HBSE Class 9 Question Paper 2018 Maths

Code No. 603
CLASS : 9th (Ninth) Series : 9-M/2018
Roll No.











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

le; : 3 ?k.Vs ] [ iw.kk±d : 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk iz'u
19 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
19 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.

603 P. T. O.

(2) 603
• 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.
lkekU; funsZ'k %
(i) lHkh iz'u vfuok;Z gSaA
(ii) bl ç'u-i= esa 19 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 lksyg
(i-xvi) 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 7 rd dqy
N% ç'u gSaA çR;sd ç'u 2 vadksa dk gSA
[k.M ^^ll* % bl [k.M esa ç'u la[;k 8 ls 15 rd dqy
vkB ç'u gSaA çR;sd ç'u 4 vadksa dk gSA
603

(3) 603
[k.M ^^nn* % bl [k.M esa ç'u la[;k 16 ls 19 rd dqy
pkj 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 19 questions
which are divided into four Sections :'A', 'B',
'C' and 'D' :
Section 'A' : Question No. 1 of this Section
has sixteen (i-xvi) Objective
Type Questions. Each question
carries 1 mark.
Section 'B' : This Section contains six
questions from Question Nos. 2
to 7, each of 2 marks.
Section 'C' : This Section contains eight
questions from Question Nos. 8
to 15, each of 4 marks.
Section 'D' : This Section contains four
questions from Question Nos.
16 to 19, 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.

603 P. T. O.

(4) 603
[k.M – v
SECTION – A

1. (i) fuEufyf[kr la[;kvksa esa vifjes; la[;k dkSu-lh gS \ 1
(A) 16 (B) 36
(C) 48 (D) 64
Which of the following numbers is an
irrational number ?
(A) 16 (B) 36
(C) 48 (D) 64
(ii) (36)1/ 2 dk eku gksxk % 1
(A) 6 (B) 12
(C) 18 (D) 9
The value of (36)1/ 2 will be :
(A) 6 (B) 12
(C) 18 (D) 9
(iii) fuEufyf[kr chth; O;atdksa esa dkSu-lk ,d cgqin gS \ 1
1
(A) x 2 + 5x + 6 (B) y+
2y
1
(C) 5 t +3 (D)
5x + 3
Which of the following algebraic expressions
is a polynomial ?
1
(A) x 2 + 5x + 6 (B) y +
2y
1
(C) 5 t +3 (D)
5x + 3

603

(5) 603
(iv) cgqin p(x ) = 2x + 5 dk 'kwU;d gksxk % 1

5 5
(A) (B) −
2 2
2 2
(C) (D) −
5 5
The zero of polynomial p(x ) = 2x + 5 will be :
5 5
(A) (B) −
2 2
2 2
(C) (D) −
5 5
(v) lehdj.k 4 = 5x – 3y dks ax + by + c = 0 ds :i
esa fyf[k, o c dk eku crkb, % 1
(A) 5 (B) –3
(C) 0 (D) –4
Write equation 4 = 5x – 3y in the form of
ax + by + c = 0 and indicate the value of c :
(A) 5 (B) –3
(C) 0 (D) –4
(vi) dkrhZ; ry esa {kSfrt vkSj Å/okZ/kj js[kkvksa ls cus ry ds
izR;sd Hkkx dk uke fyf[k,A 1
What is the name of each part of the plane
formed by horizontal and the vertical lines
in the Cartesian plane ?
(vii) ;wfDyM dh nwljh vfHk/kkj.kk D;k gS \ 1
What is second postulate of Euclid ?

603 P. T. O.

(6) 603
(viii) fn, gq, nks fHkUu fcUnqvksa ls gksdj fdruh js[kk,¡ [khaph
tk ldrh gSa \ 1
(A) ,d vf}rh; (B) nks
(C) vusd (D) dksbZ ugha
How many lines can pass through two
distinct given points ?
(A) A unique (B) Two
(C) Infinite (D) No line
(ix) nks dks.kksa dk ;ksx 180° gks] rks ,sls dks.k dgykrs gSa % 1
(A) U;wu dks.k
(B) iwjd dks.k
(C) laiwjd dks.k
(D) izfrorhZ dks.k
The sum of two angles is 180°. Then these
are called as :
(A) Acute angle
(B) Complementary angles
(C) Supplementary angles
(D) Reflex angles
(x) ßnks f=Hkqt lokZaxle gksrs gSa] ;fn ,d f=Hkqt dh nks
Hkqtk,¡ vkSj mudk varxZr dks.k nwljs f=Hkqt dh nks
Hkqtkvksa vkSj muds varxZr dks.k ds cjkcj gksaAÞ ;g
fuEufyf[kr esa ls lokZaxlerk dk dkSu-lk fu;e gS \ 1
(A) AAS (B) ASA
(C) SAS (D) SSS
"Two triangles are congruent if two sides
and the included angle of one triangle are
equal to the two sides and the included
angle of the other triangle." Which rule of
congruence it is ?
(A) AAS (B) ASA
(C) SAS (D) SSS

