Rajasthan Board Class 10 Question Paper 2022 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, 2022
SECONDARY EXAMINATION, 2022

TEAR HERE TO OPEN THE QUESTION PAPER
J{UV
MATHEMATICS

àíZ nÌ H$mo ImobZo Ho$ {bE `hm± \$m‹S>|
g_` : 2 KÊQ>o 45 {_{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 6005 [ 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«$‘m§H$ 17 go 23 VH$ ‘| AmÝV[aH$ {dH$ën h¢&
There are internal choices in Question Nos. 17 to 23.
8) AnZr CÎma-nwpñVH$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 6005

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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) ~hþnX P ( x ) = ( 3 − x )( x − 4 ) H$s KmV h¡ - [1]

A) 2 ~) 4

g) 0 X) 3

The degree of the polynomial P ( x ) = ( 3 − x )( x − 4 ) is -

A) 2 B) 4

C) 0 D) 3

ii) `{X 6 nXm| dmbr EH$ g_mÝVa loT>r H$m àW_ VWm ApÝV_ nX H«$_e… 2 VWm 10 h¡, V~ g_mÝVa loT>r H$m
`moJ\$b h¡ - [1]

A) 72 ~) 36

g) 135 X) 24

If first and last term of an arithmetic progression having 6 terms are 2 and 10 respectively,
then sum of arithmetic progression is -

A) 72 B) 36

C) 135 D) 24

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iii) {~ÝXþ P (5, – 4) H$mo x-Aj go Xÿar h¡ - [1]

A) 5 ~) 0

g) 4 X) 16

The distance of the point P (5, – 4) from x-axis is -

A) 5 B) 0

C) 4 D) 16

iv) {ZåZ _| go An[a_o` g§»`m h¡ - [1]

A) 2 ~) 2.232425....

g) 2.23 X) 2.23

Which of the following is an irrational number?

A) 2 B) 2.232425....

C) 2.23 D) 2.23

v) k Ho$ {H$g _mZ Ho$ {bE {ZåZ a¡{IH$ g_rH$aUm| Ho$ `w½_ H$m H$moB© hb Zht h¡? [1]

3x + y = 1; ( 2k − 1) x + y = 2k + 1

A) 2 ~) 1

g) 3 X) 4

For which value of k, the following pair of linear equations has no solution?

3x + y = 1; ( 2k − 1) x + y = 2k + 1

A) 2 B) 1

C) 3 D) 4

S–09–Mathematics 6005

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vi) {H$gr {ÛKmV g_rH$aU a x 2 + b x + c = 0 Ho$ _yb dmñV{dH$ Zht h¢, `{X - [1]

A) b 2 − 4 ac > 0 ~) b2 − 4ac = 0

g) b2 − 4ac < 0 X) b2 − 4ac ≥ 0

Roots of any quadratic equation a x 2 + b x + c = 0 are not real, if

A) b 2 − 4 ac > 0 B) b2 − 4ac = 0

C) b2 − 4ac < 0 D) b2 − 4ac ≥ 0

vii) {~ÝXþAm| A ( x + 4, y + 5) VWm B ( 6 − x,3 − y ) H$mo {_bmZo dmbo aoImIÊS> Ho$ _Ü` {~ÝXþ Ho$ {ZX}em§H$ h¢ -
[1]

A) ( x, y ) ~) (5, 4)

5 4
g) ( x + 5, y + 4 ) X)  , 
2 2

The coordinates of the midpoint of line segment joining the points A ( x + 4, y + 5) and

B ( 6 − x,3 − y ) is -

A) ( x, y ) B) (5, 4)

5 4
C) ( x + 5, y + 4 ) D)  , 
2 2

S–09–Mathematics 6005 [ Turn Over

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1
viii) `{X sin A = hmo, Vmo 2 sin A cos A H$m _mZ h¡ - [1]
2

