Rajasthan Board 10th Model Paper 2026 Maths

RAJASTHAN BOARD

MODEL
PAPER
2026

PRACTICE PAPERS

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iz’u&i= dh ;kstuk & 2026
d{kk & 10
fo"k; & xf.kr
vof/k & 3-15 ?k.Vs iw.kkZad & 80
1- mn~n's ; gsrq vadHkkj&
Ø-l-a mn~n’s ; vadHkkj izfr’kr
1- Kku 16 20-00
2- vocks/k 24 30+-00
3- Kkuksi;ksx 25 31-25
4- dkS’ky 8 10-00
5- fo'ys"k.k 7 8-75
;ksx 80 100 %

2- iz'uksa ds izdkj vuqlkj vadHkkj&
Ø-la- iz’uksa dk izdkj iz’uksa dh vad izfr dqy vad izfr’kr izfr’kr laHkkfor
la[;k iz’u ¼vadksa dk½ ¼iz’uksa le;
dk½
1- cgqfodYikRed 18 1 18 22-50 33-96 36
2- fjDr LFkku 6 1 06 7-50 11-32 15
3- vfry?kwÙkjkRed 12 1 12 15-00 22-64 42
4- y?kwÙkjkRed 10 2 20 25-00 18-87 40
5- nh?kZmŸkjh; iz’u 04 3 12 15-00 7-55 32
6- fuca/kkRed 03 4 12 15-00 5-66 30
;ksx 53 80 100 100 195
feuV
fodYi ;kstuk % [k.M ^l* ,oa ^n* esa gSa
3- fo"k; oLrq dk vadHkkj&
Ø- fo"k; oLrq vadHkkj izfr'kr
l-a
1 okLrfod la[;k,¡ 4 5-00
2 cgqin 4 5-00
3 nks pj okys jSf[kd lehdj.k ;qXe 4 5-00
4 f}/kkr lehdj.k 4 5-00
5 lekarj Jsf<;ka 6 7-50
6 f=Hkqt 4 5-00
7 funsZ'kkad T;kefr 7 8-75
8 f=dks.kfefr dk ifjp; 8 10-00
9 f=dks.kfefr ds dqN vuqiz;ksx 5 6-25
10 o`Ÿk 6 06-25
11 o`Ÿkksa ls lacaf/kr {ks=Qy 5 7-50
12 i`"B+h; {ks=Qy vkSj vk;ru 6 05-00
13 lkaf[;dh 13 16-25
14 izkf;drk 4 5-00
;ksx 80 100

gLrk{kj gLrk{kj
uke] in] inLFkkiu LFkku o fnukad uke] in] inLFkkiu LFkku o fnukad

iz'u&i= CY;wfizUV 2026

d{kk &10 fo"k; %& xf.kr le;%& 3-15 ?k.Vs iw.kkZad& 80

Ø- Kku vocks/k Kkuksi;ksx dkS'ky fo’ys"k.k ;ksx
la- mÌs';
bdkbZ@mi

vfry?kqÙkjkRed

vfry?kqÙkjkRed

vfry?kqÙkjkRed

vfry?kqÙkjkRed

vfry?kqÙkjkRed
cgqfodYikRed

cgqfodYikRed

cgqfodYikRed

cgqfodYikRed

cgqfodYikRed
nh?kZmÙkjkRed

nh?kZmÙkjkRed

nh?kZmÙkjkRed

nh?kZmÙkjkRed

nh?kZmÙkjkRed
y?kqÙkjkRed

y?kqÙkjkRed

y?kqÙkjkRed

y?kqÙkjkRed

y?kqÙkjkRed
bdkbZ

fucU/kkRed

fucU/kkRed

fucU/kkRed

fucU/kkRed

fucU/kkRed
fjDrLFkku

fjDrLFkku

fjDrLFkku

fjDrLFkku

fjDrLFkku
1 okLrfod la[;k,¡ 2(2) 2(2) 24(4)

2 cgqin 1(1)
2(1) 1(1) 44(3)

3 nks pj okys jSf[kd 2(1) 1(1) 1(1) 44(3)
lehdj.k ;qXe
4 f}/kkr lehdj.k 1(1) 3(1) 44(2)

5 lekarj Js<ha;k 1(1) 1(1) 1(1) 1(1) 2(1) 6(5)

