HBSE Class 9 Question Paper 2021 Maths

Code No. 1403
CLASS : 9th (Ninth) Series : 9-April/2021
Roll No.











xf.kr
MATHEMATICS
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/School Candidates)

le; : 2 21 ?k.Vs ] [ iw.kk±d : 80

Time allowed : 2 21 hours ] [ Maximum Marks : 80

• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk iz'u 14 gSaA
Please make sure that the printed pages in this question paper are 16 in number
and it contains 14 questions.
• iz'u-i= esa lcls Åij fn;s x;s dksM uEcj dks Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. on the top of the question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ksaA
Before beginning to answer a question, its Serial Number must be written.
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr% vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u
dkVsaA
Except answer-book, no extra sheet will be given. Write to the point and do not
strike the written answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i= iw.kZ o lgh gS] ijh{kk ds mijkUr bl
lEcU/k esa dksbZ Hkh nkok Lohdkj ugha fd;k tk;sxkA
Before answering the question, ensure that you have been supplied the correct and
complete question paper, no claim in this regard, will be entertained after
examination.

1403 P. T. O.

(2) 1403
lkekU; funsZ'k %
(i) lHkh iz'u vfuok;Z gSaA
(ii) bl ç'u-i= esa 14 ç'u gSa] tks fd pkj [k.Mksa % ^v*
^v*] ^c*] ^l* ,oa ^n* esa ck¡Vs x, gSa %
[k.M ^v* % bl [k.M ds ç'u la[;k 1 esa pkyhl (40) oLrqfu"B çdkj ds ç'u gSaA çR;sd ç'u
1 vad dk gSA

[k.M ^^cc* % bl [k.M esa ç'u la[;k 2 ls 6 rd dqy ik¡p ç'u gSaA çR;sd ç'u 2 vadksa dk gSA
[k.M ^^ll* % bl [k.M esa ç'u la[;k 7 ls 11 rd dqy ik¡p ç'u gSaA çR;sd ç'u 3 vadksa dk
gSA
[k.M ^^nn* % bl [k.M esa ç'u la[;k 12 ls 14 rd dqy rhu ç'u gSaA çR;sd ç'u 5 vadksa dk
gSA
(iii) bl ç'u-i= esa lexz :i ls dksbZ fodYi ugha gS] fQj Hkh 5 vadksa okys nks ç'uksa esa vkUrfjd
p;u çnku fd;k x;k gSA ,sls ç'uksa esa ls vkidks fn, x, p;u esa ls dsoy ,d gh ç'u djuk gSA
General Instructions :

(i) All questions are compulsory.

(ii) This question paper consists of 14 questions which are divided into four
Sections : 'A', 'B', 'C' and 'D' :

Section 'A' : Question No. 1 of this Section has forty (40) Objective Type
Questions. Each question carries 1 mark.

Section 'B' : This Section contains five questions from Question Nos. 2 to 6,
each of 2 marks.

Section 'C' : This Section contains five questions from Question Nos. 7 to
11, each of 3 marks.

Section 'D' : This Section contains three questions from Question Nos. 12 to
14, each of 5 marks.

(iii) There is no overall choice. However, an internal choice has been provided in
two questions of 5 marks. You have to attempt only one of the given choice in
such questions.

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(3) 1403
SECTION – A
[k.M – v
1. (1) fuEu esa ls dkSu-lh ifjes; la[;k ugha gS \ 1

(A) 2 (B) 0
(C) 4 (D) − 16
Which of the following is not a rational number ?
(A) 2 (B) 0
(C) 4 (D) − 16

p
(2) 0.47 dk :i ----------- gSA 1
q
p
The form of 0.47 is ……… .
q

(3) 3 vkSj 4 ds chp ,d ifjes; la[;k crk,¡A 1
Find one rational number between 3 and 4.

(4) fuEufyf[kr esa ls dkSu-lh la[;k 4 vkSj 9 ds chp esa ugha gS \ 1
5 5
3 5
(A) (B)
5 5
6 8
(C) (D)
5 5
4 9
Which of the following number is not in between and ?
5 5
3 5
(A) (B)
5 5
6 8
(C) (D)
5 5

(5) 2 − x 2 + x 3 esa x 2 dk xq.kkad ------------- gSA 1

The coefficient of x 2 in 2 − x 2 + x 3 is …………. .