1 3
A) ~)
4 2

1
g) 1 X)
2

1
If sin A = , then value of 2 sin A cos A is -
2

1 3
A) B)
4 2

1
C) 1 D)
2

2 tan 30°
ix) H$m _mZ h¡ - [1]
1 − tan 2 30°

1
A) ~) 1
3

g) 0 X) 3

2 tan 30°
The value of is -
1 − tan 2 30°

1
A) B) 1
3

C) 0 D) 3

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x) EH$ nmgo H$mo EH$ ~ma \|$H$m OmVm h¡& A^mÁ` g§»`m H$mo àmá H$aZo H$s àm{`H$Vm h¡ - [1]

1 2
A) ~)
2 3

g) 0 X) 1

A die is thrown once. The probability of getting a prime number is -

1 2
A) B)
2 3

C) 0 D) 1

xi) Am§H$‹S>m| 2, 0, 7, 3, 4, 8, 1 H$m _mÜ`H$ h¡ - [1]

A) 3 ~) 4

g) 7 X) 2

Median of data 2, 0, 7, 3, 4, 8, 1 is -

A) 3 B) 4

C) 7 D) 2

xii) `{X {ZåZ{b{IV Am±H$‹S>m| H$s ~maå~maVmAm| H$m `moJ 60 h¡, Vmo x H$m _mZ h¡ - [1]

dJ© 0-10 10-20 20-30 30-40 40-50 50-60

~maå~maVm 5 x 20 15 7 5

A) 7 ~) 8

g) 15 X) 20

If the sum of frequency of following data is 60, then the value of x is -

Class 0-10 10-20 20-30 30-40 40-50 50-60

Frequency 5 x 20 15 7 5

A) 7 B) 8

C) 15 D) 20

S–09–Mathematics 6005 [ Turn Over

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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) {ZåZ{b{IV g_mÝVa loT>r _|, [aº$ ñWmZm| Ho$ nXm| H$mo {b{IE& [1]

1
5, , ,9 .
2

In the following Arithmetic Progression, write the missing terms in the boxes.

1
5, , ,9 .
2

a1 a2 c1
ii) a¡{IH$ g_rH$aU `w½_ a1x + b1 y + c1 = 0 Am¡a a2 x + b2 y + c2 = 0 _| `{X b = b = c h¢, V~
1 2 2

{Zê${nV aoImE| _______ h¢& [1]

a1 a2 c1
In pair of linear equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0 , if = = , then
b1 b2 c2
lines represented are _______.

iii) 7.5 go_r bå~o aoImIÊS> H$mo 2:1 _| {d^m{OV H$aZo na ~‹S>o ^mJ H$s bå~mB© ________ go_r hmoJr& [1]
A 7.5 cm long line segment is divided in the ratio 2:1, then the length of large portion will be
________ cm.

iv) {~ÝXþAm| (3, – 2) VWm (4, 5) H$mo Omo‹S>Zo dmbo aoImIÊS> H$s bå~mB© ________ h¡& [1]
The length of a line segment joining points (3, – 2) and (4, 5) is _______.

v) cos 48° − sin 42° H$m _mZ ________ h¡& [1]

The value of cos 48° − sin 42° is _________.

vi) {ZåZ{b{IV Am±H$‹‹S>m| H$m ~hþbH$ ________ h¢& [1]
2, 6, 4, 5, 0, 2, 1, 3, 2, 3
Mode of following data is ________.

2, 6, 4, 5, 0, 2, 1, 3, 2, 3

S–09–Mathematics 6005

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3) A{V bKwÎmamË_H$ àíZ&>

Very short answer type questions.

i) g§»`mAm| 72 Am¡a 120 H$m bKwÎm_ g_mndË`© (LCM) kmV H$s{OE& [1]

Find the least common multiple (LCM) of numbers 72 and 120.

ii) EH$ {ÛKmV ~hþnX kmV H$s{OE, {OgHo$ eyÝ`H$m| H$m `moJ VWm JwUZ\$b H«$_e… – 3 Am¡a 2 h¡& [1]

Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2 respectively.

iii) ~hþnX P ( x ) = x 2 − 2 x − 8 Ho$ eyÝ`H$ kmV H$s{OE& [1]

