HBSE Class 10 Mathematics (B) Question Paper 2019

CLASS : 10th (Secondary) Code No. 4204
Series : Sec. M/2019
Roll No.

xf.kr
MATHEMATICS
( Academic/Open )
[ fgUnh ,oa vaxszth ek/;e ]
[ Hindi and English Medium ]
(Only for Blind Candidates)
(Only for Fresh/Re-appear Candidates)
le; % 4 ?k.Vs ] [ iw.kk±d % 80
Time allowed : 4 hours ] [ Maximum Marks : 80
• d`i;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 17 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
17 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj dks Nk=
mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. on the right side of the question paper
should be written by the candidate on the front page
of the answer-book.
• d`i;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.

4204 P. T. O.

(2) 4204
• 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 %
General Instructions :
(i) LkHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u&i= esa dqy 17 iz'u gSa] tks fd pkj
pkj&&[k.Mksa %
v] c] l vkSj n esa ck¡Vs x, gSa %
[k.M ^v* % bl [k.M esa ,d iz'u gS] ftlesa oLrqfu"B
izdkj ds lksyg (i-xvi) iz'u gS]a izR;sd
iz'u 1 vad dk gSA lgh mÙkj viuh
mÙkj&iqfLrdk esa fy[ksaA
4204

(3) 4204
[k.M ^c* % bl [k.M esa 2 ls 6 rd dqy ik¡p iz'u
gSa] izR;sd iz'u 3 vadksa dk gSA
[k.M ^l* % bl [k.M esa 7 ls 12 rd dqy N% iz'u
gSa] izR;sd iz'u 4 vadksa dk gSA
[k.M ^n* % bl [k.M esa 13 ls 17 rd dqy ik¡p
iz'u gSa] izR;sd iz'u 5 vadksa dk gSA
This question paper consists of 17 questions
in all, which are divided into four
Sections : A, B, C and D :
Section 'A' : This section consists of one
question which has Sixteen
(i-xvi) Objective type questions,
each of 1 mark. Write correct
answer in your answer-book.
Section 'B' : This section consists of five
questions from 2 to 6, each of
3 marks.
Section 'C' : This section consists of six
questions from 7 to 12, each
of 4 marks.
Section 'D' : This section consists of five
questions from 13 to 17, each
of 5 marks.
(iii) lexz :i ls dksbZ fodYi ugha gS] ysfdu [k.M ^n* ds nks
iz'uksa esa vkUrfjd fodYi fn, x, gSaA ,sls iz'uksa esa ls
vkidks dsoy ,d gh iz'u djuk gSA
There is no overall choice, but in two
questions of Section 'D' internal choices are
given. You have to attempt only one of the
given choice in such questions.

4204 P. T. O.

(4) 4204
[k.M & v
SECTION – A

1. (i) 140 ds vHkkT; xq.ku[k.Mksa dks xq.kuQy ds :i esa O;Dr
dhft,A 1

Express 140 as a product of its prime
factors.

(ii) fuEufyf[kr esa ls dkSu-lh ifjes; la[;k gS \ 1

(A) 8 (B) 18

(C) 25 (D) 27

Which of the following is rational number ?

(A) 8 (B) 18

(C) 25 (D) 27

(iii) f}?kkr cgqin 4x 2 + 8x ds 'kwU;d Kkr dhft,A 1

Find the zeroes of quadratic polynomial
4x 2 + 8 x .

(iv) f}?kkr cgqin x 2 + 7x + 10 ds 'kwU;dksa dk ;ksx Kkr
dhft,A 1

Find the sum of zeroes of quadratic

polynomial x 2 + 7x + 10 .
4204

(5) 4204
(v) p ds fdu ekuksa ds fy, jSf[kd lehdj.kksa ds ;qXe dk
vf}rh; gy gS \ 1
4x + py + 8 = 0
2x + 2y + 2 = 0
For which value of p does the pair of
equations given below has unique solution ?
4x + py + 8 = 0
2x + 2y + 2 = 0

(vi) 4x 2 + 4x + 1 = 0 dk fofoDrdj Kkr dhft,A 1

Find the discriminant of 4x 2 + 4x + 1 = 0 .
(vii) A. P. : 2, 7, 12, ………….. dk 10oka in Kkr

dhft,A 1

Find 10th term of an A. P. : 2, 7, 12,
………….. .

