Rajasthan Board Class 10 Question Paper 2023 Maths

Rajasthan Board

QUESTION
PAPER

Zm_m§H$ Roll No.

Tear Here
Sl.No. :

No. of Questions – 23 S–09–Mathematics
No. of Printed Pages – 15

_mÜ`{_H$ narjm, 2023
SECONDARY EXAMINATION, 2023

TEAR HERE TO OPEN THE QUESTION PAPER
J{UV
MATHEMATICS

àíZ nÌ H$mo ImobZo Ho$ {bE `hm± \$m‹S>|
g_` : 3 KÊQ>o 15 {_{ZQ>
nyUmªH$ : 80

narjm{W©`m| Ho$ {bE gm_mÝ` {ZX}e …
GENERAL INSTRUCTIONS TO THE EXAMINEES :
1) narjmWu gd©àW_ AnZo àíZ nÌ na Zm_m§H$ A{Zdm`©V… {bI| &
Candidate must write first his / her Roll No. on the question paper
compulsorily.
2) g^r àíZ hb H$aZo A{Zdm`© h¢ &
All the questions are compulsory.
3) àË`oH$ àíZ H$m CÎma Xr JB© CÎma-nwpñVH$m _| hr {bI| &
Write the answer to each question in the given answer-book only.
4) {OZ àíZmo§ ‘| AmÝV[aH$ IÊS> h¢, CZ g^r Ho$ CÎma EH$ gmW hr {bI|&
For questions having more than one part, the answers to those parts
`hm± go H$m{Q>E

are to be written together in continuity.

S–09–Mathematics 1205 [ Turn Over

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5) àíZ nÌ Ho$ {hÝXr d A§J«oOr ê$nmÝVa ‘| {H$gr àH$ma H$s Ìw{Q> / AÝVa / {damoYm^mg hmoZo na {hÝXr ^mfm
Ho$ àíZ H$mo hr ghr ‘mZ|&
If there is any error / difference / contradiction in Hindi & English versions of
the question paper, the question of Hindi version should be treated valid.
6) àíZ H$m CÎma {bIZo go nyd© àíZ H$m H«$_m§H$ Adí` {bI|&
Write down the serial number of the question before attempting it.

7) àíZ H«$‘m§H$ 21 go 23 VH$ ‘| AmÝV[aH$ {dH$ën h¢&
There are internal choices in Question Nos. 21 to 23.
8) AnZr CÎma-nwpñVH$m Ho$ n¥ð>m| Ho$ XmoZm| Amoa {b{IE& ¶{X H$moB© aµ\$ H$m¶© H$aZm hmo, Vmo CÎma-nwpñVH$m Ho$
A§{V‘ n¥ð>m| na H$a| Am¡a BÝh| {VaN>r bmBZm| go H$mQ>H$a CZ na "aµ\$ H$m¶©' {bI X|&
Write on both sides of the pages of your answer-book. If any rough work
is to be done, do it on last pages of the answer-book and cross with slant
lines and write ‘Rough Work’ on them.
9) àíZ H«$‘m§H$ 21 H$m boIm{MÌ J«m’$ nona na ~ZmBE&
Draw the graph of Question No. 21 on graph paper.

S–09–Mathematics 1205

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IÊS> - A
SECTION - A

(dñVw{Zð> Ed§ A{VbKwÎmamË_H$ àíZ)

(Objective and Very Short Answer Type Questions)

1) {ZåZ dñVw{Zð> àíZm| Ho$ CÎma H$m ghr {dH$ën M`Z H$a CÎma nwpñVH$m _| {b{IE&
Answer the following questions and write them in the answer book by selecting the
correct option.

i) 196 Ho$ A^mÁ¶ JwUZIÊ‹S>m| H$s KmVmo H$m ¶moJ’$b h¡ : [1]

A) 1 ~) 2

g) 4 X) 6

The sum of the powers of the prime factors of 196 is
A) 1 B) 2
C) 4 D) 6

ii) ¶{X {ÛKmV g‘rH$aU x 2  kx  4  0 Ho$ ‘yb g‘mZ hmo, Vmo k H$m ‘mZ hmoJm - [1]

A) 1 ~) 2

g) 3 X) 4

If roots of the quadratic equation x 2  kx  4  0 are equal, then the value of
k will be -

A) 1 B) 2

C) 3 D) 4

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iii) {~ÝXþ (3, 4) H$s y-Aj go Xÿar hmoJr - [1]

