HBSE Class 10 Question Paper 2020 Maths

CLASS : 10th (Secondary) Code No. 4803
Series : Sec. M/2020
Roll No. SET : A
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 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 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.

• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side 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.

4803/(Set : A) P. T. O.

(2) 4803/(Set : A)
• 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 questions, 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 Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :

4803/(Set : A)

(3) 4803/(Set : A)
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.

[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.

[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.

[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.

(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.

4803/(Set : A) P. T. O.

(4) 4803/(Set : A)
[k.M & v
SECTION – A

p
1. 0.375 dks ds :i eas O;Dr dhft,A 1
q

p
Express 0.375 in the form .
q

2. 6x 2 − 7x − 3 ds 'kwU;d gSa % 1
1 3
(A) − ,
3 2
7 3
(B) − , −
3 6
7 3
(C) , −
6 6
(D) buesa ls dksbZ ugha
The zeroes of 6x 2 − 7x − 3 are :
1 3
(A) − ,
3 2
7 3
(B) − , −
3 6
7 3
(C) , −
6 6
(D) None of these

4803/(Set : A)

(5) 4803/(Set : A)
3. x + y = 14, x − y = 4 dks gy dhft,A 1
Solve :
x + y = 14, x − y = 4

4. dkSu&lh ,d Js.kh A. P. gS \ 1

(A) 2, 4, 8, 12, …….
(B) 0.2, 0.22, 0.222, ……
(C) –10, –6, –2, 2, ……
(D) 1, 3, 9, 27, …...

Which one is an A. P. series ?

(A) 2, 4, 8, 12, …….

(B) 0.2, 0.22, 0.222, ……

(C) –10, –6, –2, 2, ……

(D) 1, 3, 9, 27, …...

5. 2, 7, 12, …… . A. P. dk 10ok¡ in Kkr dhft,A 1

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

6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1

lHkh o`Ùk ---------- gksrs gSaA ¼lokZaxle] le:i½
4803/(Set : A) P. T. O.

(6) 4803/(Set : A)
Fill in the blank using correct word given in
bracket :

All circles are ………… . (congruent, similar)

7. nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 4 : 9 gS] rks muds
{ks=Qyksa dk vuqikr gS % 1

(A) 16 : 81 (B) 8 : 18

(C) 81 : 16 (D) 12 : 27

Sides of two similar triangles are in the ratio 4 : 9.
Areas of their triangles are in the ratio :

(A) 16 : 81 (B) 8 : 18

(C) 81 : 16 (D) 12 : 27

8. ;fn nks le:i f=Hkqtksa dk {ks=Qy Øe'k% 36 eh2 vkSj
121 eh2 gS] rks mudh laxr Hkqtkvksa dk vuqikr gS % 1

(A) 11 : 6

(B) 6 : 11

(C) 9 : 11

(D) buesa ls dksbZ ugha
4803/(Set : A)

(7) 4803/(Set : A)
If the areas of two similar triangles are 36 m2
and 121 m2 respectively, the ratio of there
corresponding sides is :
(A) 11 : 6 (B) 6 : 11
(C) 9 : 11 (D) None of these

9. ,d fcUnq Q ls ,d o`Ùk ij Li'kZ js[kk dh yEckbZ 24 lseh rFkk
Q dh dsUæ ls nwjh 25 lseh gSA o`Ùk dh f=T;k Kkr dhft,A 1

From a point Q, the length of tangent to a circle
is 24 cm and distance of Q from centre is 25
cm. Find the radius of circle.

10. (2, 3) vkSj (4, 1) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1

Find the distance between the points (2, 3) and
(4, 1).

11. ;fn js[kk[k.M dk e/; fcUnq (3, 4) gS ftldk ,d fljk
(7, –2) gS] rks nwljs fljs dk funsZ'kkad fcUnq Kkr dhft,A 1

If (3, 4) is mid point of the line segment whose
one end is (7, –2), then find the coordinates of
the other end point.

4803/(Set : A) P. T. O.