(viii) A. P. : −4, −10, −16, −22, ….. dk lkoZvarj gksxk % 1

(A) 6 (B) −6
(C) 4 (D) 8
The common difference of an A. P. : −4, −10,
−16, −22, ………….. will be :
(A) 6 (B) −6
(C) 4 (D) 8

4204 P. T. O.

(6) 4204
(ix) fcanv
q ksa (2, 3) vkSj (4, 1) ds chp dh nwjh Kkr dhft,A 1
Find the distance between points (2, 3) and
(4, 1).
(x) fuEufyf[kr esa ls ewy fcanq ds funs'Z kkad gksrs gSa \ 1
(A) (1, 1) (B) (2, 1)
(C) (0, 0) (D) (2, 2)
Which of the following are the coordinates
of the origin ?
(A) (1, 1) (B) (2, 1)
(C) (0, 0) (D) (2, 2)
(xi) sin2 45o + cos 2 45o dk eku gksxk % 1
1
(A) 1 (B)
2
3
(C) 2 (D)
2
2 2
The value of sin 45 + cos 45o will be :
o

1
(A) 1 (B)
2
3
(C) 2 (D)
2
4
(xii) ;fn sin θ = gS] rks cos θ dk eku gksxk % 1
5
5
(A) 0 (B)
4
3 3
(C) (D)
5 4

4204

(7) 4204
4
If sin θ = , then cos θ will be :
5
5
(A) 0 (B)
4
3 3
(C) (D)
5 4
(xiii) f=T;k r okys o`Ùk dh ifjf/k gksxh % 1

(A) 2πr 2 (B) 2πr

(C) 3πr 2 (D) πr 2

The circumference of a circle with radius r
will be :

(A) 2πr 2 (B) 2πr

(C) 3πr 2 (D) πr 2

(xiv) csyu dk vk;ru Kkr dhft, ftldh f=T;k o Å¡pkbZ
Øe'k% 7 lseh o 5 lseh gSA 1

Find the volume of cylinder whose radius
and height are 7 cm and 5 cm respectively.

(xv) nks f[kykM+h oaf'krk vkSj rstLoh Vsful dk ,d eSp [ksyrs
gSaA ;g Kkr gS fd oaf'krk }kjk eSp thrus dh çkf;drk
0.62 gSA rstLoh ds thrus dh D;k çkf;drk gS \ 1

4204 P. T. O.

(8) 4204
Two players, Vanshita and Tejasvi play a
tennis match. It is known that the
probability of Vanshita winning the match
is 0.62. What is the probability of Tejasvi
winning the match ?

(xvi) 52 iÙkksa dh vPNh izdkj ls QsaVh xbZ ,d xìh esa ls ,d

iÙkk fudkyk tkrk gSA rks yky jax dk ckn'kkg izkIr djus
dh izkf;drk Kkr dhft,A 1

One card is drawn from a well shuffled deck
of 52 cards. Find the probability of getting a
king of red colour.

[k.M & c

SECTION – B

2. 867 vkSj 255 dk HCF ;wfDyM foHkktu çesf;dk dk ç;ksx

djds Kkr dhft,A 3

Use Euclid's algorithm to find the HCF of 867
and 255.

4204

(9) 4204
3. ,d f}?kkr cgqin Kkr dhft,] ftlds 'kwU;dksa ds ;ksx rFkk
xq.kuQy Øe'k% 1 rFkk −1 gksaA 3
4
Find a quadratic polynomial, the sum and
1
product of whose zeroes are and −1
4
respectively.

4. rhu vadksa okyh fdruh la[;k,¡ 7 ls foHkkT; gSa \ 3

How many three digit numbers are divisible by 7 ?