Find the zeroes of the polynomial P ( x ) = x 2 − 2 x − 8 .

iv) 5 nopÝgb Am¡a 7 noZ H$m Hw$b _yë` H 50 h¡, O~{H$ 7 nopÝgb Am¡a 5 noZ H$m Hw$b _yë` H 46 h¡& Bg g_ñ`m
H$mo a¡{IH$ g_rH$aUm| Ho$ `w½_ Ûmam àX{e©V H$s{OE& [1]

5 pencils and 7 pens together cost H 50, whereas 7 pencils and 5 pens together cost H 46.
Express this problem by the pair of linear equations.

v) ( x − 2 ) − x = 3x ( x − 2 ) H$mo {ÛKmV g_rH$aU Ho$ ê$n _| {b{IE& [1]

Write ( x − 2 ) − x = 3x ( x − 2 ) in the form of quadratic equation.

vi) 5 go_r bå~mB© H$m EH$ aoImIÊS> ItM H$a Bgo g_{Û^m{OV H$s{OE& [1]

Draw a line segment of length 5 cm and bisect it.

vii) {ÛKmV g_rH$aU 3x 2 − 8 x − 16 = 0 Ho$ _ybm| H$s àH¥${V kmV H$s{OE& [1]

Find the nature of roots of quadratic equation 3 x 2 − 8 x − 16 = 0 .

viii) `{X {~ÝXþ Q (0, 1), {~ÝXþAm| P (5, – 4) Am¡a R (x, 6) H$m _Ü`{~ÝXþ h¡, V~ x H$m _mZ kmV H$s{OE& [1]

If point Q (0, 1) is midpoint of the points P (5, – 4) and R (x, 6), then find the value of x.

S–09–Mathematics 6005 [ Turn Over

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ix) 2 tan 2 45° + cos2 30° − sin 2 60° H$m _mZ kmV H$s{OE& [1]

Find the value of 2 tan 2 45° + cos 2 30° − sin 2 60° .
x) EH$ W¡bo _| 3 bmb Am¡a 5 H$mbr J|Xo h¢& Bg W¡bo _| go EH$ J|X `mÑÀN>`m {ZH$mbr OmVr h¡& BgH$s Š`m
àm{`H$Vm h¡ {H$ `h J|X bmb hmoJr? [1]
A bag contains 3 red and 5 black balls. A ball is drawn at random from this bag. What is the
probability that the drawn ball will be red?
xi) `{X tan A = cot B , V~ A + B H$m _mZ kmV H$s{OE& [1]
If tan A = cot B , then find the value of A + B.

xii) ~§Q>Z 6, 11, 21, 23, 14, 5 H$m _mÜ` kmV H$s{OE& [1]
Find the mean of distribution 6, 11, 21, 23, 14, 5.

IÊS> - ~
SECTION - B

4) g_mÝVa loT>r … 10, 7, 4, ....., – 32 Ho$ nXm| H$s g§»`m kmV H$s{OE& [2]
Find the number of terms of AP : 10, 7, 4, ..., – 32.

5) àW_ 200 YZ nyUmªH$m| H$m `moJ\$b kmV H$s{OE& [2]
Find the sum of first 200 positive integers.

6) {ÛKmV g_rH$aU x 2 − 8 x − 180 = 0 Ho$ _yb kmV H$s{OE& [2]

Find the roots of quadratic equation x 2 − 8 x − 180 = 0 .

7) {ZåZ a¡{IH$ g_rH$aU `w½_ H$mo hb H$s{OE … [2]
x − 3 y = 7 ; x + 4 y = 14
Solve the following pair of linear equations :
x − 3 y = 7 ; x + 4 y = 14

S–09–Mathematics 6005

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8) Xmo g§»`mAm| 616 Am¡a 32 H$m _hÎm_ g_mndV©H$ (HCF) kmV H$s{OE& [2]
Find the highest common factor (HCF) of two numbers 616 and 32.