6 f=Hkqt 1(1) 1(1) 2(1) 44(3)

7 funsZ'kkad T;kefr 1(1) 2(1) 3(1) 1(1) 77(4)

8 f=dks.kfefr dk 1(1) 1(1) 1(1) 1(1) 3(1) 1(-) 88(5)
ifjp;
9 f=dks.kfefr ds 1(1) 3(1) 1(-) 55(2)
dqN vuqiz;ksx
10 o`Ÿk 1(1) 1(1)
1(1)
1(1)
2(1)
66(5)

11 o`Ÿkksa ls lacaf/kr 1(1) 2(2) 2(1) 55(4)
{ks=Qy
12 i`"B+h; {ks=Qy vkSj 1(1) 1(1) 3(1)
1(-)
66(3)
vk;ru

13 lkaf[;dh 1(1) 1(1)
2(2)
2(1)
1(1) 1(1) 1(-)
1(-) 2(-) 1(-) 113(7)

14 izkf;drk 1(1) 2(1) 1(1) 44(3)

9(9) 3(3) 2(2) 2(1) 6(6) 3(3) 8(8) 4(2) 3(1) 1(1) 1(1) 9(5) 6(2) 8(3) 4(1) 1(1) 3(-) 1(1) 1(1) 3(-) 2(2)
;ksx
loZ;ksx 16 24 25 8 7 80(53)

fodYiksa dh ;kstuk %& [k.M ^l* ,oa ^n* esa izR;sd esa ,d vkarfjd fodYi gS uksV%&dks"Bd ds ckgj dh la[;k ^vadks*a dh rFkk vanj dh la[;k ^iz'uksa* ds |ksrd gSA

विशेष :- उक्त ब्ल्यू प्रिन्ट मॉडल प्रश्न पत्र का है जो प्रश्नों के प्रकारों को समझने की सुविधा मात्र के लिए है। मूल प्रश्न पत्र का ब्ल्यू प्रिन्ट भिन्न हो सकता
है।

gLrk{kj gLrk{kj lgla;kstd la;kstd
uke] in] inLFkkiu LFkku o fnukad uke] in]inLFkkiu LFkku o fnukad uke] in]inLFkkiu LFkku o fnukad uke] in] inLFkkiu LFkku o fnukad

ekè;fed f'k{kk cksMZ jktLFkku] vtesj
e‚My ç'u i= ekè;fed ijh{kk 2026
fo"k;% xf.kr ¼ MATHS½
d{kk& 10
le;% 3 ?kaVs 15 feuV iw.kkZad% 80
ijh{kkÆFk;ksa ds fy, lkekU; funsZ'k%

GENERAL INSTRUCTION FOR EXAMINEES.
1- ijh{kkFkÊ loZçFke vius ç'u i= ij ukekad vfuok;Zr% fy[ksaA

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

All the questions are compulsory.
3- çR;sd ç'u dk mÙkj nh xà mÙkj iqfLrdk es gh fy[ksaA

Write the answer to each question in the given answer book only.
4- ftu ç'uksa es 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- ç'u dk mÙkj fy[kus ls iwoZ ç'u dk Øekad vo'; fy[ksaA

Write down the serial number of the question before attempting it.
6- ç'u i= ds fgUnh o vaxt
zs h :ikUrj.k esa fdlh çdkj dh =qfV@vUrj@fojksèkkHkkl gksus ij fgUnh Hkk"kk ds ç'u
dks gh lgÈ ekusaA

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

[k.M&v
SECTION- A
¼cgqfodYih; iz’u ,oa vfry?kqŸkjkRed iz’u½
(Multiple Choice Question & Very Short Answer Type Question)

1- fuEu cgqfodYih; iz’u ¼i ls xviii½ ds mŸkj dk lgh fodYi p;u dj
mŸkj iqfLrdk esa fyf[k,A
Choose the correct option to answer the following multiple choice
question (i to xviii) and write in the answer book.
(i) fuEu esa ls vifjes; la[;k gSA
¼v½ 2 ¼c½ 4
4
¼l½ 2 ¼n½ ¼1½
9
Which of the following is an irrrational number is.
(a) 2 (b) 4
4
(c) 2 (d)
9
(ii) fuEu esa ls dkSu lk dFku lgh gS ;fn HCF (a, b)  LCM (a, b) 
¼v½ a  b ¼c½ a  b
¼l½ a  b ¼n½ a  b ¼1½
Which statement is correct if HCF (a, b)  LCM (a, b) 
(a) a  b (b) a  b
(c) a  b (d) a  b
(iii) fdlh cgqin p ( x) ds fy, y  p ( x) xzkQ esa p ( x) ds ’kwU; dh la[;k gS&
y
x'
o x
y'

