Rajasthan Board 10th Maths Sample Paper 2021

ek/;fed ijh{kk ekWMy iz'u&i= 2021
SECONDARY EXAMINATION, MODEL QUESTION PAPER-2021
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MATHEMATICS

le;% 3¼ ?k.Vs iw.kkZd 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 mast 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.
6- iz'u dk mÙkj fy[kus ls iwoZ iz'u dk Øekad vo'; fy[ksaA
Write down the serial number of the question before attempting it.
7- iz'uksa dk vadHkkj fuEukuqlkj gSA
Weightage of marks for the question is as follows.

[k.M iz'uksa dh la[;k dqy vad Hkkj vad izR;sd iz'u
[k.M&v(A) 1 ( i to x ), 2 to 11 20 1
[k.M&c(B) 12 to 19 = 8 16 2
[k.M&l(C) 20 to 23 = 4 16 4
[k.M&n(D) 24 to 25 = 2 10 5
[k.M&;(E) 26 to 28= 3 18 6

7- iz'u la[;k 20 ls 28 esa vkUrfjd fodYi fn;s x;s gSaA

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¼[k.M& v½

iz'u 01 fuEukafdr iz'uksa esa ls fn;s x;s lgh fodYi dk p;u dj viuh mÙkj iqfLrdk esa fyf[k, A
izR;sd iz'u 01 vad dk gSA ¼10X1¾10½
¼i½ 17 dk oxZ gksxk &
¼v½ 189 ¼c½ 289
¼l½ 389 ¼n½ 169 1
The Square of 17 will be :
¼A½ 189 ¼ B½ 289
¼ C½ 389 ¼ D½ 169
¼ii½ cgqin esa j[kus ij cgqin dk eku gksxk &
¼v½ 10 ¼c½ 8
¼l½ 12 ¼n½ 6 1
By putting x=2 in polynomial , the value of polynomial will be :
¼A½ 10 ¼ B½ 8
¼ C½ 12 ¼ D½ 6
¼iii½ f}?kkr cgqin ds 'kwU;dks dk ;ksx gksxk &
¼v½ &2 ¼c½ & 8
¼l½ 2 ¼n½ 8 1
The sum of zeros of polynomial x2-2x-8 will be :
¼A½ &2 ¼ B½ &8
¼ C½ 2 ¼ D½ 8
¼iv½ dk eku gksxk &

¼v½ 1 ¼c½

¼l½ ¼n½ 0 1
The value of will be :

¼A½ 1 ¼ B½

¼ C½ ¼ D½ 0
¼v½ ,d m/okZ/kj [kEcs dh ijNkbZ] [kEcs dh m¡pkbZ ds cjkcj gS] rks lw;Z dk
mUu;u dks.k gksxk &
¼v½ 450 ¼c½ 300
¼l½ 600 ¼n½ 500 1

The shadow of a vertical pole is same the height of pole, then angle of elevation of sun will be :
¼A½ 450 ¼ B½ 300
¼ C½ 600 ¼ D½ 500
¼vi½ fcUnq ¼5] &2½ dh & v{k ls nwjh gksxh &
¼v½ 5 ¼c½ 2
¼l½ 3 ¼n½ 4 1
Distance of point (5, -2) from x-axis will be :
¼A½ 5 ¼ B½ 2
¼ C½ 3 ¼ D½ 4
¼vii½ vkd`fr esa DE II BC gks] AD¾ 4 lseh] BD¾6 lseh rFkk AE ¾ 5 lseh gks] rks EC
dk eku gksxk &

¼v½ 6-5 lseh ¼c½ 7-0 lseh
¼l½ 7-5 lseh ¼n½ 8-0 lseh 1
¼vii½ In the given figure DE II BC, AD=4 cm, DB=6cm and AE= 5cm, then measure of EC will be :