9) EH$ {ÛKmV ~hþnX kmV H$s{OE, {OgHo$ eyÝ`H$ 3 VWm − 3 h¢& [2]

Find a quadratic polynomial, whose zeroes are 3 and − 3 .

10) {~ÝXþAm| (5, – 6) Am¡a (– 1, – 4) H$mo Omo‹S>Zo dmbo aoImIÊS> H$mo y-Aj {H$g AZwnmV _| {d^m{OV H$aVm h¡, kmV
H$s{OE& [2]
Find the ratio, in which y-axis divides the line segment joining the points (5, – 6) and (– 1, – 4).

11) 7.6 go_r bå~m EH$ aoImIÊS> It{ME Am¡a Bgo 1:2 _| {d^m{OV H$s{OE& [2]
Draw a line segment of length 7.6 cm and divide it into ratio 1:2.

3
12) `{X sin A = hmo, V~ tan A + cos A H$m _mZ kmV H$s{OE& [2]
5

3
If sin A = , then find the value of tan A + cos A .
5

13) {gÕ H$s{OE … ( sec A+ tan A )(1 − sin A ) = cos A . [2]

Prove that : ( sec A + tan A )(1 − sin A ) = cos A .

14) {ZåZ ~maå~maVm ~§Q>Z H$m _mÜ` kmV H$s{OE … [2]
x 0 4 8 12 16 20
f 1 3 5 4 2 1
Find the mean of the following frequency distribution :
x 0 4 8 12 16 20
f 1 3 5 4 2 1

S–09–Mathematics 6005 [ Turn Over

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15) {ZåZ{b{IV ~maå~maVm ~§Q>Z H$mo "A{YH$ Ho$' àH$ma Ho$ ~§Q>Z _| ~X{bE … [2]
dJ© AÝVamb 50-55 55-60 60-65 65-70 70-75 75-80
~maå~maVm 2 8 12 24 38 16
Change the following frequency distribution to ‘more than’ type distribution :
Class interval 50-55 55-60 60-65 65-70 70-75 75-80
Frequency 2 8 12 24 38 16

16) Xmo {Ibm‹S>r A Am¡a B Q>o{Zg H$m EH$ _¡M IobVo h¢& `h kmV h¡ {H$ A Ho$ _¡M OrVZo H$s àm{`H$Vm 0.62 h¢& B Ho$ _¡M
OrVZo H$s Š`m àm{`H$Vm h¡? [2]
Two players, A and B play a tennis match. It is known that the probability of A winning the match
is 0.62. What is the probability of B winning the match?

IÊS> - g
SECTION - C

17) `{X {H$gr g_mÝVa loT>r Ho$ àW_ 16 nXm| H$m `moJ 728 h¡ VWm àW_ nX 8 h¡, V~ 20 dm§ nX kmV H$s{OE& [3]
If the sum of first 16 terms of an Arithmetic Progression is 728 and first term is 8, then find the 20th
term.
AWdm/OR
`{X {H$gr g_mÝVa loT>r Ho$ àW_ n nXm| H$m `moJ\$b 4n – n2 h¡, V~ BgH$m 10 dm§ nX kmV H$s{OE& [3]
If the sum of first n terms of an Arithmetic Progression is 4n – n , then find its 10 term.
2 th

18) 5 go_r ^wOm dmbo EH$ g_~mhþ {Ì^wO Ho$ g_ê$n {Ì^wO H$s aMZm H$s{OE {OgH$s ^wOmE| {X`o J`o {Ì^wO H$s g§JV

2
^wOmAm| H$s hm|& [3]
3

2
Construct a triangle similar to an equilateral triangle of side 5 cm, with its sides equal to of the
3
corresponding sides of the given triangle.
AWdm/OR
5 go_r {ÌÁ`m Ho$ EH$ d¥Îm na Eogr Xmo ñne© aoImE| It{ME, Omo nañna 60° Ho$ H$moU na PwH$s hm|& [3]
Draw a pair of tangents to a circle of radius 5 cm, which are inclined to each other at an angle of
60°.