¼v½ 0 ¼c½ 1
¼l½ 2 ¼n½ 3 ¼1½
1

The graph of y  p ( x) is given in following fig. for polynomia p ( x) . Find the
number of zeros of p ( x ) is -
y
x'
o x
y'

(a) 0 (b) 1
(c) 2 (d) 3
(iv) nks ljy js[kk,a a1 x  b1 y  c1  0 rFkk a2 x  b2 y  c2  0 izfrPNsn djsxh
;fn”
a1 b1 a1 c1
¼v½ a  b ¼c½ a  c
2 2 2 2

a1 b1 a1 c1
¼l½ a  b ¼n½ a  c ¼1½
2 2 2 2

Two lines a1 x  b1 y  c1  0 and a2 x  b2 y  c2  0 will intersect if -
a1 b1 a1 c1
(a) a  b (b) a  c
2 2 2 2

a1 b1 a1 c1
(c) a  b (d) a  c
2 2 2 2

1 5 9 13
(v) lekUrj Js<+h , , , ....... esa lkoZvUrj gS &
3 3 3 3
1 2
¼v½ ¼c½
3 3
4 4
¼l½  ¼n½ ¼1½
3 3
1 5 9 13
The common difference of the A.P. , , , ....... is -
3 3 3 3
1 2
(a) (b)
3 3
4 4
(c)  (d)
3 3
2

(vi) izFke ‘n’ /ku iw.kkZdksa ds ;ksx dk lw= gS &
n( n  1) n( n  1)
¼v½ ¼c½
2 2
n(1  n) n(n2  1)
¼l½ ¼n½ ¼1½
2 2
Formula for sum of first ‘n’ positive integers is -
n(n  1) n(n  1)
(a) (b)
2 2
n(1  n) n(n2  1)
(c) (d)
2 2
(vii) vkd`fr esa fdl fu;e ls  ABC   DEF gS &
A D
500 500
s eh

4l

6l
s eh
2l

3l

s eh
seh

B C E F
¼v½ S-S-S fu;e ¼c½ S-A-S fu;e
¼l½ A-S-A fu;e ¼n½ A-A-A fu;e ¼1½
In the fig, by which rule  ABC   DEF is -
A D
500 500
4c

6c
m
m

m

3c

m
2c

B C E F
(a) S-S-S Rule (b) S-A-S Rule
(c) A-S-A Rule (d) A-A-A Rule
(viii) fcUnq (3, 4) dh x- v{k ls nwjh gS &
¼v½ 3 ¼c½ 4
¼l½ 7 ¼n½ 1 ¼1½
Distance of a point (3, 4) from the x- axis is -
(a) 3 (b) 4
(c) 7 (d) 1

3

(ix) fn;s x, ledks.k f=Hkqt ABC esa cos C dk eku gS &
C

5
cm

3 cm
A B
4 cm
3 4
¼v½ ¼c½
5 5
5 4
¼l½ ¼n½ ¼1½
3 5
In given right angle triangle ABC, the value of cos C is -

C

5
cm
3 cm

A B
4 cm

3 4
(a) (b)
5 5
5 4
(c) (d)
3 5

(x) /kjrh ij ,d ehukj m/okZ/kj [kM+h gSA /kjrh ds ,d fcUnq ls tks ehukj ds
ikn fcUnq ls 15 ehVj nwj gS] ehukj ds f’k[kj dk mUu;u dks.k 600 gSA ehukj
dh mapkbZ gS &
¼v½ 3 15 ehVj ¼c½ 15 3 ehVj
15 3
¼l½ ehVj ¼n½ ehVj ¼1½
3 15