5. ;fn sec 4A = cosec(A − 20°), tgk¡ 4A ,d U;wu dks.k gS]
rks A dk eku Kkr dhft,A 3

If sec 4A = cosec(A − 20°), where 4A is an acute
angle, then find the values of A.

6. fdlh QSDVjh ds 50 Jfedksa dh nSfud etnwjh ds fuEufyf[kr
caVu ij fopkj dhft, % 3

nSfud etnwjh 100-120 120-140 140-160 160-180 180-200

¼` es½a

Jfedksa dh la[;k 12 14 8 6 10

bl QSDVjh ds Jfedksa dh ek/; nSfud etnwjh Kkr dhft,A

4204 P. T. O.

( 10 ) 4204
Consider the following distribution of daily
wages of 50 workers of a factory :

Daily Wages (in `) 100-120 120-140 140-160 160-180 180-200

Number of Workers 12 14 8 6 10

Find the mean of daily wages of this factory
workers.

[k.M & l

SECTION – C

7. ,d fØdsV Vhe ds dksp us 7 cYys rFkk 6 xsansa 3,800 ` esa
[kjhnhA ckn esa] mlus 3 cYys rFkk 5 xsansa 1,750 ` esa [kjhnhA
çR;sd cYys vkSj çR;sd xsan dk ewY; Kkr dhft,A 4

The Coach of a cricket team buys 7 bats and 6
balls for ` 3,800. Later, she buys 3 bats and 5
balls for ` 1,750. Find the cost of each bat and
each ball.

1 1 1 1 13
8. lehdj.kksa + = 2 rFkk + = ds ;qXeksa dks
2x 3y 3x 2y 6
jSf[kd lehdj.kksa ds ;qXe esa cnydj gy djsaA 4

4204

( 11 ) 4204
1 1
Solve pair of equations + =2 and
2x 3y
1 1 13
+ = by reducing them to pair of linear
3x 2y 6
equations.

9. y-v{k ij ,d ,slk fcanq Kkr dhft,] tks fcanqvksa A(6, 5) vkSj

B(−4, 3) ls lenwjLFk gksA 4

Find a point on the y-axis which is equidistant
from the points A(6, 5) and B(−4, 3).

10. ,d leprqHkqZt dk {ks=Qy Kkr dhft, ftlds 'kh"kZ] blh Øe esa
(3, 0), (4, 5), (−1, 4) vkSj (−2, − 1) gSaA 4

Find the area of a rhombus if its vertices are
(3, 0), (4, 5), (−1, 4) and (−2, − 1) taken in order.

11. f=T;k 21 lseh okys o`Ùk dk ,d pki dsUæ ij 60° dk dks.k
varfjr djrk gSA Kkr dhft, % (i) pki dh yEckbZ (ii) pki
}kjk cuk, x, f=T;k[kaM dk {ks=QyA 2+2=4

In a circle of radius 21 cm, an arc subtends an
angle of 60° at the centre. Find : (i) the length of
the arc (ii) area of the sector formed by the arc.

4204 P. T. O.

( 12 ) 4204
12. ,d fiXxh cSad es]a 50 iSls ds lkS flDds gS]a 1 ` ds ipkl
flDds gSa] 2 ` ds chl flDds vkSj 5 ` ds nl flDds gSaA ;fn
fiXxh cSad dks fgykdj mYVk djus ij dksbZ ,d flDdk fxjus ds
ifj.kke leçkf;d gSa] rks bldh D;k çkf;drk gS fd og fxjk
gqvk flDdk (i) 1 ` dk gksxk \ (ii) 50 iSls dk ugha gksxk \
2+2=4

A piggy bank contains hundred 50 paise coins,
fifty ` 1 coins, twenty ` 2 coins and ten ` 5
coins. If it is equally likely that one of the coins
will fall out when the bank is turned upside
down. What is the probability that the coin (i)
will be ` 1 coin ? (ii) will not be 50 paise coin ?