S–09–Mathematics 6005

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19) {gÕ H$s{OE … [3]

tan 49° tan 24° tan 60° tan 41° tan 66° = 3

Prove that :

tan 49° tan 24° tan 60° tan 41° tan 66° = 3

AWdm/OR

1 + sin A
{gÕ H$s{OE … 1 − sin A = sec A + tan A [3]

1 + sin A
Prove that : = sec A + tan A
1 − sin A

20) {ZåZ{b{IV dJuH¥$V Am±H$‹S>mo H$m H$pënV _mÜ` {d{Y Ûmam _mÜ` kmV H$s{OE … [3]

dJ© AÝVamb 0-10 10-20 20-30 30-40 40-50

~maå~maVm 2 5 8 4 1

Find the mean of the following grouped data using the assumed mean method :

Class interval 0-10 10-20 20-30 30-40 40-50

Frequency 2 5 8 4 1

AWdm/OR
{ZåZ ~maå~maVm ~§Q>Z H$m ~hþbH$ kmV H$s{OE … [3]

dJ© AÝVamb 10-20 20-30 30-40 40-50 50-60

~maå~maVm 12 20 25 22 10

Find the Mode of following frequency distribution :

Class interval 10-20 20-30 30-40 40-50 50-60

Frequency 12 20 25 22 10

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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 = 8 ; y = 2x − 7

Solve the following pair of linear equations by graphical method :

x + y = 8 ; y = 2x − 7

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

3x − 2 y = 9 ; x = y + 2

Solve the following pair of linear equations by graphical method :

3x − 2 y = 9 ; x = y + 2

22) EH$ {Ì^wO ABC ~ZmBE, {Og_| ^wOmE± BC = 6 go_r, AB = 5 go_r Am¡a ∠ ABC = 60° hmo& {\$a EH$ {Ì^wO
3
H$s aMZm H$s{OE, {OgH$s ^wOmE± Δ ABC H$s g§JV ^wOmAm| H$s hm|& [4]
4

Draw a triangle ABC with sides BC = 6 cm, AB = 5 cm and ∠ ABC = 60° .Then construct a
3
triangle, whose sides are of the corresponding sides of the triangle ABC.
4

AWdm/OR
8 go_r ì`mg H$m EH$ d¥Îm It{ME& BgHo$ Ho$ÝÐ go 8 go_r Xÿa pñWV EH$ {~ÝXþ go d¥Îm na ñne© aoIm `w½_ H$s aMZm
H$s{OE Am¡a CZH$s bå~mB©`m§ _m{nE& [4]

Draw a circle of diameter 8 cm. From a point 8 cm away from its centre, construct a pair of
tangents to the circle and measure their lengths.

S–09–Mathematics 6005

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23) ZrMo {X`o J`o ~§Q>Z H$m _mÜ`H$ kmV H$s{OE … [4]

dJ© AÝVamb 1-4 4-7 7-10 10-13 13-16 16-19

~maå~maVm 6 30 40 16 4 4

Find the median of the following distribution :

Class interval 1-4 4-7 7-10 10-13 13-16 16-19

Frequency 6 30 40 16 4 4

AWdm/OR

EH$ nm¡Yo H$s 75 n{Îm`m| H$s bå~mB`m± {ZH$Q>V_ {_br _rQ>am| _| _mnr OmVr h¡ VWm àmá Am±H$‹S>m| H$mo {ZåZ{b{IV
gmaUr Ho$ ê$n _| {Zê${nV {H$`m OmVm h¡ … [4]

bå~mB© (mm) 1-9 11-19 21-29 31-39 41-49 51-59

n{Îm`m| H$s g§»`m 6 10 12 22 17 8

n{Îm`m| H$s bå~mB© H$m ~hþbH$ kmV H$s{OE&

The lengths of 75 leaves of a plant are measured correct to the nearest millimetres and the data
obtained are represented in the form of following table :

Length (mm) 1-9 11-19 21-29 31-39 41-49 51-59

Numbers of leaves 6 10 12 22 17 8

Find the mode of the leaves length.



S–09–Mathematics 6005

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