A) 1 ~) 2

g) 3 X) 4

The distance of the point (3, 4) from the y - axis will be -

A) 1 B) 2

C) 3 D) 4

iv) 3 x  2 y  11 H$mo gÝVwï> H$aZo dmbm ¶w½‘ h¡ - [1]

A) (1, 4) ~) (2, 3)

g) (3, 5) X) (1, 3)

The pair satisfying 3 x  2 y  11 is -

A) (1, 4) B) (2, 3)

C) (3, 5) D) (1, 3)

v) {ÛKmV g‘rH$aU 3 3x 2  10 x  3  0 H$m {d{d{³VH$a hmoJm : [1]

A) 8 ~) 30

g) 46 X) 64

Discriminant of quadratic equation 3 3x 2  10 x  3  0 will be :

A) 8 B) 30

C) 46 D) 64

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vi) ¶{X 18, a, b, –3 g‘mÝVa lo‹T>r ‘| h¡ Vmo a + b H$m ‘mZ hmoJm - [1]

A) 7 ~) 11

g) 15 X) 19

If 18, a, b, –3 are in A.P., then the value of a + b will be :

A) 7 B) 11

C) 15 D) 19

vii) 3sec 45 cos 45 H$m ‘mZ hmoJm - [1]

A) 0 ~) 1

g) 2 X) 3

Value of 3sec 45 cos 45 will be :

A) 0 B) 1

C) 2 D) 3

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viii) d¥Îm H$s dh Ordm {OgH$s bå~mB© d¥Îm H$s {ÌÁ¶m go XmoJwZr hmo, H$hbmVr h¡ - [1]

A) {ÌÁ¶IÊ‹S> ~) ì¶mg

g) joÌ’$b X) n[a{Y

A chord of a circle, whose length is twice the radius of the circle, is called :

A) Sector B) Diameter

C) Area D) Circumference

ix) EH$ d¥Îm H$s {ÌÁ¶m 3.5 go‘r h¡, Vmo d¥Îm H$s n[a{Y hmoJr - [1]

A) 11 go‘r ~) 22 go‘r

g) 33 go‘r X) 44 go‘r

Radius of a circle is 3.5 cm. Find its circumference.

A) 11 cm B) 22 cm

C) 33 cm D) 44 cm

x) KZ H$m gånyU© n¥ð>r¶ joÌ’$b 486 dJ© go‘r h¡, KZ H$s ^wOm H$m ‘mn hmoJm - [1]

A) 6 go‘r ~) 7 go‘r

g) 8 go‘r X) 9 go‘r

The total surface area of a cube is 486 cm2. Measure of side of the cube will
be -

A) 6 cm B) 7 cm

C) 8 cm D) 9 cm

S–09–Mathematics 1205

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xi) ~§Q>Z 3, 5, 7, 4, 2, 1, 4, 3 Am¡a 4 H$m ~hþbH$ h¡ - [1]
A) 1 ~) 3
g) 4 X) 7
The mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3 and 4 is -
A) 1 B) 3
C) 4 D) 7
xii) EH$ nmgo H$mo ’|$H$Zo na 4 go ~‹S>m A§H$ AmZo H$s àm{¶H$Vm kmV H$s{OE& [1]

1 1
A) ~)
2 3

3
g) X) 1
4
In a throw of a die, determine the probability of getting a number more than 4 :

1 1
A) B)
2 3

3
C) D) 1
4

2) {ZåZ{b{IV àíZm| _| [aº$ ñWmZm| H$s ny{V© H$aVo hþE CÎmanwpñVH$m _| {b{IE&
Fill in the blanks in the following questions and write them in the answerbook.
i) 95 VWm 152 H$m ‘hÎm‘ g‘mndÎm©H$ (HCF) __________ h¢& [1]
Highest Common Factor (HCF) of 95 and 152 is __________.
ii) d¥Îm na pñWV EH$ {~ÝXþ go ________ ñne© aoIm ItMr Om gH$Vr h¡& [1]
________ tangent can be drawn from a point on the circle.

S–09–Mathematics 1205 [ Turn Over

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iii) cos 2 45 H$m ‘mZ _____________ h¡& [1]

The value of cos 2 45 is _____________.

iv) d¥Îm VWm CgH$s ñne© aoIm Ho$ C^¶{ZîR> {~ÝXþ H$mo _______ H$hVo h¢& [1]

The common point of the circle and its tangent line is called __________.

v) ¶{X 5, 7, 9, x H$m g‘mÝVa ‘mܶ 9 hmo, Vmo x H$m ‘mZ _________ hmoJm& [1]

If Arithmetic mean of a distribution 5, 7, 9, x is 9, then value of x will
be _________.

vi) Xmo nmgm| H$mo EH$ gmW ’|$H$Zo na A§H$m| H$m ¶moJ 7 AmZo H$s àm{¶H$Vm __________ hmoJr& [1]

In a single throw of two dice, probability of getting a total of 7 will
be __________.