4

A tower stands vertically on the ground, from a point on the ground, which is
15 m away from the foot of tower, the angle of elevation of the top of the tower
found to be 600. The height of the tower is -
(a) 3 15 m (b) 15 3 m
15 3
(c) m (d) m
3 15
(xi) o`Ÿk ij fLFkr ,d fcUnq ls [khaph tkus okyh Li’kZ js[kkvksa dh la[;k gS &
¼v½ 1 ¼c½ 2
¼l½ 0 ¼n½ vuUr ¼1½
From a point on a circle, the number of tangents are -
(a) 1 (b) 2
(c) 0 (d) Not define
(xii) 5 lseh f=T;k okys ,d o`Ÿk ds fcUnq P ij Li’kZ js[kk PQ dsUnz O ls tkus
okyh ,d js[kk ls fcUnq Q ij bl izdkj feyrh gS fd OQ = 12 lsehA PQ
dh yEckbZ gS &
¼v½ 12 lseh ¼c½ 13 lseh
¼l½ 8-5 lseh ¼n½ 119 lseh ¼1½
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the
centre O at a point Q so that OQ =12 cm. Length PQ is -
(a) 12 cm (b) 13 cm
(c) 8.5 cm (d) 119 cm
(xiii) dks.k ' ' okys o`Ÿk ds f=T; [k.M dk {ks=Qy gS &
 
¼v½ 0
.2 r ¼c½ 0
. r 2
360 360
3600 3600
¼l½ . r 2
¼n½ .2 r ¼1½
 
Area of secter of angle ' ' of the circle is -
 
(a) 0
.2 r (b) . r 2
360 3600

5

3600 3600
(c) . r 2 (d) .2 r
 
(xiv) ,d Bksl v/kZ xksys dk lEiw.kZ i`"Bh; {ks=Qy Kkr djus dk lw= gS &
¼v½  r 2 ¼c½ 3 r 2
¼l½ 2  r 2 ¼n½ 4 r 2 ¼1½
The formula for finding the total surface area of solid hemisphere is -
(a)  r 2 (b) 3 r 2
(c) 2  r 2 (d) 4 r 2
(xv) nks ?kuks]a ftuesa ls izR;sd dk vk;ru 27 lseh3 gS] ds layXu Qydksa dks feykdj
,d Bksl ?kukHk cuk;k tkrk gS] rc ?kukHk dk vk;ru gS &
¼v½ 54 lseh3 ¼c½ 81 lseh3
¼l½ 90 lseh3 ¼n½ 72 lseh3 ¼1½
Two cubes each of volume 27 cm3 are joined end to make a solid cuboid, then
volume of cuboid is -
(a) 54 cm3 (b) 81 cm3
(c) 90 cm3 (d) 72 cm3
(xvi) d{kk 10 esa xf.kr ijh{kk esa 10 fo|kfFkZ;ksa ds }kjk izkIr vad fuEufyf[kr gS &
10] 8] 9] 10] 9] 7] 4] 9] 6] 9
bu vkadM+ksa dk cgqyd Kkr dhft,A
¼v½ 9 ¼c½ 8
¼l½ 7 ¼n½ 4 ¼1½
In class 10 marks obtained by 10 students, in maths test are given below.
10, 8, 9, 10, 9, 7, 4, 9, 6, 9
Find mode of the data.
(a) 9 (b) 8
(c) 7 (d) 4
(xvii) ek/; ( x ) ] ek/;d ( m) vkSj cgqyd ( z ) esa laca/k gS &
¼v½ 3m  z  2 x ¼c½ 3m  2 x  z
¼l½ 3m  2 z  x ¼n½ 3m  2 z  x ¼1½