1403 P. T. O.

(4) 1403
(6) 4y 2 − 4y + 1 dk xq.ku[k.M gS % 1

(A) (2y + 1)2 (B) (4y − 1)2

(C) (2y − 1)2 (D) (2y − 2)2

Factors of 4y 2 − 4y + 1 is :

(A) (2y + 1)2 (B) (4y − 1)2

(C) (2y − 1)2 (D) (2y − 2)2

(7) 27 − 125a 3 − 135a + 225a 2 dk xq.ku[k.M gS % 1

(A) (3 + 5a )2 (B) (3a + 5)3
(C) (3a − 5)2 (D) (3 − 5a )3
Factors of 27 − 125a 3 − 135a + 225a 2 is :
(A) (3 + 5a )2 (B) (3a + 5)3
(C) (3a − 5)2 (D) (3 − 5a )3

(8) p(x) = 3x + 1 dk 'kwU;d ----------- gSA 1
Zero of p(x) = 3x + 1 is ………… .

(9) (x + 4) (x + 10) dk xq.kuQy D;k gS \ 1
What is product of (x + 4) (x + 10) ?

(10) lehdj.k (2x + 1) = x + 3 dk D;k gy gS \ 1
What is solution of (2x + 1) = x + 3 ?

(11) lehdj.k x − 2y = 4 dk gy gS % 1
(A) (0, 2) (B) (4, 0)
(C) (1, 1) (D) (2, 0)
The solution of equation x − 2y = 4 is :
(A) (0, 2) (B) (4, 0)
(C) (1, 1) (D) (2, 0)

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(5) 1403
(12) fcUnq (4, 1) fdl js[kk ds lehdj.k dks larq"V djrk gS \ 1
(A) x + 2y = 5 (B) x + 2y = −6
(C) x + 2y = 6 (D) x + 2y = 16
Point (4, 1) satisfies to which equation of line ?
(A) x + 2y = 5 (B) x + 2y = −6
(C) x + 2y = 6 (D) x + 2y = 16

(13) ;fn fdlh ?kukHk dk vk;ru 3x 2 − 12x gS] rks bldh foekvksa ds fy, laHko O;atd gksaxs % 1
(A) 3, x, x + 4 (B) 3, x − 4, x
(C) −3, −x, −x − 4 (D) buesa ls dksbZ ugha
Possible dimensions of Cuboid whose volume 3x 2 − 12x is :
(A) 3, x, x + 4 (B) 3, x − 4, x
(C) −3, −x, −x − 4 (D) None of these

(14) fcUnq (5, −7) dkSu-ls prqFkk±'k esa gS \ 1

Point (5, −7) lies in which Quadrant ?

(15) fcUnq (0, 0) tgk¡ x-v{k vkSj y-v{k ijLij çfrPNsn djrs gSa] mls -------------- dgrs gSaA 1
The point (0, 0) where x-axis and y-axis intersect is called …………… .

(16) fcanq (−4, −3) dk Hkqt vkSj dksfV D;k gS \ 1
(A) x = −4, y = −3 (B) x = −3, y = −4
(C) x = 4, y = 3 (D) dksbZ ugha
What is abscissa and ordinate of point (−4, −3) ?
(A) x = −4, y = −3 (B) x = −3, y = −4
(C) x = 4, y = 3 (D) None

(17) fcUnqvksa (0, 0), (0, 2), (2, 2) vkSj (2, 0) dks feykus ij dkSu-lh vkÑfr çkIr gksrh gS \ 1
(A) oxZ (B) vk;r
(C) leprqHkqZt (D) lekarj prqHkqZt
On joining the points (0, 0), (0, 2), (2, 2) and (2, 0) we obtain a :
(A) Square (B) Rectangle
(C) Rhombus (D) Parallelogram

1403 P. T. O.

(6) 1403
(18) f=Hkqt dh fdUgha nks Hkqtkvksa dk ;ksx rhljh Hkqtk ls ------------- gksrk gSA 1
The sum of any two sides of a triangle is …………… than the third side.

(19) ,d vk;r ds fod.kZ ------------- gksrs gSaA 1
The diagonals of a rectangle are ………….. .

(20) ;fn fdlh prqHkqZt ds fod.kZ ijLij ledks.k ij çfrPNsn djsa] rks ;g vkÑfr D;k gksxh \ 1

(A) lekarj prqHkqZt (B) oxZ
(C) le prqHkqZt (D) leyac prqHkqZt
If diagonals of quadrilateral bisect each other at right angles, then it is a :

(A) Parallelogram (B) Square

(C) Rhombus (D) Trapezium

(21) ,d gh o`Ùk[kaM ds dks.k ----------- gksrs gSaA 1
Angles in the same segment of a circle are …………… .

