vadHkkj izfr'kr
1- Kku 25 31.25
2- vocks/k 30 37-50
3- vfHkO;fDr 15 18-75
4- ekSfydrk 10 12-50
;ksx 80 100%

2- iz'uksa ds izdkjokj vadHkkj &
Ø- iz'uksa dk izdkj iz'uksa dh vad izfr dqy vad izfr'kr izfr'kr laHkkfor
la- la[;k iz'u iz'uksa dk le;
1- oLrqfu"B 18 1 18 (22.50%) 36 35
2- vfry?kwÙkjkRed 12 1 12 (15%) 24 25
3- y?kwÙkjkRed& I 13 2 26 (32.5%) 26 45
4- y?kwÙkjkRed & II 4 3 12 (15%) 08 30
5- fuca/kkRed 3 4 12 (15%) 06 30
;ksx 50 80 (100%) 100 165

fodYi ;kstuk % vkUrfjd
3- fo"k; oLrq dk vadHkkj &
Ø-l-a fo"k; oLrq vadHkkj izfr'kr
1 ¼1½ okLrfod la[;k,a 04 5%
2 ¼2½ cgqin 05 6.25%
3 ¼3½ nks pjks okys jSf[kd lehdj.k ;qXe 09 11.25%
4 ¼4½ f}?kkr lehdj.k 05 6.25%
5 ¼5½ lekUrj Js.kh 09 11.25%
6 ¼11½ jpuk,¡ 11 13.75%
7 ¼7½ funsZ’kkad T;kfefr 06 7.5%
8 ¼8½ f=dks.kfefr ifjp; 12 15%
9 ¼14½ lkaf[;dh 15 18.75%
10 ¼15½ izkfidrk 04 5%
;ksx %& 80 100%

CY;w fizUV
d{kk & X fo"k; %& xf.kr iw.kkZad & 80
Ø- mÌs'; bdkbZ@mi Kku vocks/k Kkuksi;ksx@vfHkO;fDr dkS'ky@ekSfydrk ;ksx
la- bdkbZ

y?kq mRrjkRed

y?kq mRrjkRed

y?kq mRrjkRed

y?kq mRrjkRed
nh?kZmRrjh;
nh?kZmRrjh;

nh?kZmRrjh;

nh?kZmRrjh;
fucU/kRed

fucU/kRed

fucU/kRed

fucU/kRed
oLrqfu"B

vfr-y?kq

vfr-y?kq

vfr-y?kq

vfr-y?kw
oLrqf"B

oLrqf"B

oLrqf"B
1 okLrfod
1¼1½ & & & & & & 2¼1½ & & & & & & & & 1¼1½ & & & 4¼3½
la[;k,a
2 cgqin & 1¼1½ & & & 1¼1½ & & & & & 1¼1½ 2¼1½ & & & & & & & 5¼4½
3 nks pjks okys
jSf[kd
1¼1½ & & & & & & & & & 1¼1½ & & & & & 1¼1½ 2¼1½ & 4¼1½ 9¼5½
lehdj.k
;qXe
4 f}?kkr & 1¼1½ 2¼1½ & & 1¼1½ & & & & & 1¼1½ & & & & & & & & 5¼4½
lehdj.k
5 lekUrj Js.kh 1¼1½ & & & & & & 2¼1½ & & & & 2¼1½ & & 1¼1½ & & 3¼1½ & 9¼5½
6 jpuk,¡ & & & & & 1¼1½ & & & & 1¼1½ & 2¼1½ & & & 1¼1½ 2¼1½ & 4¼1½ 11¼6½
7 funsZ’kkad
1¼1½ 1¼1½ & & & & & & & & & & & 3¼1½ & 1¼1½ & & & & 6¼4½
T;kfefr
8 f=dks.kfefr & & 2¼1½ 3¼1½ & 1¼1½ 1¼1½ 2¼1½ & & 1¼1½ 1¼1½ & & & 1¼1½ & & & & 12¼8½
ifjp;
9 lkaf[;dh 1¼1½ & & & & & & & 3¼1½ & 1¼1½ & 2¼1½ & 4¼1½ 1¼1½ 1¼1½ 2¼1½ & &15¼8½
10 izkfidrk & & 2¼1½ & & 1¼1½ 1¼1½ & & & & & & & & & & & & 14¼3½
;ksx %& 5¼5½ 3¼3½ 6¼3½ 3¼1½ & 5¼5½ 2¼2½ 6¼3½ 3¼1½ & 4¼4½ 3¼3½ 8¼4½ 3¼1½ 4¼1½ 4¼4½ 4¼4½ 6¼3½ 3¼1½ 8¼2½ 80¼50½
fodYiksa dh ;kstuk %& iz-la- 17 ls 23 esa ,dkfUrd vkarfjd fodYi gS uksV%& dks"Bd esa ckgj dh la[;k vadksa dh rFkk Hkhrj iz'uksa dh |ksrd gSA