6

Relation among Mean ( x ) , Median (m) and Mod ( z ) are -
(a) 3m  z  2 x (b) 3m  2 x  z
(c) 3m  2 z  x (d) 3m  2 z  x
(xviii) fuEufyf[kr esa ls A dh izkf;drk P(A) ds fy, lR; dFku gS &
¼v½ P ( A)  P( A)  1 ¼c½ P( A)  P( A)  1
¼l½ P( A)  P( A)  1 ¼n½ P( A)  P( A)  1  0 ¼1½
Among the following the true statement for the probality P(A) of event A is -
(a) P ( A)  P( A)  1 (b) P( A)  P( A)  1
(c) P( A)  P( A)  1 (d) P( A)  P( A)  1  0
2- fuEufyf[kr iz’uksa (i ls vi) esa fjDr LFkkuksa dh iwfrZ djrs gq, mŸkj iqfLrdk esa
fyf[k,A
Fill in the blanks in the following questions (i to vi) and write them in the answer
book.
(i) ;fn f}?kkr lehdj.k 2 x 2  kx  3  0 ds nksukas ewy cjkcj gks rks
k =--------------------- gksxkA ¼1½
If both roots of quadralic equation 2 x 2  kx  3  0 are equal then
k = ............... will be.
1 1 1
(ii) lekUrj Js<h , , ........... dk lkoZ vUrj gSA ¼1½
15 12 10
1 1 1
Common difference of A.P. , , ........... is
15 12 10
(iii) loZlfedk sec 2   1  --------------- gSA ¼1½
Inditities sec 2   1  ............ is.
(iv) lHkh --------------- f=Hkqt le:i gksrs gSA ¼lef}ckgq] leckgq½ ¼1½
All ................ triangles are similar (Isosceles, Equilateral)
(v) o`Ÿk rFkk mlds Li’kZ js[kk ds mHk;fu"B fcUnq dks --------------- dgrs gSA ¼1½
The common point of a tangent to a circle and the circle is called ---------------
(vi) ,d ikls dks ,d ckj mNkyus ij le vad vkus dh izkf;drk ------------ gksxhA
¼1½
A die throw once probabilities getting even number will ...........

7

3- vfry?kqŸkjkRed iz’u (i ls xii)
Very short answer type question (i to xii)
(i) ;fn LCM (96, 404) = 9696 rc HCF (96, 404) dk eku D;k gksxkA ¼1½
If LCM (96, 404) = 9696 then find the value of HCF (96, 404)
(ii) 3825 dks vHkkT; xq.ku[k.Mksa ds xq.ku[kaM ds :i esa O;Dr djksA ¼1½
Express 3825 as a product of its prime factors.
(iii) ,d f}?kkr cgqin Kkr dhft,] ftlds ’kwU;kdksa dk ;ksx rFkk xq.kuQy
Øe’k% &3 vkSj 2 gSA ¼1½
Find a quadratic polynomial, the sum and product of whose zeroes are -3
and 2, respectively.
(iv) nks js[kk,a fuEu lehdj.kksa 2 x  4 y  4 vkSj 2 x  4 y  12 }kjk fu:fir dh
xbZ gSA D;k ljy js[kk,a ,d nwljs dks dkVsxhA ¼1½
Two lines are represented by the equations 2 x  4 y  4 and 2 x  4 y  12 ,
will the line intersect each other.
(v) AP 21, 18, 15 .........dk dkSu lk in ’kwU; gSA ¼1½
Which term of AP 21, 18, 15 ......... is zero.
(vi) x vkSj y esa ,d ,slk laca/k Kkr dhft, fd fcUnq (x, y) fcUnqvksa (3, 6)
vkSj (-3, 4) ls lenwjLFk gksA ¼1½
Find a relation between x and y, such that the point (x, y) is equidistant from
the point (3, 6) and (-3, 4)
(1  sin  ) (1  sin  )
(vii) ;fn 8cot   7 rks (1  cos  ) (1  cos  ) dk eku Kkr dhft,A ¼1½

(1  sin  ) (1  sin  )
If 8cot   7 , evaluate (1  cos  ) (1  cos  )

(viii) ;fn ,d fcUnq P ls O dsUnz okys fdlh o`Ÿk ij PA vkSj PB Li’kZ js[kk,a ijLij
800 ds dks.k ij >qdh gks rks  POA dk eku gksxkA ¼1½
If tangents PA and PB from a point P to a circle with centre O are inclined to
each other at angle of 800 , then the value of  POA will.
(ix) f=T;k 21 lseh okys o`Ÿk dk ,d pki dsUnz ij 600 dk dks.k varfjr djrk
gS rks pki dh yEckbZ Kkr dhft,A ¼1½
8