(22) ,d pØh; prqHkqZt ABCD esa AOC o`Ùk dk O;kl gSA ;fn ∠CAD = 50° gks] rks ∠ACD dk
eku D;k gS \ 1

D C

50° O
A B

In cyclic quadrilateral ABCD, AOC is the diameter of circle. If
∠CAD = 50°, then ∠ACD is :

D C

50° O
A B

1403

(7) 1403
(23) o`Ùk dk dsUæ o`Ùk ds -------------- esa fLFkr gksrk gSA 1

(A) cfgHkkZx (B) ifjf/k
(C) vH;Urj (D) ifjeki
The centre of a circle lies in …………… of the circle :
(A) exterior (B) circumference
(C) interior (D) perimeter

(24) lsV ds ;qXe esa f=Hkqt ds dks.k gksrs gSa % 1

(A) 30°, 60°, 90° (B) 30°, 30°, 45°

(C) 75°, 25°, 80° (D) 65°, 15°, 100°
In a pair of set, a triangle is with angles :

(A) 30°, 60°, 90° (B) 30°, 30°, 45°

(C) 75°, 25°, 80° (D) 65°, 15°, 100°

(25) fdlh f=Hkqt dh jpuk ds fy, mlds de ls de -------------- Hkkx fn, gksus pkfg,A 1
To construct a triangle we must know at least its …………. parts.

(26) 22 1 ° ds dks.k dh jpuk djus ds fy, ge dkSu-ls dks.k dk lef}Hkktu djrs gSa \ 1
2
To construct an angle of 22 1 ° which angle we bisect ?
2

(27) ,d lef}ckgq f=Hkqt dk ifjeki 30 cm gS vkSj mldh cjkcj Hkqtk,¡ 12 cm yEckbZ dh gSaA
bl f=Hkqt dk {ks=Qy gksxk % 1

(A) 8 15 cm2 (B) 7 12 cm2

(C) 9 15 cm2 (D) 15 15 cm2

Perimeter of an isosceles triangle is 30 cm and its equal sides are of
12 cm, then area of the triangle is :

(A) 8 15 cm2 (B) 7 12 cm2

(C) 9 15 cm2 (D) 15 15 cm2

1403 P. T. O.

(8) 1403
(28) ,d f=Hkqt dk vk/kkj 12 cm rFkk Å¡pkbZ 8 cm gSA bldk {ks=Qy D;k gksxk \ 1
Base of a triangle is 12 cm and its height is 8 cm, then what will be its
area ?

(29) a Hkqtk okys leckgq f=Hkqt dk {ks=Qy -------------- gksxkA 1
Area of equilateral triangle with side a is …………. .

(30) ?kukHk dk i`"Bh; {ks=Qy -------------- gksrk gSA 1
The surface area of a cuboid is …………. .

(31) v/kZxksys dk vk;ru ftldh f=T;k r gS oks -------------- gksxkA 1
Volume of a hemisphere with radius r will be ………….. .

(32) yac o`Ùkh; 'kadq dk vk;ru Kkr dhft, ftldh f=T;k 6 cm vkSj Å¡pkbZ 7 cm gSA 1
Find the volume of right circular cone with radius 6 cm and height 7 cm.
(33) csyu dk dqy i`"Bh; {ks=Qy D;k gksxk] tc mldh f=T;k r rFkk Å¡pkbZ h nh xbZ gS \ 1

(A) 2πrh (B) 2πr (r + h)

(C) πr 2 h (D) 2πr 2
What will be the total surface area of a cylinder, when radius r and height
h is given ?
(A) 2πrh (B) 2πr (r + h)

(C) πr 2 h (D) 2πr 2
(34) ,d ?kukHkkdkj crZu 10 m yack vkSj 8 m pkSM+k gSA bldks fdruk Å¡pk cuk;k tk, fd blesa
380 ?ku ehVj æo vk lds \ 1

(A) 4.50 m (B) 3.75 m
(C) 4.75 m (D) 3.50 m
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made
to hold 380 cubic meters of a liquid ?
(A) 4.50 m (B) 3.75 m
(C) 4.75 m (D) 3.50 m

1403

(9) 1403
(35) 20 ds lHkh laHko xq.ku[k.Mksa dk ek/; -------------- gksxkA 1
The mean of all possible factors of 20 will be …………. .