603

(7) 603
(xi) fdlh f=Hkqt dh Å¡pkbZ vkSj vk/kkj Øe'k% 8 cm o 3 cm
gSa] mldk {ks=Qy gksxk % 1
(A) 24 cm (B) 12 cm
(C) 12 cm2 (D) 24 cm2
The altitude and base of a triangle are 8 cm
and 3 cm respectively. Then its area will be :
(A) 24 cm (B) 12 cm
(C) 12 cm2 (D) 24 cm2
(xii) vkÑfr esa] o`Ùk ds Nk;kafdr Hkkx dks dgrs gSa % 1

.O

(A) nh?kZ f=T;k[kaM (B) nh?kZ o`Ùk[kaM
(C) y?kq f=T;k[kaM (D) y?kq o`Ùk[kaM
In fig, the shaded part of the circle is known
as :

.O

(A) Major sector (B) Major segment

(C) Minor sector (D) Minor segment

603 P. T. O.

(8) 603
(xiii) ,d ?ku dk fdukjk 12 cm gS] rks bldk vk;ru gksxk % 1
(A) 1728 cm3 (B) 1728 cm2
(C) 36 cm3 (D) 36 cm2
The edge of a cube is 12 cm, then its
volume will be :
(A) 1728 cm3 (B) 1728 cm2
(C) 36 cm3 (D) 36 cm2
(xiv) 14 cm O;kl okys xksys dk i`"Bh; {ks=Qy gksxk % 1

(A) 28 cm (B) 28 cm2
(C) 42 cm2 (D) 616 cm2
The surface area of a sphere with diameter
14 cm will be :
(A) 28 cm (B) 28 cm2
(C) 42 cm2 (D) 616 cm2
(xv) ,d flDds dks ,d ckj mNkyus ij iV izkIr djus dh
izkf;drk gksrh gS % 1

(A) 1 (B) 1
2 3

(C) 2 (D) 1
3 6
When a coin tossed once, then the
probability of getting a tail is :

(A) 1 (B) 1
2 3

(C) 2 (D) 1
3 6
603

(9) 603
(xvi) ,d fØdsV eSp es]a ,d efgyk cYysckt [ksyh xbZ 30
xsanksa esa 6 ckj pkSdk ekjrh gSA mlds }kjk pkSdk ekjus
dh izkf;drk gksxh % 1

(A) 4 (B) 2
5 5
(C) 1 (D) 3
5 5
In a cricket match, a batswoman hits a
boundary 6 times out of 30 balls she plays.
The probability that she hit a boundary will
be :
(A) 4 (B) 2
5 5
(C) 1 (D) 3
5 5
[k.M – c
SECTION – B
3
 2 
2. x − y  dks izlkfjr :i esa fyf[k,A 2
 3 
3
 2 
Write x − y  in expanded form.
 3 

3. fuEufyf[kr inksa esa ls izR;sd dh ifjHkk"kk nhft, % 2
(i) lekarj js[kk,¡
(ii) js[kk[kaM
Give a definition for each of the following terms :
(i) Parallel lines
(ii) Line segment

603 P. T. O.

( 10 ) 603
4. ;fn ,d lekarj prqHkZqt ds fod.kZ cjkcj gksa] rks n'kkZb, fd og
,d vk;r gSA 2

If the diagonals of a parallelogram are equal,
then show that it is a rectangle.

5. 15° eki ds dks.k dh jpuk dhft,A 2
Construct the angle 15°.

6. Å¡pkbZ 14 cm okys ,d yEc o`Ùkh; csyu dk oØ i`"Bh;
{ks=Qy 88 cm2 gSA csyu ds vk/kkj dk O;kl Kkr dhft,A 2
The curved surface area of a right circular
cylinder of height 14 cm is 88 cm2. Find the
diameter of the base of the cylinder.

7. 40 n'keyo LFkku rd 'kq) π dk eku uhps fn;k x;k gS % 2

3.1415926535897932384626433832795028841971

n'keyo fcUnq ds ckn tkus okys 0 ls 9 rd ds vadksa dk ,d
ckjackjrk caVu cukb,A
The value of π upto 40 decimal places is given
below :

3.1415926535897932384626433832795028841971

Make a frequency distribution of the digits from
0 to 9 after the decimal point.

603

( 11 ) 603
[k.M – l
SECTION – C

1
8. ds gj dk ifjes;dj.k dhft,A 4
7+3 2

1
Rationalise the denominator of .
7+3 2

9. lehdj.k x + 2y = 6 ds pkj vyx-vyx gy Kkr dhft,A 4
Find four different solutions of the equation
x + 2y = 6.