(A½ 6-5 cm ¼ B½ 7-0 cm
¼ C½ 7-5 cm ¼ D½ 8-0 cm
¼viii½ rhu lajs[kh; fcUnqvksa ls xqtjus okys o`Ùkksa dh la[;k gS &
¼v½,d ¼c½ nks
¼l½ 'kwU; ¼n½ vuUr 1
Number of circles which passes through three collinear points is :
¼A½ One ¼ B½ two
¼ C½ zero ¼ D½ infinite
¼ix½ xksys dk O;kl 6 lseh gS] xksys dk vk;ru gksxk &
¼v½ 16 ?ku lsea h ¼c½ 20 ?ku lseh
¼l½ 36 ?ku lseh ¼n½ 30 ?ku lseh 1
The diameter of a sphere is 6 cm, the volume of sphere will be :
¼A½ 16 cm3 ¼ B½ 20 cm3
¼ C½ 36 cm3 ¼ D½ 30 cm3

¼x½ cVau 1]3]2]5]9 dk ek/;d gS &
¼v½ 3 ¼c½ 4
¼l½ 2 ¼n½ 5 1
The median of distribution 1,3,2,5,9 is :
¼A½ 3 ¼ B½ 4
¼ C½ 2 ¼ D½ 5
iz- 2 lw= *fuf[kye~* dk iz;ksx dj 105 dk oxZ Kkr dhft, A 1
Find the square of 105 by using 'sutra Nikhilam' .
iz- 3 12 dk ?kuQy lw= *fuf[kye~* ls Kkr dhft,A 1
Find the cube of 12 by using 'sutra Nikhilam' .
iz- 4 lekUrj Js.kh 6]9]12]15 ---------------- dk 7 oka in Kkr dhft, A 1
Find the 7th term of the A.P. 6,9,12,15 .................. .
iz- 5 nks f[kykMh jke vkSj ';ke 'krjat [ksyrs gS A ;g Kkr gS fd jke }kjk 1
eSp thrus dh izkf;drk gS rks ] ';ke ds thrus dh izkf;drk D;k gksxh \
Two players Ram and Shyam plays a chess match. It is given that probability of winning of the match

by Ram is . Find the probability of winning of the match by Shyam.

iz- 6 ,d ikls dh ,d Qsd
a esa **vHkkT; la[;k** vkus dh izkf;drk Kkr dhft,A 1
In a throw of a dice, find the probability of getting a 'prime number'.
iz- 7 ** jksd n`f"V nwjh ** dk lehdj.k fyf[k,A 1
Write the equation of ' Stopping distance sight'.
iz- 8 okguksa ds fy, vko';d ih- ;w- lh- dk iwjk uke fyf[k,A
Write the full name of P.U.C. which is essential for every vehicle.
iz- 9 fcUnqvksa ¼2] 3½ vkSj ¼5] 6½ ds chp dh nwjh ------------------------------------ gksxhA 1
The distance between the points (2,3) and (5,6) will be..................... .
iz- 10 ,d fu;r fcUnq ls lnSo leku nwjh ij pyus okys fcUnq dk fcUnq iFk ------------------------- gksxkA 1
The locus of a points which are equidistant from a certain point will be ............ .

iz- 11 ,d ikls dks Qsd
a us ij **4 ls NksVk vad " vkus dh izkf;drk ---------- gksxhA 1
In a throw of a dice the probability of getting ' a number less than from 4' will be ...............
[k.M & ch
Section B
iz- 12 ** }U} ;ksx** fof/k ls 7225 dk oxZewy Kkr dhft,A 2
Find the square root of 7225 by using ' Dwandwa Yoga Method'.
iz- 13 ,d f}/kkr cgqin Kkr dhft,] ftlds 'kwU;dksa dk ;ksx rFkk 2
xq.kuQy Øe'k% & 3 vkSj 2 gSA

Find a quadratic equation whose sum of zeros and product are -3 and 2 respectively.

iz- 14 vlfedk dk vkys[kh; fof/k ls gy leqP;; n'kkZb;sA 2
Show the solution set of the inequality , graphically.
iz- 15 dk eku Kkr dhft,A 2
Find the value of .
iz- 16 ,d igkMh dk <yku {kSfrt ls 600 dk dks.k cukrk gSA ;fn f'k[kj rd igq¡pus esa 500 2
ehVj pyuk iMrk gS rks igkM+h dh m¡pkbZ Kkr dhft,A
The slope of a hill makes an angle of 600 with horizontal. If to reach at top, 500 meter distance have to covered
then to find the height of the hill.

iz- 17 nh xbZ vkd`fr esa ;fn lseh] lseh rFkk ] thok ij yEc gS rks dk eku
Kkr dhft,A 2