(8) 4803/(Set : A)
tan 65 o
12. dk eku Kkr dhft,A 1
cot 25 o

tan 65 o
Find the value of .
cot 25 o

13. ;fn sin A = 3 , rks cos A gS % 1
4
4 7
(A) (B)
7 4
3
(C) (D) buesa ls dksbZ ugha
7

3
If sin A = , then cos A is :
4

4 7
(A) (B)
7 4

3
(C) (D) None of these
7

14. f=T;k 4 lseh okys ,d o`Ùk ds f=T;k[kaM dk {ks=Qy Kkr
dhft,] ftldk dks.k 30° gSA ¼π = 3.14 dk ç;ksx dhft,½ 1
Find the area of a sector of a circle with radius
4 cm, if angle of the sector is 30°. (Use π = 3.14)

4803/(Set : A)

(9) 4803/(Set : A)
15. yEco`Ùkh; csyu ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gSA oØ i`"Bh; {ks=Qy gS % 1

(A) πr 2h

(B) 2πrh

(C) 2πr (r + h)

(D) buesa ls dksbZ ugha
The diameter of the base of right circular
cylinder is 2r and its height is h. The curved
surface area is :
(A) πr 2h
(B) 2πrh
(C) 2πr (r + h)
(D) None of these

16. ,d FkSys esa 3 uhyh xsan] 2 lQsn xsan vkSj 4 yky xsan gSaA ;fn
,d xsan FkSys ls ;kn`fPNd fudkyh tkrh gS] rks blds lQsn gksus
dh çkf;drk D;k gksxh \ 1

A bag contains 3 blue balls, 2 white balls and 4
red balls. If one ball is taken out at random from
the bag. What is the probability that it will be
White ?

4803/(Set : A) P. T. O.

( 10 ) 4803/(Set : A)
[k.M & c
SECTION – B

17. fl) dhft, fd 2 ,d vifjes; la[;k gSA 3

Prove that 2 is an irrational number.

18. cgqin p(x ) = 3x 3 + x 2 + 2x + 5 dks cgqin
2
q (x ) = x + 2x + 1 ds }kjk Hkkx dhft,A HkkxQy vkSj
'ks"kQy Kkr dhft,A 3

Divide the polynomial p(x ) = 3x 3 + x 2 + 2x + 5
by the polynomial q (x ) = x 2 + 2x + 1 . Find the
quotient and remainder.

19. 90 lseh dh yEckbZ okyh ,d yM+dh cYc yxs ,d [kaHks ds
vk/kkj ls ijs 1.2 eh/ls- dh pky ls py jgh gSA ;fn cYc
Hkwfe ls 3.6 eh dh Å¡pkbZ ij gS] rks 4 lsd.M ckn ml yM+dh
dh Nk;k dh yEckbZ Kkr dhft,A 3

A girl of height 90 cm is walking away from the
base of a lamp-post at a speed of 1.2 m/s. If the
lamp is 3.6 m above the ground, find the length
of her shadow after 4 seconds.

20. fl) dhft, % 3

sec A (1 − sin A) (sec A + tan A) = 1

4803/(Set : A)

( 11 ) 4803/(Set : A)
Prove that :

sec A (1 − sin A) (sec A + tan A) = 1

21. o`Ùk dh ifjf/k Kkr dhft, ftldk {ks=Qy 6.16 lseh2 gSA 3

Find the circumference of a circle whose area is
6.16 cm2 .

[k.M & l
SECTION – C

22. gy dhft, % 4

5 1 6 3
+ = 2 vkSj − =1
x −1 y − 2 x −1 y − 2

Solve :

5 1 6 3
+ = 2 and − =1
x −1 y − 2 x −1 y − 2

23. ,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 4

4803/(Set : A) P. T. O.

( 12 ) 4803/(Set : A)
The speed of motor-boat is 18 km/h in still
water. It takes one hour more to 24 km
upstream than to return downstream the same
distance. Find the speed of the stream.

24. A. P. : 24, 21, 18, …… ds fdrus in fy, tk,¡] rkfd
mudk ;ksx 78 gks \ 4

How many terms of A. P. : 24, 21, 18, ……
should be taken so that their sum is 78 ?

25. fdlh cká fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh yEckb;k¡
cjkcj gksrh gSa] fl) dhft,A 4

Prove that the length of tangents drawn from an
external point to a circle are equal.

26. fcUnq (−4, 6)] fcUnqvksa A(−6, 10) vkSj B(3, −8) dks tksM+us
okys js[kk[k.M dks fdl vuqikr esa foHkkftr djrk gSA 4
In what ratio does the point (−4, 6) divides the
line segment joining the points A(−6, 10) and
B(3, −8).