10. fuEufyf[kr la[;k ;qXeksa dks dkrhZ; ry ds fcUnqvksa ds :i esa
vkysf[kr dhft, % 4

x –2 –3 3 0

y –3 7 –1 –1.5

Plot the following ordered pairs (x, y) of numbers
as points in the Cartesian Plane :

x –2 –3 3 0

y –3 7 –1 –1.5

603 P. T. O.

( 12 ) 603
11. vkÑfr es]a AB ||CD vkSj CD||EF gSA lkFk gh EA ⊥ AB
gSA ;fn ∠BEF = 55° gS] rks x, y vkSj z ds eku Kkr
dhft,A 4
A C E
z
55°
D
y

B x
F

In fig., AB ||CD and CD ||EF . And EA ⊥ AB. If
∠BEF = 55° then find the values of x, y and z.

A C E
z
55°
D
y

B x
F

12. vkÑfr esa] ABCD ,sd lekarj prqHkqZt gS] AE ⊥ DC vkSj
CF ⊥ AD gSA ;fn AB = 16 cm, AE = 8 cm vkSj
CF = 10 cm gS] rks AD Kkr dhft,A 4
A B

F

D E C

603

( 13 ) 603
In fig., ABCD is a parallelogram, AE ⊥ DC
and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and
CF = 10 cm. Find AD.
A B

F

D E C

13. ,d f=Hkqt ABC dh jpuk dhft,] ftlesa BC = 8 lseh,
∠B = 45° vkSj AB – AC = 3.5 lseh gksA 4

Construct a triangle ABC in which BC = 8 cm,
∠B = 45° and AB – AC = 3.5 cm.

14. ,d f=Hkqt dh Hkqtkvksa dk vuqikr 3 : 5 : 7 gS vkSj mldk
ifjeki 300 lseh gSA bl f=Hkqt dk {ks=Qy Kkr dhft,A 4
Sides of a triangle are in the ratio of 3 : 5 : 7 and
its perimeter is 300 cm. Find its area.

15. gkWdh dh ,d Vhe }kjk vusd eSpksa esa izkIr fd, x, vad ;s
gSa % 4

24, 10, 8, 14, 5, 48, 10, 8, 7, 18, 28, 15, 27, 10, 2, 7

Vhe }kjk izkIr fd, x, vadksa dk ek/;] ek/;d o cgqyd Kkr
dhft,A

603 P. T. O.

( 14 ) 603
The points scored by a Hockey team in a series
of matches are as follows :
24, 10, 8, 14, 5, 48, 10, 8, 7, 18, 28, 15, 27, 10, 2, 7
Find the mean, median and mode of points
scored by team.

[k.M – n
SECTION – D

16. f}?kkr cgqin 6x 2 + 5x − 6 ds xq.ku[k.M Kkr dhft,A 5

Factorize the quadratic polynomial 6x 2 + 5x − 6 .

vFkok
OR

xq.ku[k.M dhft, % 27x 3 + y 3 + z 3 − 9xyz
Factorize : 27x 3 + y 3 + z 3 − 9xyz

17. n'kkZb, fd fdlh leckgq f=Hkqt dk izR;sd dks.k 60° gksrk gSA 5
Show that the angles of an equilateral triangle
are 60° each.

18. fdlh xksnke dh eki 40 m × 25 m × 15 m gSA bl xksnke
esa 1.5 m × 1.25 m × 0.5 m dh eki okys ydM+h ds fdrus
vf/kdre ØsV j[ks tk ldrs gSa \ 5

603

( 15 ) 603
A godown measures 40 m × 25 m × 15 m. Find
the maximum number of wooden crates each
measuring 1.5 m × 1.25 m × 0.5 m that can be
stored in the godown.

vFkok
OR
,d yac o`Ùkh; 'kadq dk vk;ru 9856 cm3 gSA ;fn blds
vk/kkj dk O;kl 28 cm gS] rks Kkr dhft, %
(i) 'kadq dh Å¡pkbZ
(ii) 'kadq dh fr;Zd Å¡pkbZ
(iii) 'kadq dk oØ i`"Bh; {ks=Qy
The volume of a right circular cone is 9856 cm3.
If the diameter of the base is 28 cm. Find :
(i) Height of the cone
(ii) Slant height of the cone
(iii) Curved surface area of the cone

19. nks flDdksa dks ,d lkFk 500 ckj mNkyus ij] gesa ;g izkIr
gksrk gS % 5
nks fpr : 105 ckj
,d fpr : 275 ckj
dksbZ Hkh fpr ugha : 120 ckj
buesa ls izR;sd ?kVuk ds ?kVus dh izkf;drk Kkr dhft,A
603 P. T. O.

( 16 ) 603
Two coins are tossed simultaneously 500 times
and we get :

Two heads : 105 times

One heads : 275 times

No heads : 120 times

Find the probability of occurrence of each of
these events.

S

603