gLrk{kj

ek/;fed f'k{kk cksMZ jktLFkku]vtesj
ekWMy iz’u i= ek/;fed ijh{kk 2022
fo"k;& xf.kr
d{kk&10
le;% 2 ?k.Vs 45 feuV iw.kkZad%80

ijh{kkfFkZ;ksa ds fy, lkekU; funZs'k %&

GENERAL INSTRUCTION TO THE EXAMINEES:

1- ijh{kkFkhZ loZizFke vius iz'u i= ij ukekad vfuok;Zr% fy[ksaA

Candidate must write first his/her Roll No. on the question paper
compulsorily.
2- lHkh iz'u djus vfuok;Z gSA

All the questions are compulasory.
3- izR;sd iz'u dk mÙkj nh xbZ mÙkj iqfLrdk esa gh fy[ksaA
Write the answer to each question in the given answer book only.
4- ftu iz'uksa esa vkUrfjd [k.M gS mu lHkh ds mÙkj ,d lkFk gh fy[ksaA
For questions having more than one part the answers to those parts are to be
written together in continuity.
5- iz'u i= ds fgUnh ij vaxzsth :ikUrj.k esa fdlh izdkj dh =qfV@ vUrj@fojks/kkHkkl gksus ij
fgUnh Hkk"kk ds iz'u dks lgh ekusAa

If there is any error/difference/contradiction in Hindi & English version of the
question paper, the question of the Hindi version should be treated valid.

¼[k.M v½
oLrqfu"B iz'u
iz'u&01 fuEu iz'uksa ds mRrj dk lgh fodYi p;u dj mRrj iqfLrdk esa fyf[k, %&
(i) ifjes; la[;k 129 dk n’keyo izlkj gS& 1
25 X 5 7 X 57

¼v½ lkar ¼c½ vlkar ¼l½ vlkar vko`fÙk ¼n½ vlkar vuko`fÙk

Decimal Expansion of Rational Number 129
2 X 57 X 57
5

(A) Terminating (B) Non Terminating
(C) Non Terminating Repeating (D) Non Terminating Non Repeating

(ii) fuEu esa ls ,d f}?kkr cgqin ugha gS& 1
¼v½ X2 ¼c½ X2- 4 ¼l½ X – 4X+4
2
¼n½ X –3X +3X -1
3 2

One of these is not a quadratic polynomial.
¼A½ X2 ¼B½ X2- 4 ¼C½ X2 – 4X+4 ¼D½ X3–3X2 +3X -1

(iii) fuEu jSf[kd lehdj.k ;qXe ds gy gS X+Y = 4, X-Y = 2 1
¼v½ X=3 Y=1 ¼c½ X=1 Y=3 ¼l½ X=Y =2 ¼n½ X=4 Y=0

Which is the solution of linear pair equation X+Y = 4, X-Y = 2
¼A½ X=3 Y=1 ¼B½ X=1 Y=3 ¼C½ X=Y =2 ¼D½ X=4 Y=0

(iv) fuEufyf[kr esa ls dkSu f}?kkr lehdj.k dks gy djus dh ,d fof/k gS& 1
¼v½ xq.ku[k.M fof/k ¼c½ iw.kZ oxZ fof/k ¼l½ f}?kkr lw= ¼n½ mijksDr lHkh

Which one of method use to solve quadratic equation -
¼A½ Factorisation ¼B½ Perfect Square ¼C½ Quadratic formula ¼D½ All Above

(v) lekUrj Js.kh 4]10]16] 22-------------------- dk izFke in vkSj lkoZvUrj D;k gksxk& 1
¼v½ ¼10] 5½ ¼c½ ¼4] 6½ ¼l½ ¼4] 10½ ¼n½ ¼6] 10½

Which is the first term and common difference for AI 4, 10, 16, 22.................
¼A½ (10, 5) ¼B½ (4, 6) ¼C½ (4, 10) ¼D½ (6, 10)

(vi) 3-5 lseh f=T;k okys o`Ùk dk O;kl gksxk& 1
¼v½ 6 lseh ¼c½ 7 lseh ¼l½ 8-5 lseh ¼n½ buesa ls dksbZ ugha