27. vPNh çdkj ls QsaVh xbZ 52 iÙkksa dh ,d xM~Mh esa ls ,d iÙkk
fudkyk tkrk gSA çkf;drk Kkr dhft, fd ;g iÙkk (i) ,d
bDdk gksxk] (ii) ,d bDdk ugha gksxkA 4

4803/(Set : A)

( 13 ) 4803/(Set : A)
One card is drawn from a well-shuffled deck of
52 cards. Calculate the probability that the card
will (i) be an ace, (ii) not be an ace.

[k.M & n
SECTION – D

28. iw.kZ oxZ cukus dh fof/k ls lehdj.k 2x 2 − 5x + 3 = 0 dks
gy dhft,A 5
Solve the equation 2x 2 − 5x + 3 = 0 by
completing the square method.

29. 4 lseh, 5 lseh vkSj 6 lseh Hkqtkvksa okys ,d f=Hkqt dh jpuk
dhft, vkSj fQj blds le:i ,d vU; f=Hkqt dh jpuk
dhft,] ftldh Hkqtk,¡ fn, gq, f=Hkqt dh laxr Hkqtkvksa dh 2
3
xquh gksaA 5
Construct a triangle whose sides are 4 cm, 5 cm
and 6 cm and construct a similar triangle whose
2
sides are th of the corresponding sides of
3
given triangle.

30. fl) dhft, % 5

sin θ + cos θ − 1 1
=
sin θ − cos θ + 1 sec θ + tan θ

4803/(Set : A) P. T. O.

( 14 ) 4803/(Set : A)
Prove that :

sin θ + cos θ − 1 1
=
sin θ − cos θ + 1 sec θ + tan θ

vFkok
OR

1.2 eh yach ,d yM+dh Hkwfe ls 88.2 eh dh Å¡pkbZ ij ,d
{kSfrt js[kk esa gok esa mM+ jgs xqCckjs dks ns[krh gSA fdlh Hkh
{k.k yM+dh dh vk¡[k ls xqCckjs dk mUu;u dks.k 60° dk gSA
dqN le; ckn mUu;u dks.k ?kVdj 30° gks tkrk gSA bl
vUrjky ds nkSjku xqCckjs }kjk r; dh xbZ nwjh Kkr dhft,A
A 1.2 m tall girl spots a balloon moving with the
wind in a horizontal line at a height of 88.2 m
from the ground. The angle of elevation of the
balloon from the eyes of the girl at any instant is
60°. After some time, the angle of elevation
reduces to 30°. Find the distance travelled by
the balloon during the interval.

31. nks ?kuksa] ftuesa ls çR;sd dk vk;ru 64 lseh3 gS] ds layXu
Qydksa dks feykdj ,d Bksl cuk;k tkrk gSA blls çkIr ?kukHk
dk i`"Bh; {ks=Qy Kkr dhft,A 5

4803/(Set : A)

( 15 ) 4803/(Set : A)
Two cubes each of volume 64 cm3 are joined
end to end. Find the surface area of the resulting
cuboid.

32. uhps fn;k gqvk caVu ,d d{kk ds 30 fo|kfFkZ;ksa dk Hkkj n'kkZ
jgk gSA fo|kfFkZ;ksa dk ek/;d Hkkj Kkr dhft, % 5

Hkkj ¼fd0xzk0 esa½ 40-45 45-50 50-55 55-60 60-65 65-70 70-75
fo|kfFkZ;ksa dh 2 3 8 6 6 3 2
la[;k
The distribution below gives the weight of 30
students of a class. Find the median weight of
the students :

Weight (in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75

Number of 2 3 8 6 6 3 2

Students

vFkok
OR

fdlh eksgYys ds 25 ifjokjksa dk Hkkstu ij O;; fuEufyf[kr gSA
Hkkstu ij gqvk ek/; O;; Kkr dhft, %
[kpZ ¼#0 esa½ 100-150 150-200 200-250 250-300 300-350

ifjokjksa dh la[;k 4 5 12 2 2

4803/(Set : A) P. T. O.

( 16 ) 4803/(Set : A)
The table below shows daily expenditure on food
of 25 households in a locality. Find the mean
daily expenditure :

Expenditure (in Rs.) 100-150 150-200 200-250 250-300 300-350

No. of households 4 5 12 2 2



4803/(Set : A)