[k.M & n
SECTION – D

13. ,d ledks.k f=Hkqt dh Å¡pkbZ blds vk/kkj ls 7 lseh de gSA
;fn d.kZ 13 lseh dk gks] rks vU; nks Hkqtk,¡ Kkr dhft,A 5
The height of a right triangle is 7 cm less than
its base. If the hypotenuse is 13 cm, find the
other two sides.

vFkok
OR

4204

( 13 ) 4204
,d eksVj cksV ftldh fLFkj ty esa pky 18 fdeh/?k.Vk gS]
24 fdeh /kkjk ds çfrdwy tkus esa] ogh nwjh /kkjk ds vuqdwy
tkus dh vis{kk 1 ?kaVk vf/kd ysrh gSA /kkjk dh pky Kkr
dhft,A 5
A motorboat whose speed is 18 km/h in still
water takes 1 hour more to go 24 km upstream
than to return downstream to the same spot.
Find the speed of the stream.

14. fdlh A.P. ds pkSFks vkSj 8osa inksa dk ;ksx 24 gS rFkk NBs vkSj
10osa inksa dk ;ksx 44 gSA bl A. P. ds çFke rhu in Kkr
dhft,A 5

The sum of the 4th and 8th terms of an A. P. is
24 and the sum of the 6th and 10th terms is 44.
Find the first three terms of the A. P.

15. ,d ehukj ds ikn fcanq ls ,d Hkou ds f'k[kj dk mUu;u dks.k
30° gS vkSj Hkou ds ikn fcanq ls ehukj ds f'k[kj dk mUu;u
dks.k 60° gSA ;fn ehukj 50 eh Å¡ph gks] rks Hkou dh Å¡pkbZ
Kkr dhft,A 5

The angle of elevation of the top of a building
from the foot of the tower is 30° and the angle of
elevation of the top of the tower from the foot of
the building is 60°. If the tower is 50 m high,
find the height of the building.

4204 P. T. O.

( 14 ) 4204
16. dksbZ crZu ,d [kks[kys v/kZxksys ds vkdkj dk gS ftlds Åij
,d [kks[kyk csyu v/;kjksfir gSA bl crZu dh dqy Å¡pkbZ 13
lseh rFkk v/kZxksys dk O;kl 14 lseh gSA bl crZu dk vkarfjd
i`"Bh; {ks=Qy Kkr dhft,A 5
A vessel is in the form of a hollow hemisphere
mounted by a hollow cylinder. The diameter of
the hemisphere is 14 cm and the total height of
the vessel is 13 cm. Find the inner surface area
of the vessel.

17. fuEufyf[kr lkj.kh fdlh vLirky esa ,d fo'ks"k o"kZ esa HkrhZ gq,
jksfx;ksa dh vk;q dks n'kkZrh gS % 5

vk;q ¼o"kks± esa½ 5-15 15-25 25-35 35-45 45-55 55-65
jksfx;ksa dh 6 11 21 23 14 5
la[;k
mijksDr vk¡dM+ksa ds cgqyd Kkr dhft,A
The following table shows the ages of the
patients admitted in a hospital during a year :

Ages (in Years) 5-15 15-25 25-35 35-45 45-55 55-65

Number of 6 11 21 23 14 5
Patients

Find the mode of the data .

4204

( 15 ) 4204
vFkok
OR

fuEufyf[kr ckjackjrk caVu fdlh eksgYys ds 70 miHkksDrkvksa
dh fctyh dh ekfld [kir n'kkZrk gSA bu vk¡dM+ksa dk ek/;d
Kkr dhft, % 5

ekfld [kir ¼bdkb;ksa esa½ miHkksDrkvksa dh la[;k

65-85 4

85-105 5

105-125 13

125-145 20

145-165 14

165-185 8

185-205 4

4204 P. T. O.

( 16 ) 4204
The following frequency distribution gives the
monthly consumption of electricity of 70
consumers of a locality. Find the median :

Monthly Consumption Number of
(in Units) Consumers

65-85 4

85-105 5

105-125 13

125-145 20

145-165 14

165-185 8

185-205 4

4204
S