In a circle of radius of 21 cm, an arc subtends an angle of 600 at a centre. Find
length of the arc.
(x) 5 lseh f=T;k okys ,d o`Ÿk ds ,d f=T;[k.M dk {ks=Qy Kkr dhft,]
ftldk dks.k 600 gS \ ¼1½
Find the area of a sector of a circle with redius 5 cm, if angle of the sector is
600.
(xi) ;fn fuEu vkadM+kas dk cgqyd 7 gks rks ‘k’ dk eku Kkr dhft,A
2, 4, 6, 7, 5, 6 10, 6, 7, 2k+1, 9, 7 ¼1½
If the mode of the following data is 7, then find the value of ‘k’
2, 4, 6, 7, 5, 6 10, 6, 7, 2k+1, 9, 7
\(xii) fuEu ckjEckjrk vkadM+ksa dk ek/;d Kkr dhft,A
izkIrkad 20 25 28 29 33 38 42 43
fo|kfFkZ;ksa dh la[;k 6 20 28 24 15 4 2 1 ¼1½
Find the median of the following data .
Marks obtained 20 25 28 29 33 38 42 43
Number of students 6 20 28 24 15 4 2 1

[k.M&c
SECTION-B
y?kqŸkjkRed iz’u (Very short answer type question)

4- f}?kkr cgqin x 2  7 x  10 ds ’kwU;d Kkr dhft, vkSj ’kwU;dksa rFkk xq.kkadksa ds
chp ds laca/k dh lR;rk dh tkap dhft,A ¼2½
Find the zeroes of the quadratic polynomial x 2  7 x  10 and verify the
relations between the zeroes and the coefficients.
5- nks vadksa dh ,d la[;k ,oa mlds vadksa dks myVus ij cuh la[;k dk ;ksx 66
gSA ;fn la[;k ds vadksa dk varj 2 gks rks la[;k Kkr dhft,A ,slh la[;k,a
fdruh gS? ¼2½

9

The sum of the two digit number and the number obtained by reversing the
digits is 66. If the digits of the number differ by 2, find the number. How many
such numbers are there?
6- og A.P. fu/kkZfjr dhft, ftldk rhljk in 5 vkSj 7oka in 9 gSA
Determine the A.P. whose 3rd term is 5 and the 7th term is 9. ¼2½
7- vkd`fr esa Øe’k% OP, OQ vkSj OR ij fLFkr fcUnq vkSj bl izdkj gS fd
AB  PQ vkSj AC  PR gSA n’kkZb, fd BC  QR gSA

P

A

B O C
Q R
¼2½
In Fig. A, B and C are points on OP, OQ and OR, respectively such that
AB  PQ and AC  PR , show that BC  QR
P

A

B O C
Q R

8- fu/kkZfjr dhft, fd D;k fcUnq (1, 5), (2, 3) vkSj (-2, -11) laj[s kh gSA ¼2½
Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
9-  OPQ es]a ftldk dks.k P ledks.k gS] OP = 7 lseh vkSj OQ-PQ = 1lseh]
sin Q vkSj cos Q ds eku Kkr dhft,A ¼2½
In  OPQ , right angle at P, OP = 7 cm and OQ-PQ = 1 cm. Determine the
value of sin Q and cos Q .
10- dsUnz O okys o`Ÿk ij ckã fcUnq T ls nks Li’kZ js[kk,a TP rFkk TQ [khaph xbZ gSA
fl} dhft, fd  PTQ  2 OPQ

10

P

T O

¼2½
Q

Two tangents TP and TQ are drawn to a circle with centre O from external
point T. Prove that  PTQ  2 OPQ
P

T O

Q

11- fdlh dkj ds nks okbij gS] ijLij dHkh vkPNkfnr ugha gksrs gSA izR;sd okbij
dh iŸkh dh yEckbZ 25 lseh gS vkSj 1150 ds dks.k rd ?kwedj lQkbZ dj ldrs
gSA ifŸk;ksa dh izR;sd cqgkj ds lkFk ftruk {ks=Qy lkQ gks tkrk gS] og Kkr
dhft,A ¼2½
A car has two wipers which do not overlap. Each wiper has a blade of length
25 cm sweeping through an angle of 1150. Find the total area cleared at each
sweep of the blades.
12- fuEufyf[kr lkj.kh 35 uxjksa dh lk{kjrk nj ¼izfr’kr esa½ n’kkZrh gSA ek/;
lk{kjrk nj Kkr dhft,A
lk{kjrk nj ¼izfr’kr esa½ 45&55 55&65 65&75 75&85 85&95
uxjksa dh la[;k 3 10 11 8 3 ¼2½
The following table gives the literacy rate (in percentage) of 35 cities. Find the
mean literacy rate.
Literacy rate ( In %) 45&55 55&65 65&75 75&85 85&95
Number of cities 3 10 11 8 3
13- 52 iŸkksa dh vPNh QsVa h xbZ ,d xM~Mh esa ls ,d iŸkk fudkyk tkrk gSA
fuEufyf[kr dks izkIr djus dh izkf;drk Kkr dhft,A