In the given figure if OA=5cm, AB=8cm, and OD perpendicular to chord AB then to find the value of CD.

iz- 18 ,d 10 lseh yEckbZ dk ,d js[kk [k.M [khap dj mldk 2:3 esa vkUrfjd foHkktu dhft,A 2
Draw a line segment of length 10 cm and divide it into 2:3 internally.
iz- 19 ,d lh/ks o 12 ehVj Å¡ps iksy ds 'kh"kZ ij ,d CCTV dSejk yxkuk gS rkfd
iksy ds 'kh"kZ ls 13 ehVj nwj n`f"Vjs[kk ds vkxs dk ;krk;kr ns[kk tk ldsA
bl fLFkfr esa iksy ds ikn ¼Feet½ ls og nwjh] ftlds vkxs ls ;krk;kr fn[kkbZ
nsrk gS] Kkr dhft,A 2
A CCTV camera is placed on the top of a 12 m high pole in such a way that traffic can be seen beyond 13 metre of
line of sight of it. Find the distance from the feet of pole beyond which the traffic on road is visible.

[k.M & lh
Section C
iz- 20 fl) dhft, dh fcUnq ¼1]&2½] ¼3] 0½] ¼1] 2½ vkSj ¼&1]0½ ,d oxZ ds 'kh"kZ gSA 4
fl) dhft, dh nks leku dksf.kd f=Hkqt ijLij le:i gksrs gSA

Prove that points ¼1]&2½] ¼3] 0½] ¼1] 2½ and ¼&1]0½ are vertices of the square.
OR
Prove that two equiangular triangles are similar.

iz- 21 fl) dhft, fd fcUnq ] vkSj ,d 4
leckgq f=Hkqt ds 'kh"kZ gSA
;fn nks f=Hkqtksa esa laxr Hkqtkvks dk vuqikr cjkcj gkas rks fl) dhft, fd nksuks f=Hkqt
ijLij le:i gksaxsA

Prove that points ] and are vertices of a equilateral triangle.

OR
If the ratio of the corresponding sides of two triangles is equal, then to prove that the triangles are similar.

iz- 22 nh xbZ vkd`fr esa v}Zo`Ùk dh f=T;k 7 lseh gS ]v)Zo`r esa cus o`Ùk dk {ks=Qy Kkr dhft,A 4

nh xbZ vkd`fr eas o`Ùk dk dsUnz O rFkk f=T;k 5 lseh gSA ;fn ] ]
AB II CD, AB=8 lseh vkSj CD =6 lseh gksa rks PQ Kkr dhft,

In the given figure radius of the semicircle is 7 cm. Find the area of the circle formed inside the semicircle.

OR

In the given figure centre of the circle 'o' with radius 5 cm. If , , AB II CD, AB=8 and CD=6
cm. Then find PQ

iz- 23 nh xbZ vkd`fr esa AB o`r dk O;kl gS rFkk AC = 6 lseh o BC= 8 lseh gks rks Nk;kafdr Hkkx 4

dk {ks=Qy Kkr dhft,A
nh xbZ vkd`fr esa DE II BC gS ;fn AD =X , DB=X-2, AE=X+2 vkSj EC=X-1 gks rks X dk eku Kkr dhft,A

In the given figure AB is diameter of a circle, AC=6 cm and BC=8 cm. Find the area of shaded portion.

OR
In the given figure DE II BC, if AD = x, DB=x-2, AE=x+2 and EC=x-1 then find the value of x.

[k.M & Mh

Section D

iz 24 3 lseh f=T;k ysdj ,d o`Ùk cukb, ] ftlds dsUnz ls 5 lseh nwj fLFkr fcUnq P ls o`Rr dh nks Li'kZ
js[kk,a [khafp, vkSj mudh yEckbZ dh x.kuk }kjk tk¡p dhft, A 4

lqefs yr dhft,
1 csyu dk vk;ru A
2 o`Rr dh ifjf/k B
3 /kukHk dk fod.kZ C

4 Bksl v)Z xksys dk i`"Bh; {kS=Qy D
5 /ku dk vk;ru E
6 xksys dk i`"Bh; {kS=Qy F
7 /kukHk dk vk;ru G
8 nks ladsUnzh; o`Rrksa }kjk ifjc) {kS=Qy H
9 xksys dk vk;ru I
10 csyu dk odzi`"B dk {kS=Qy J ( )
Draw a circle of radius 3 cm. Construct a pair of tangents from point P 5 cm away from its centre. Also measure
the tangents and verify by calculation .
OR
Match the following
1 Volume of cylinder A
2 Circumference of the circle B
3 Diagonal of cuboid C