(36) oxZ 150-160 dk oxZ fpg~u gS % 1
(A) 145 (B) 310
(C) 10 (D) 155
Class mark of class 150-160 is :
(A) 145 (B) 310
(C) 10 (D) 155
(37) fdlh d{kk ds 9 fo|kfFkZ;ksa dh Å¡pkbZ ¼lseh eas½ nh xbZ gS % 1
155, 160, 145, 149, 150, 147, 152, 144, 148
bu vk¡dM+ksa dk ek/;d gS %
(A) 150 (B) 147
(C) 149 (D) 148
The heights of 9 students of a class are given (in cm) as follows :
155, 160, 145, 149, 150, 147, 152, 144, 148
The median of this data is :
(A) 150 (B) 147
(C) 149 (D) 148
(38) ,d fØdsV eSp esa] ,d efgyk cYysckt [ksyh xbZ 30 xsanksa esa 6 ckj pkSdk ekjrh gSA pkSdk u
ekjs tkus dh çkf;drk -------------- gksxhA 1
In a cricket match a lady batsman hits a boundary 6 times out of 30 balls
she plays. The probability that she will not hit a boundary in the next ball
is ………….. .
(39) fdlh ?kVuk ds ?kVus dh çkf;drk -------------- ds chp gksrh gSA 1
(A) 0 vkSj 1 (B) −1 vkSj 1
(C) 1 vkSj 2 (D) 2 vkSj 3
The probability of an event lies between :
(A) 0 and 1 (B) −1 and 1
(C) 1 and 2 (D) 2 and 3
(40) ,d ikls dks ,d ckj mNkyk x;kA vHkkT; la[;k çkIr djus dh çkf;drk D;k gksxh \ 1
What will be the probability of a prime number when a fair die is tossed ?
1403 P. T. O.

( 10 ) 1403
SECTION – B
[k.M – c
p
2. 0.6 dks ds :i esa O;Dr dhft,] tgk¡ p vkSj q iw.kk±d gSa rFkk q ≠ 0 gSA 2
q
p
Express 0.6 in the form , where p and q are integers and q ≠ 0.
q

3. nks pjksa okys jSf[kd lehdj.k 3 = 2x + y dk vkys[k [khafp,A 2
Draw the graph of linear equation 3 = 2x + y in two variables.
Y 2
4.
6

5

4

3
B D
2

1
X' X
−5 −4 −3 −2 −1 0 1 2 3 4 5 6

−1

−2

−3
H

−4

E −5

vkÑfr esa ns[kdj fuEufyf[kr dks fyf[k, %
(i) B ds funsZ'kkad
(ii) funsZ'kkad (−3, −5) }kjk igpkuk x;k fcanq
(iii) fcanq D dk Hkqt
(iv) fcanq H ds funsZ'kkad
1403

( 11 ) 1403
Y

6

5

4

3
B D
2

1
X' X
−5 −4 −3 −2 −1 0 1 2 3 4 5 6

−1

−2

−3
H

−4

E −5

Write the answer of each of following from figure :
(i) The coordinates of B
(ii) The point identified by the coordinates (−3, −5)
(iii) The abscissa of the point D
(iv) The coordinate of point H

5. vkÑfr esa] x vkSj y dk eku Kkr dhft,] fn;k gS AB||CD 2

P
50° R
A x B

y
s D
C 130°
Q

1403 P. T. O.

( 12 ) 1403
Find value of x and y from given figure, AB||CD .
P
50° R
A x B

y
s D
C 130°
Q

6. çFke N% fo"ke la[;kvksa dk ek/; D;k gksxk \ 2
What will be mean of first six odd numbers ?

SECTION – C

[k.M – l
7. xq.ku[k.M Kkr dhft, % 3

x 3 − 2x 2 − x + 2
Factorise :

x 3 − 2x 2 − x + 2

8. fn[kkb, fd leprqHkqZt ds fod.kZ ijLij ledks.k ij lef}Hkkftr djrs gSaA 3
Show that the diagonals of a rhombus are perpendicular to each other.

9. vkÑfr esa ∠ABC = 69° vkSj ∠ACB = 31° gks] rks ∠BDC Kkr dhft,A 3
A
D

69° 31°
B C

1403

( 13 ) 1403
In figure ∠ABC = 69° and ∠ACB = 31°, find ∠BDC.

A
D

69° 31°
B C

10. ,d f=Hkqt ABC dh jpuk dhft,] ftlesa BC = 7cm, ∠B = 75° vkSj AB + AC = 13 cm gSA 3

Construct a triangle ABC in which BC = 7cm, ∠B = 75° and AB + AC = 13 cm.