3) A{V bKwÎmamË_H$ àíZ&>
Very short answer type questions.

i) k Ho$ {H$g ‘mZ na g‘rH$aU ¶w½‘ 3 x  2 y  0 VWm kx  5 y  0 Ho$ AZÝV hb hm|Jo? [1]

For which value of k, linear pair 3 x  2 y  0 and kx  5 y  0 will have Infinite
Solutions?

ii) {ÛKmV g‘rH$aU ax 2  bx  c  0 Ho$ ‘yb kmV H$aZo H$m lrYamMm¶© gyÌ {b{IE& [1]

Write the Sridharacharya formula to find roots of quadratic equation
ax 2  bx  c  0 .

iii) {H$gr g‘mÝVa lo‹T>r (A.P.) H$m àW‘ nX “a” Ed§ gmd©AÝVa “d ” hmo, Vmo nm±Mdm nX ³¶m hmoJm?[1]
What will be the Fifth term of a Arithmetic Progression (A.P.) whose First
term is “a” and common difference is “d ”?

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iv) g‘ê$n AmH¥${V¶m| H$mo n[a^m{fV H$s{OE& [1]

Define similar figures.

2 tan 30
v) H$m ‘mZ kmV H$s{OE& [1]
1  tan 2 30

2 tan 30
Find the value of .
1  tan 2 30

vi) 1  cos 2  H$m ‘mZ   60 na kmV H$s{OE& [1]

Find the value of 1  cos 2  at   60 .

vii) 10 ‘rQ>a D±$Mr ‘rZma Ho$ {eIa go n¥Ïdr na EH$ {~ÝXþ H$m AdZ‘Z H$moU 30° h¡& {~ÝXþ H$s ‘rZma Ho$
AmYma go Xÿar {H$VZr hmoJr? [1]

From the top of 10 meter high tower, angle of depression at a point on earth is
30°. What will be the distance of point from the base of tower?

viii) EH$ CÜdm©Ya N>‹S> H$s bå~mB© VWm BgH$s N>m¶m H$s bå~mB© H$m AZwnmV 1: 3 hmo, Vmo gy¶© H$m CÝZ¶Z
H$moU kmV H$s{OE& [1]

If ratio of length of a vertical rod and length of its shadow is 1: 3 , then find
the angle of elevation of Sun.

ix) 3 go‘r {ÌÁ¶m boH$a EH$ d¥Îm ~ZmB©¶o VWm Ho$ÝÐ O go 5 go‘r Xÿa pñWV {~ÝXþ P go d¥Îm H$s Xmo ñne© aoImE±
It{ME Am¡a CZH$m ‘mn {b{IE& [1]

Draw a circle with centre O and radius 3 cm and draw two tangents to the
circle from a point P which is 5 cm away from its centre and write the
measurement of them.

S–09–Mathematics 1205 [ Turn Over

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x) 5 go‘r bå~m EH$ aoImIÊ‹S> AB It{ME Ed§ Cgo 2 : 3 Ho$ AZwnmV ‘| {d^m{OV H$s{OE& XmoZm| ^mJm| H$m
‘mn {b{IE& [1]

Draw a line segment AB of length 5 cm and divide it into the ratio 2 : 3. Write
the measurement of both the parts.

xi) {H$gr d¥Îm H$m {ÌÁ¶IÊ‹S> Cg d¥Îm H$m MVwWmªe h¢, Vmo {ÌÁ¶IÊ‹S> ‘| Ho$ÝÐ na ~ZZo dmbo H$moU H$m ‘mn
³¶m hmoJm? [1]

If the sector of a circle is a quadrant of that circle, then what will be the
measure of the angle formed by the sector on centre?

xii) AÀN>r àH$ma go ’|$Q>r JB© 52 nÎmm| H$s EH$ JS²>‹S>r ‘| go EH$ nÎmm {ZH$mbm OmVm h¡& Bg nÎmo Ho$ Xhbm hmoZo
H$s àm{¶H$Vm kmV H$s{OE& [1]

A card is drawn from a well shuffled deck of 52 cards. Find the probability of
it being a ten.