Radius of a circle is 3.5 cm then Dimeter of circle is -
¼A½ 6 cm ¼B½ 7 cm ¼C½ 8.5 cm ¼D½ none of these
(vii) fcUnq ¼&3] 5½ dkSu ls prqZFkka’k esa gksxk& 1
¼v½ izFke ¼c½ f}rh; ¼l½ r`rh; ¼n½ prqFkZ

Point (-3, 5) belongs to in which quadrant -
¼A½ First ¼B½ Second ¼C½ Third ¼D½ Fourth

(viii) tan 450 + cot 450 dk eku gksxk & 1
¼v½ 1 ¼c½ 2 ¼l½ 3 ¼n½ 0

Value of tan tan 450 + cot 450 is -
¼A½ 1 ¼B½ 2 ¼C½ 3 ¼D½ 0

(ix) cos (900-480) dk eku gksxk & 1
¼v½ sec 480 ¼c½ tan 480 ¼l½ sin 48 0
¼n½ cot 48 0

Value of cos (900-480) is -
¼A½ sec 480 ¼B½ tan 480 ¼C½ sin 480 ¼D½ cot 480

(x) fuEu esa ls ,d ek/; Kkr djus dk lw= ugha gS & 1

(v) ∑x ¼c½ ∑x + ah ¼l½ ∑fx ¼n½ ∑fd
n n N N

(x) One of these is not a formula to find mean -
(A) ∑x (B) ∑x + ah (C) ∑fx (D) ∑fd
n n N N

(xi) fuEu dk cgqyd Kkr djks & 1

x 5 7 9 11
f 4 8 6 2

¼v½ 9 ¼c½ 5 ¼l½ 7 ¼n½ 11

(xi) Find the Mode of data-
x 5 7 9 11
f 4 8 6 2

¼A½ 9 ¼B½ 5 ¼C½ 7 ¼D½ 11

(xii) fuEufyf[kr esa ls dkSulh la[;k fdlh ?kVuk dh izkf;drk ugha gks ldrh & 1
¼v½ 2/3 ¼c½ -1.5 ¼l½ 15% ¼n½ 0.7

Which of the following can not be the probability of an event -
¼A½ 2/3 ¼B½ -1.5 ¼C½ 15% ¼D½ 0.7

Q-2 Fill in the Blanks :-

fuEufyf[kr iz'uksa esa fjDr LFkkuksa dh iwfÙkZ djrs gq, mRrj iqfLrdk esa fyf[k,&

(i) ;fn gks rks lehdj.k fudk; dk gy ------------------ gksrk gS & 1

If , then solution of linear pair of equation is ..................

(ii) l-Js- 10] 8] 6] 4 -------------------------------- dk 7ok¡ in ------------------------------ gSA 1

7th Term of AP 10, 8, 6, 4.................................... is ...................................

(iii) fdlh ckgjh fcUnq ls o`Ùk ij ------------------------------- Li’kZ js[kk,a [khaph tk ldrh gSA 1

How many tangent drawn circle from point of out site the circle ...................................

(iv) funsZ’kkad T;kfefr esa nks fcUnqvksa ds chp dh nwjh Kkr djus dk lw=----------------------- gS A 1

Find Formula for Distance between two points in a co-ordinate geometry is.................

(v) sin (900 - ) = ................................ 1

sin (900 - ) = ................................

(vi) caVu 7]4]6]3]8]5]9 dh ekf/;dk ---------------------------------------------- gksxhA 1

Median of distribution 7,4,6,3,8,5,9 is ..................................

Hkkx & v
PART – A
iz'u la- 03 vfry?kqrjkRed iz'u ¼Very Short answer type of questions½
(i) nks la[;kvksa dk xq.kuQy 180 gS rFkk egRre lekiorZd 3 gS rks y?kqRre lekiorZd Kkr
djks \ 1

If Product of two numbers is 180 and HCF is 3 then find their LCM .

(ii) X2 +3X+1 dks X-2 ls Hkkx nsus ij 'ks"kQy Kkr dhft, \ 1

Find the reminder if X2 +3X+1 divided by X-2

(iii) cgqin X2 -6X+7 esa 'kwU;kadksa dk ;ksx vkSj xq.kuQy fyf[k, \ 1

Write the sum and product of zeroes of polynomial X2 -6X+7

(iv) nks pj okys lehdj.k fudk; dk gy vf}rh; gksus dh 'krZ fyf[k, \ 1

Find the condition of unique solution for pair if linear equation in two variables.