11

(1) yky jax dk ckn’kkg (2) gqdqe dk iŸkk
(3) yky jax dh rLohj okyk iŸkk (4) ,d rLohj okyk iŸkk ¼2½
One card is drawn from a well shuffled deck of 52 cards. Find the probalities
of getting.
(1) A king of red colour (2) A shade
(3) A red face card (4) A face card

[k.M&l
SECTION- C
nh?kZ mŸkjh; iz’u (Long answer type question)

14- nks Øekxr /kukRed iw.kkZd
a Kkr dhft,] ftuds oxksZ dk ;ksx 365 gksA ¼3½
Find two consecative positive integers, sum of whose squares is 365.
vFkok@ OR
f}?kkr lehdj.k kx ( x  2)  6  0 esa k dk ,slk eku Kkr dhft, fd muds nks
cjkcj ewy gksA ¼3½
Find the value of k for the quadratic equation kx ( x  2)  6  0 , so that they
have two equal roots.
15- og vuqikr Kkr dhft,] ftlesa fcUnqvksa A (1, -5) vkSj B (-4, 5) dks feykus
okyk js[kk[k.M x v{k ls foHkkftr gksrk gSA bl foHkktu fcUnq ds funsZ’kkad Hkh
Kkr dhft,A ¼3½
Find the ratio in which the line segment joining A (1, -5) and B (-4, 5) is divided
by the x axis. Also find the coordinates of the point of division.
vFkok@ OR
;fn A vkSj B Øe’k% (-2, -2) vkSj (2, -4) gks rks fcUnq P ds funsZ’kkad Kkr
3
dhft, rkfd AP  AB gks vkSj P js[kk[k.M AB ij fLFkr gksA ¼3½
7
If A and B are (-2, -2) and (2, -4), respectively find the coordinates of P, such
3
that AP  AB and P lies on the line segment AB.
7

12

16- fl} dhft, fd
cot A  cos A cos ec A  1

cot A  cos A cos ec A  1
Prove that
cot A  cos A cos ec A  1
 ¼3½
cot A  cos A cos ec A  1
vFkok@ OR
fl} dhft, fd
1  sin A
 Sec A  tan A
1  sin A
tgka A U;wu dks.k gSA ¼3½
Prove it

1  sin A
 Sec A  tan A
1  sin A
Where A is acute angle.
17- fdlh Ldwy dh d{kk X dh 51 yM+fd;ksa dh ÅapkbZ;ksa ¼lseh esa½ dk ,d losZ{k.k
fd;k x;k vkSj fuEufyf[kr vkadM+s izkIr fd, x,A
ÅapkbZ ¼lseh½ yM+fd;ksa dh la[;k
140 ls de 4
145 ls de 11
150 ls de 29
155 ls de 40
160 ls de 46
165 ls de 51
ek/;d ÅapkbZ Kkr dhft,A ¼3½

A survey regarding the heights (in cm) of 51 girls of class X of a school was
conducted and the following data was obtained.

13

Height (in cm) Number of girls
Less than 140 4
Less than 145 11
Less than 150 29
Less than 155 40
Less than 160 46
Less than 165 51
Find the median height.
vFkok@ OR
;fn uhps fn, gq, caVu dk ek/;d 28-5 gks rks x vkSj y ds eku Kkr dhft, \
oxZ varjky ckjEckjrk
0&10 5
10&20 x
20&30 20
30&40 15
40&50 y
50&60 5
60 ¼3½

If the median of the distribution given below is 28.5, find the values of x and y.
Class interval Frequency
0&10 5
10&20 x
20&30 20
30&40 15
40&50 y
50&60 5
60

14

[k.M&n
SECTION- D
fucU/kkRed iz’u (Essay type question)