IÊS> - ~
SECTION - B

13
4) n[a‘o¶ g§»¶m H$m Xe‘bd àgma {b{IE& [2]
125

13
Write down the decimal expansion of the rational number .
125

5) ~hþnX x 2  x  6 Ho$ eyݶH$ kmV H$s{OE& [2]

Find the zeroes of the polynomial x 2  x  6 .

S–09–Mathematics 1205

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6) {ÛKmV g_rH$aU 4 x 2  12 x  9  0 Ho$ _ybm| H$s àH¥${V H$m nVm bJmB©¶o& [2]

Find out the nature of roots of the quadratic equation 4 x 2  12 x  9  0 .

7) {~ÝXþAm| (0, 0) Am¡a (5, –3) H$mo OmoS>Zo dmbo aoImIÊ‹S> Ho$ ‘ܶ {~ÝXþ Ho$ {ZX}em§H$ kmV H$s{OE? [2]

Find the co-ordinates of the mid point of the line segment joining the points (0, 0)
and (5, –3).

8) EH$ g‘Vb O‘rZ na I‹S>r ‘rZma H$s N>m¶m Cg pñW{V ‘| 40 ‘rQ>a A{YH$ bå~r hmo OmVr h¡ O~{H$ gy¶© H$m
CÝZVm§e H$moU 60° go KQ>H$a 30° hmo OmVm h¡& ‘rZma H$s D±$MmB© kmV H$s{OE& [2]

The shadow of a tower on a level ground is increased by 40 meter, when the
altitude of the Sun changes from 60° to 30°. Find the height of the tower.

9) 6 go‘r ^wOm Ho$ Zmn dmbo EH$ g‘~mhþ{Ì^wO H$s aMZm H$s{OE Am¡a {’$a EH$ Aݶ {Ì^wO H$s aMZm H$s{OE,
2
{OgH$s ^wOmE± {XE hþE {Ì^wO H$s g§JV ^wOmAm| H$s JwZr hm|& [2]
3

Construct an equilateral triangle whose measurement of side is 6 cm and then
2
construct another triangle whose sides are times the corresponding sides of the
3
given equilateral triangle.

10) 4 go‘r {ÌÁ¶m Ho$ EH$ d¥Îm na Eogr Xmo ñne© aoImE± It{ME Omo EH$ Xÿgao Ho$ g‘mÝVa hmo& [2]

Draw a pair of tangents to a circle of radius 4 cm, which are parallel to each other.

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11) ¶{X Xmo g‘ê$n {Ì^wOm| Ho$ joÌ’$b ~am~a hmo, Vmo {gÕ H$s{OE {H$ do {Ì^wO gdmªJg‘ hmoVo h¢? [2]
If the area of the two similar triangles are equal, prove that they are congruent?

12) EH$ d¥Îm H$s {ÌÁ¶m 7 go‘r h¡ VWm EH$ Mmn Ûmam Ho$ÝÐ na AÝV[aV H$moU 60° h¡& Bg {ÌÁ¶IÊ‹S> H$m joÌ’$b
kmV H$s{OE& [2]
Radius of a circle is 7 cm and the angle subtended at the centre by an arc is 60°.
Find the area of this sector.

13) EH$ e§Hw$ Ho$ {N>ÝZH$ H$s {V¶©H$ D±$MmB© 4 go‘r h¡ VWm BgHo$ d¥Îmr¶ {gam| Ho$ n[a‘mn (n[a{Y¶m±) 18 go‘r Am¡a
6 go‘r h¢& Bg {N>ÝZH$ H$m dH«$ n¥îR>r¶ joÌ’$b kmV H$s{OE& [2]
The slant height of a frustum of a cone is 4 cm and the perimeters (circumference)
of its circular ends are 18 cm and 6 cm. Find the curved surface area of the
frustum.

14) Xmoo KZm|, {OZ‘| go à˶oH$ H$m Am¶VZ 64 go‘r3 h¡, Ho$ g§b½Z ’$bH$m| H$mo {‘bmH$a EH$ R>mog ~Zm¶m OmVm h¡&
n[aUm‘r KZm^ H$m n¥îR>r¶ joÌ’$b kmV H$s{OE& [2]
Two cubes each of volume 64 cm3 are joined end to end. Find the surface area of
the resulting cuboid.