(v) f}?kkr lehsdj.k 2X2 + 3X+4 =0 esa ewyksa dk ;ksx Kkr dhft, \ 1

Find the sum of roots of quadratic equation 2X2 + 3X+4 =0

(vi) f}?kkr lehsdj.k ds ewy Kkr djus ds fy;s Jh /kjkpk;Z lw= fyf[k, \ 1

Write SHREE DHARACHARYA Formula for finding roots of quadratic equation.

(vii) fdlh o`Ùk dh f=T;k vkSj ml ij [khaph xbZ Li’kZ js[kk ds e/; fdrus fMxzh dk dks.k
gksrk gS \ 1

Find the triangle between radius of a circle and tangent of circle .

(viii) funsZ’kkad ¼4] 3½ esa Hkqt vkSj dksVh Kkr dhft, \ 1

Find the abscissa and ordinate in co-ordinate (4, 3)

(ix) eku Kkr dhft, cos 300 – sin 600 1

Find the value cos 300 – sin 600

(x) ;fn sin 3x=1 rks X dk eku Kkr dhft, \ 1

If sin 3x=1 then find the value of X

(xi) caVu 10] 12] 8] 7] 13 dk ek/; Kkr djks \ 1

Find the mean of distribution 10, 12, 8, 7, 13

(xii) ;fn ,d flDds dks ,d ckj mNkyk tkrk gS rks fpr vkSj iV vkus dh laHkkouk
D;k gksxh \ 1
Find the probability of getting a head and a tail when a coin is tossed once.

Hkkx & c
PART – B
Q-4. ;wfDyM foHkktu fof/k }kjk 90 vkSj 144 dk egÙke lekiorZd Kkr dhft,A 2

Find the HCF of 90 and 144 by using EUCLID’S division method.

Q-5. f}?kkr cgqin X2 -2x-15 ds 'kwU;d Kkr dhft,A 2

Find the Zero of a quadratic polynomial X2 -2x-15 .

Q-6. fuEu jSf[kd lehdj.k ;qXe dks foyksiu fof/k ls gy dhft,A 2
2x+y = 6, 2x-y = 2

Solve the following pair of linear equations by elimination method.
2x+y = 6, 2x-y = 2

Q-7. xq.ku[k.M fof/k ls fuEu f}?kkr lehdj.k ds ewy Kkr dhft,A 2
2
2X + X– 6 = 0
Find the roots of the following quadratic equations by factorisation.
2X2 + X– 6 = 0
Q-8. fuEufyf[kr lekarj Js.kh esa ls fdrus in gSA 2
7, 13, 19, ............................. 205

Find the number of terms of the following APs .
7, 13, 19, ............................. 205

Q-9. rhu vadksa okyh fdruh la[;k,a 7 ls foHkkT; gS \ 2

How many Three Digit numbers are divisible by 7 ?

Q-10. 5 lseh yEck ,d js[kk[k.M [khafp, vkSj bls 2 % 3 vuqikr esa foHkkftr
dhft, \ 2

Draw a line segment of length 5 cm and divide in the ration 2:3 .
0
Q-11. 5 lseh f=T;k ds ,d o`Ùk ij nks Li’kZ js[kk,a [khafp,a] tks ijLij 60 ds dks.k
ij >qdh gksAa 2

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an
0
angle 60

Q-12. ;fn rks cos A vkSj tan A dk eku ifjdfyr dhft,A 2

If calculate cos A and tan A .

Q-13. fuEufyf[kr dk eku fudkfy,A 2
2 tan2 450 + cos2 300 – sin2 600

If Evaluate the following -
2 tan2 450 + cos2 300 – sin2 600

Q-14. fuEu caVu dk ek/; Kkr dhft,A 2

izkIrkad 25 35 45 55 65
Nk=ksa dh 4 28 42 20 6
la[;k

Find the mean of the following frequency –

Score 25 35 45 55 65
No. Of 4 28 42 20 6
Students

Q-15. fuEu caVu dk cgqyd Kkr dhft,A 2

oxZ 0&20 20&40 40&60 60&80 80&100 100&120
varjky
ckjackjrk 10 35 52 61 38 20

Find the mean of the following frequency –

Class 0&20 20&40 40&60 60&80 80&100 100&120
Interval
Frequency 10 35 52 61 38 20

Q-16. ,d FkSys esa 5 lQsn o 2 yky xsn
a s gSA bl FkSys esa ls ,d xsna ;knqPN;k fudkyh tkrh gSA
bldh D;k izkfidrk gS fd fudkyh xbZ xsna ----------------------------------- gksxh \ 2

¼A½ lQsn ¼AA½ yky

A bag contains 5 white and 2 red balls. From this bag one ball is drawn randomly. What
is the probability that drawn ball is ...............................