18- Hkwfe ds ,d fcUnq P ls ,d 10 ehVj Åaps Hkou ds f’k[kj dk mUu;u dks.k 300
gSA Hkou ds f’k[kj ij ,d /ot dks ygjk;k x;k gS vkSj P ls /ot ds f’k[kj
dk mUu;u dks.k 450 gSA /ot naM dh yEckbZ vkSj fcUnq P ls Hkou dh nwjh
Kkr dhft,A ( 3  1.73) ¼4½
From a point P on the ground the angle of elevation of the top of a 10 m. tall
building in 300. A flag is hoisted at the top of the building and the angle of elevation
of the top of the flagstaff from P is 450. Find the length of the flagstaff and the
distance of the building from the point P. ( 3  1.73)
vFkok@ OR
leqnz ry ls 75 ehVj Åaph ykbZV gkÅl ds f’k[kj dks ns[kus ij nks leqnzh tgktksa
ds voueu dks.k 300 vkSj 450 gSA ;fn ykbZV gkÅl ds ,d gh vksj ,d tgkt]
nwljs tgkt ds Bhd ihNs gks rks nks tgktksa ds chp dh nwjh Kkr dhft,A ¼4½

As observed from the top of a 75 m, high lighthouse from the sea-level. The angle
of depression of two ships are 300 and 450. If one ship is exactly behind and
other on the same side of the lighthouse. Find the distance between the two ships.
19- ,d Bksl f[kykSuk ,d v/kZxksys ds vkdkj dk gS] ftl ij ,d yac o`Ÿkh; ’kadq
vkjksfir gSA bl ’kadq dh ÅapkbZ 2 lseh vkSj vk/kkj dk O;kl 4 lseh gSA bl
f[kykSus dk vk;ru fu/kkZfjr dhft,A ;fn ,d yac o`Ÿkh; csyu bl f[kykSus ds
ifjxr gks rks csyu vkSj f[kykSus ds vk;ruksa dk varj Kkr dhft,A ¼   3.14 yhft,½
¼4½
A solid toy is in the form of a hemisphere surmounted by a right circular cone.
The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine
the volume of the toy. If a right circular cylinder circumscribes the toy. Find the
difference of the volumes of the cylinder and the toy. (Take   3.14 )
vFkok@ OR

15

,d xqykctkequ esa mlds vk;ru dh yxHkx 30 izfr’kr phuh dh pk’kuh gksrh
gSA 45 xqykctkequ esa fdruh pk’kuh gksxh] ;fn izR;sd xqykctkequ ,d csyu ds
vkdkj dk gS] ftlds nksuksa fljs v/kZxksykdkj gS rFkk bldh yEckbZ 5 lseh vkSj
O;kl 2-8 lseh gSA ¼4½
A Gulabjamun contains sugar syrup up to about 30 % of its volume. Find
approximately how much syrup would be found in 45 Gulabjamun, each shaped
like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
20- fo|kfFkZ;ksa ds ,d lewg }kjk ,d ekSgYys ds 20 ifjokjksa ij fd, x, losZ{k.k ds
ifj.kkeLo:i fofHkUu ifjokjksa ds lnL;ksa dh la[;k ls lacaf/kr fuEufyf[kr
vkadM+s izkIr gq,A
ifjokj eki 1&3 3&5 5&7 7&9 9&11
ifjokjksa dh la[;k 7 8 2 2 1
bu vkadM+ksa dk cgqyd Kkr dhft,A ¼4½
A survey conducted on 20 households is a locality by a group of students
resulted in the following frequency table for the number of family members in a
household.
Family Size 1&3 3&5 5&7 7&9 9&11
No. of families 7 8 2 2 1
Find the mode of this data.
vFkok@ OR
fuEufyf[kr lkj.kh fdlh ekSgYys ds 25 ifjokjksa esa Hkkstu ij gq, nSfud O;;
dks n’kkZrh gSA
nSfud O;; ¼:i;ksa esa½ 100&150 150&200 200&250 250&300 300&350
ifjokjksa dh la[;k 4 5 12 2 2
,d mi;qDr fof/k }kjk Hkkstu ij gqvk ek/; O;; Kkr dhft,A ¼4½
A table below shows the daily expenditure on food of 25 households in a
locality.
Daily expenditure (in Rs.) 100&150 150&200 200&250 250&300 300&350
No. of households 4 5 12 2 2
Find the mean daily expenditure on food by a suitable method.

16

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