11. ml f=Hkqt dk {ks=Qy Kkr dhft, ftldh nks Hkqtk,¡ 18 cm vkSj 10 cm gSa rFkk mldk ifjeki
42 cm gSA 3

Find the area of a triangle two sides of which are 18 cm and 10 cm and the
perimeter is 42 cm.

SECTION – D

[k.M – n
12. fl) dhft, fd ,d lef}ckgq f=Hkqt dh cjkcj Hkqtkvksa ds lEeq[k dks.k cjkcj gksrs gSaA 5

Prove that angles opposite to equal sides of an isosceles triangle are equal.

vFkok
OR

ABCD ,d prqHkqZt gSA ftlesa P, Q, R vkSj S Øe'k% Hkqtkvksa AB, BC, CD vkSj DA ds e/; fcanq
gSaA AC mldk ,d fod.kZ gS] n'kkZb, fd %
1
(i) SR|| AC vkSj SR = AC gSA
2

(ii) PQ = SR gSA

(iii) PQRS ,d lekarj prqHkqZt gSA
1403 P. T. O.

( 14 ) 1403
D
R
S C

A Q
P
B

ABCD is a quadrilateral in which P, Q, R and S are mid points of the sides AB,
BC, CD and DA. AC is a diagonal, show that :

1
(i) SR|| AC and SR = AC
2

(ii) PQ = SR

(iii) PQRS is a parallelogram
D
R
S C

A Q
P
B

13. 'kadq ds vkdkj dk ,d racw 10 eh0 Å¡pk gS vkSj mlds vk/kkj dh f=T;k 24 eh0 gSA Kkr dhft, % 5
(i) racw dh fr;Zd Å¡pkbZA

(ii) racw esa yxs dSuokl dh ykxr] ;fn 1 eh02 dSuokl dh ykxr ` 70 gSA

A conical tent is 10 m high and the radius of its base is 24 m. Find :

(i) Slant height of the tent.

2
(ii) Cost of the canvas required to make the tent, if the cost of 1 m canvas is
` 70.

1403

( 15 ) 1403

vFkok
OR

ydM+h ds ,d csyukdkj ikbi dk vkarfjd O;kl 24 cm gS vkSj ckgjh O;kl 28 cm gSA bl ikbi
dh yEckbZ 35 cm gSA bl ikbi dk æO;eku Kkr dhft,] ;fn 1 cm 3 ydM+h dk æO;eku 0.6 xzke
gSA
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer
diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe,
if 1 cm 3 of wood has a mass of 0.6 g.

14. ,d chek dEiuh us vk;q vkSj nq?kZVukvksa ds chp ds laca/k dks Kkr djus ds fy, ,d fo'ks"k uxj ds
2000 Mªkbojksa dk ;kn`PN;k p;u fd;kA çkIr fd, x, vk¡dM+s uhps lkj.kh esa fn, x, gSa % 5

Mªkboj dh vk;q ,d o"kZ esa ?kVh nq?kZVuk,¡
¼o"kks± esa½

0 1 2 3 3 ls vf/kd

18-29 440 160 110 61 35

30-50 505 125 60 22 18

50 ls vf/kd 360 45 35 15 9

uxj ls ;kn`PN;k pqus x, ,d Mªkboj ds fy, fuEufyf[kr ?kVukvksa dh çkf;drk,¡ Kkr dhft, %

(i) 18-29 o"kZ dh vk;q dk ftlds lkFk ,d o"kZ esa Bhd-Bhd 3 nq?kZVuk,¡ ?kVh gSaA

(ii) 30-50 o"kZ dh vk;q dk ftlds lkFk ,d o"kZ esa ,d ;k vf/kd nq?kZVuk,¡ ?kVh gSaA

(iii) ftlds lkFk ,d o"kZ esa dksbZ nq?kZVuk ugha ?kVhA

1403 P. T. O.

( 16 ) 1403
An insurance company selected 2000 drivers at random in a particular city to
find a relationship between age and accidents. The data obtained are given in
the following table :

Age of drivers (in Years) Accidents in one Year

0 1 2 3 Over 3

18-29 440 160 110 61 35

30-50 505 125 60 22 18

Above 50 360 45 35 15 9

Find the probabilities of the following events for a driver chosen at random
from the city :
(i) being 18-29 years of age and having exactly 3 accidents in one year.

(ii) being 30-50 years of age and having one or more accidents in a year.

(iii) having no accidents in one year.

S

1403