(i) White (ii) Red

[k.M& l
PART – C
Q-17. ;fn fdlh lekarj Js.kh ds nwljs vkSj rhljs in Øe’k% 24 rFkk 28 gks rks] Js.kh 3
ds igys 61 inksa dk ;ksxQy Kkr dhft,A
If Second and third terms of an A.P. are 24 and 28 respectively, then find the sum of first
61 terms.
vFkok @ OR
2 vkSj 101 ds e/; 5 ls foHkkftr ¼HkkT;½ gksus okyh lHkh izkd`r la[;kvksa dk 3
;ksxQy Kkr dhft,A
Find the sum of all natural numbers divisible by 5 between 2 and 101 .

Q-18. X &v{k ij og fcUnq Kkr dhft, tks fcUnqvksa ¼&2] 3½ vkSj ¼&3] 4½ ls leku nwjh 3
ij fLFkr gSA
Find the point on X-Axis which is equidistant from the point (-2, 3) and (-3, 4)

vFkok @ OR

fcUnqvksa ¼11] 8½ vkSj ¼1] 3½ dks feykus okyh js[kk dks fcUnq ¼7] 6½ fdl vuqikr esa 3

foHkkftr djrk gSA
In which ratio, point (7, 6) divides the line joining the points (11, 8) and (1, 3) .

Q-19.
Sin 170 Cos 670 Sin 150
5 + 2 - 6 dk eku Kkr dhft,A 3
5 Cos 730 Sin 230 Cos 750
5

Sin 170 Cos 670 Sin 150
Find the value of 5 + 2 - 6
0 0
5 Cos 73 Sin 23 Cos 750
5
vFkok @ OR

fl) dhft, & cos4 + sin4 = 1-2 cos2 sin2 3
4 4 2
Prove that - cos + sin = 1-2 cos sin2

Q-20. fuEu ckjEckjrk caVu dk ek/; Kkr dhft,A 3

oxZ 0&10 10&20 20&30 30&40 40&50
fi 6 10 13 7 4

Find the mean of the following frequency distribution –

Class 0&10 10&20 20&30 30&40 40&50
fi 6 10 13 7 4

vFkok @ OR

fuEu ckjEckjrk caVu dk cgqyd Kkr dhft,A 3

oxZ 10&25 25&40 40&55 55&70 70&85 85&100
fi 6 20 44 26 3 1

Find the Mode of the following frequency distribution –

Class 10&25 25&40 40&55 55&70 70&85 85&100
fi 6 20 44 26 3 1

[k.M& n
PART – D
Q-21. fuEu jSf[kd lehdj.k ;qXe dks vkys[kh; fof/k }kjk gy dhft,A 4
3 x – 5y = 1
2x–y =3

Solve the following pair of linear equation by graphical method .
3 x – 5y = 1
2x–y =3
vFkok @ OR

fuEu jSf[kd lehdj.k ;qXe dks vkys[kh; fof/k }kjk gy dhft,A 4
4 x – 5y = 20
3 x + 5y = 15
Solve the following pair of linear equation by graphical method .
4 x – 5y = 20
3 x + 5y = 15

Q-22. ,d 10 lseh yEckbZ dk js[kk[k.M [khapdj mldk 2 % 3 esa foHkktu dhft,A 4

Draw a line segment at length 10 cm and divide into 2 : 3

vFkok @ OR

AB = 5 lseh yEckbZ dk ,d js[kk[k.M [khafp,A fcUnq B dks dsUnz ekudj 2-2 lseh 4
f=T;k dk o`Ùk cukb, rFkk bl o`Ùk ij fcUnq A ls Li’kZ js[kk,¡ [khafp,A
Draw a line segment AB of length 5 cm. Taking B as the centre, draw a circle of radius 2.2 cm
and draw tangents to the circle from point A.

Q-23. fuEu ckjEckjrk caVu dk ek/;d Kkr dhft,A 4

oxZ 10&25 25&40 40&55 55&70 70&85 85&100
fi 6 20 44 26 3 1

Find the medianof the following frequency distribution –

Class 10&25 25&40 40&55 55&70 70&85 85&100
fi 6 20 44 26 3 1

vFkok @ OR

fuEu ckjEckjrk caVu dk cgqyd Kkr dhft,A 4

izkIrkad 0&20 20&40 40&60 60&80 80&100
Nk=ksa dh 5 10 12 6 3
la[;k

Find the Mode of the following frequency distribution –

Score 0&20 20&40 40&60 60&80 80&100
No. of 5 10 12 6 3
Students