15) {ZåZ ~maå~maVm ~§Q>Z H$m ‘mܶ kmV H$s{OE& [2]
x 1 2 3 4 5 6
f 2 4 5 4 2 2
Find the mean of the following frequency distribution.
x 1 2 3 4 5 6
f 2 4 5 4 2 2

S–09–Mathematics 1205

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16) EH$ {S>ã~o ‘| 8 bmb H§$Mo, 5 g’o$X H§$Mo Am¡a 2 hao H§$Mo h¢& Bg {S>ã~o ‘| go EH$ H§$Mm ¶mÑÀN>¶m {ZH$mbm OmVm
h¡& BgH$s ³¶m àm{¶H$Vm h¡ {H$ {ZH$mbm J¶m H§$Mm : [2]

(i) bmb h¡? (ii) ham Zht h¡?
A box contains 8 red marbles, 5 white marbles and 2 green marbles. One marble is
taken out of the box at random. What is the probability that the marble taken out is :
(i) red? (ii) not green?

IÊS> - g
SECTION - C

17) Eogo àW‘ 40 YZmË‘H$ nyUmªH$m| H$m ¶moJ kmV H$s{OE Omo 6 go {d^mÁ¶ h¡& [3]
Find the sum of the first 40 Positive Integers divisible by 6.

18) Cg {Ì^wO H$m joÌ’$b kmV H$s{OE {OgHo$ erf© (2, 3), (–1, 0) VWm (2, –4) h¡& [3]
Find the area of triangle whose vertices are (2, 3), (–1, 0) and (2, –4).

19) EH$ H$jm Ho$ N>mÌm| Ho$ n«mßVm§H$ {ZåZ ~§Q>Z ‘| {XE hþE h¢& BZH$m ‘mܶH$ kmV H$s{OE& [3]

àmßVm§H$ 0-10 10-20 20-30 30-40 40-50

N>mÌm| H$s g§»¶m 4 28 42 20 6
The marks of students of a class are given in following frequency distribution.
Find their median.
Marks Obtained 0-10 10-20 20-30 30-40 40-50
No. of Students 4 28 42 20 6

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20) Ho$ÝÐ O dmbo d¥Îm na ~mø {~ÝXþ T go Xmo ñne© aoImE± TP VWm TQ ItMr JB© h¡& {gÕ H$s{OE {H$
 PTQ  2 OPQ h¡& [3]
Two tangents TP and TQ are drawn to a circle with centre O from an external
point T. Prove that  PTQ  2 OPQ .

IÊS> - X
SECTION - D

21) {ZåZ a¡{IH$ g_rH$aU `w½_ H$mo AmboIr` {d{Y Ûmam hb H$s{OE … [4]

x  y  14
x y4
Solve the following pair of linear equations graphically :
x  y  14
x y4

AWdm/OR
EH$ H$jm Ho$ 10 {dÚm{W©¶m| Zo J{UV H$s nhobr à{V¶mo{JVm ‘| ^mJ {b¶m& ¶{X bS>{H$¶m| H$s g§»¶m bS>H$m| H$s
g§»¶m go 2 A{YH$ hmo, Bg pñW{V H$m ~rOJ{UVr¶ Ed§ J«m’$s¶ {Zê$nU H$s{OE& [4]
10 students of a class took part in a mathematics quiz. If the number of girls is 2
more than the number of boys, represent the situation algebraically and graphically.

22) {gÕ H$s{OE {H$ : [4]
1  cos A
 cosec A  cot A
1  cos A
Prove that :
1  cos A
 cosec A  cot A
1  cos A
AWdm/OR

S–09–Mathematics 1205

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{gÕ H$s{OE {H$ : [4]

 sin A  cosec A    cos A  sec A   7  tan 2 A cot 2 A
2 2

Prove that :

 sin A  cosec A    cos A  sec A   7  tan 2 A cot 2 A
2 2

23) {ZåZ ~maå~maVm ~§Q>Z H$m ~hþbH$ kmV H$s{OE : [4]
dJ© 10-25 25-40 40-55 55-70 70-85 85-100
~maå~maVm 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
Frequency 6 20 44 26 3 1

AWdm/OR
{ZåZ ~maå~maVm ~§Q>Z H$m ‘mܶ kmV H$s{OE : [4]
dJ© 0-20 20-40 40-60 60-80 80-100
~maå~maVm 6 10 13 7 4
Find the mean of the following frequency distribution :
Class 0-20 20-40 40-60 60-80 80-100
Frequency 6 10 13 7 4



S–09–Mathematics 1205

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