4 Surface area of solid hemisphere D
5 Volume of cube E
6 Surface area of sphere F
7 Volume of cuboid G
8 Area of the portion between two cocentric H
circles
9 Volume of sphere I
10 Curved surface area of cylinder J ( )

iz 25 fuEu jSf[kd lehdj.k ;qXe dks vkys[kh; fof/k }kjk gy dhft, A 4

]
fuEu jSf[kd lehdj.k ;qXe dks vkys[kh; fof/k }kjk gy dhft, A

]3
Solve the following pair of linear equation by graphical method.

]
OR

Solve the following pair of linear equation by graphical method.

]3
[k.M & bZ
iz 26 ,d Vsfyfotu lsV dk fuekZrk rhljs o"kZ 600 Vh-oh- rFkk 7 osa o"kZ 700 Vh-oh- lsVksa dk mRiknu djrk gS
A ;g ekurs gq, dh izR;sd o"kZ mRiknu esa ,d leku :i ls ,d fuf'pr la[;k esa o`f) gksrh gS A 6

Kkr dhft, (i) izFke o"kZ esa mRiknu (ii) nlosa o"kZ esa mRiknu
100 ehVj pkSM+h ,d unh ds e/; esa ,d NksVk Vkiw gSA bl Vkiw ij ,d Å¡pk o`{k gS Aunh ds foijhr fdukjksa ij
nks fcUnq P o Q bl izdkj fLFkr gS fd P , Q vkSj o`{k ,d js[kk esa gS ;fn P vkSj Q ls o`{k dh pksVh dk mUu;u
dks.k vksj gks rks o`{k dh Å¡pkbZ Kkr dhft, A
fuEu ckjEckjrk caVu dk in fopyu fof/k ls ek/; Kkr dhft,
oxZ 0&10 10&20 20&30 30&40 40&50
ckjEckjrk 7 10 15 8 10
A manufacturer of T.V. sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that
the production increases uniformly by a fixed number every year, find

(i) The production in the 1st year (ii) The production in the 10th year
OR

There is a small island in 100 m broad river and there is a tall tree on this island. P and Q lie on the opposite
banks of the river such that P, Q and tree are in the same line. If angle of elevation from P and Q at top of the tree
are 300 and 450 respectively then find the height of the tree.

OR

Find the mean of the following frequency distribution by step deviation method.

Class interval 0&10 10&20 20&30 30&40 40&50
Frequency 7 10 15 8 10

iz 27 pkj la[;k,¡ lekUrj Js<+h esa gSA ;fn la[;kvks dk ;ksxQy 50 rFkk lcls cMh la[;k] lcls NksVh la[;k
dh pkj xquh gS rks la[;k Kkr dhft,A 6
fl) dhft,

fuEu ckjEckjrk dk ek/;d Kkr dhft, %&
oxZ 10&25 25&40 40&55 55&70 70&85 85&100
ckjEckjrk 6 20 44 26 3 1
Four numbers are in A.P. If sum of numbers is 50 and largest number is four times the smaller one, then find the
numbers

OR

Prove that

OR

Find median of following Frequency distribution

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

iz 28 lekUrj Js<h 3]15]27]39 --------------- 639 ds inks dh la[;k Kkr dhft, rFkk vUr ls 8oka in Kkr dhft,A
6

dk eku Kkr dhft,

fuEu caVu dk ek/; 7-5 gks rks P dk eku Kkr dhft, vkSj caVu dk ek/;d Hkh Kkr dhft,A
x 3 5 7 9 11 13
f 6 8 15 P 8 4
Find the number of terms in A.P. 3]15]27]39 --------------- 639 and find 8th term from last.

OR

Find the value of

OR

If mean of the following distribution is 7.5, then find the value of P and also find the median of distribution

x 3 5 7 9 11 13
f 6 8 15 P 8 4