HBSE Class 10 Mathematics (B) Question Paper 2020

CLASS : 10th (Secondary) Code No. 4804
Series : Sec. M/2020
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 15 rFkk
iz'u 17 gSaA
Please make sure that the printed pages in this
question paper are 15 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.

4804 P. T. O.

(2) 4804
• 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 gSa] izR;sd
iz'u 1 vad dk gSA lgh mÙkj viuh
mÙkj&iqfLrdk esa fy[ksaA
4804

(3) 4804
[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.

4804 P. T. O.

(4) 4804
[k.M & v
SECTION – A

1. (i) fuEufyf[kr esa ls dkSu-lh la[;k vifjes; la[;k gS \ 1

(A) 2 16 (B) 3 36

(C) 8 8 (D) 4 49

Which of the following numbers is an
irrational number ?

(A) 2 16 (B) 3 36

(C) 8 8 (D) 4 49

(ii) 90 vkSj 105 dk H.C.F. gS % 1

(A) 90 (B) 105

(C) 18 (D) 15

The H.C.F. of 90 and 105 is :

(A) 90 (B) 105

(C) 18 (D) 15

(iii) f}?kkr cgqin 3 x 2 − 4x + 6 ds 'kwU;dksa dk ;ksxQy
Kkr dhft,A 1

Find the sum of zeroes of quadratic
polynomial 3x 2 − 4x + 6 .

4804

(5) 4804
(iv) fuEufyf[kr esa ls dkSu-lk chth; O;atd ,d cgqin gS \ 1
1
(A) x 2 /3 + 5 (B) −1
x2
1
(C) 2x 2 + 3x + 1 (D) x+ +2
x
Which of the following algebraic expressions
is a polynomial ?
1
(A) x 2 /3 + 5 (B) −1
x2
1
(C) 2x 2 + 3x + 1 (D) x+ +2
x

(v) f}?kkr lehdj.k 2x 2 − 7x + 3 = 0 dk fofoDrdj Kkr
dhft,A 1
Find the discriminant of quadratic equation
2x 2 − 7x + 3 = 0 .

(vi) jSf[kd lehdj.k ;qXe 6x − 3y +10 = 0 o 2x −y + 9 = 0
ds xzkQh; fu:i.k dh js[kk,¡ gksaxh % 1

(A) izfrPNsnh js[kk,¡
(B) lekarj js[kk,¡
(C) laikrh js[kk,¡
(D) buesa ls dksbZ ugha

4804 P. T. O.

(6) 4804
The graphical representation of pair of linear
equations 6x − 3y + 10 = 0 and 2x −y + 9 = 0
will be :
(A) Intersecting lines
(B) Parallel lines
(C) Coincident lines
(D) None of these
(vii) A. P. 4, 10, 16, 22 ………….. dk 20ok¡ in Kkr
dhft,A 1
Find 20th term of an A. P. 4, 10, 16,
22 ………….. .
5 9 13
(viii) A. P. , , .......... dk lkoZvarj Kkr dhft,A 1
3 3 3
Find the common difference of an A. P.
5 9 13
, , .......... .
3 3 3

(ix) fcanqvksa (3, 5) o (5, 7) ds chp dh nwjh gksxhA 1

(A) 8 (B) 15

(C) 40 (D) 12

The distance between two points (3, 5) and
(5, 7) will be :

(A) 8 (B) 15

(C) 40 (D) 12

4804

(7) 4804
(x) fcUnqvksa (7, 6) o (–3, –4) dks feykus okys js[kk[k.M ds
e/; fcUnq Kkr dhft,A 1

Find the mid point of the line segment
joining the points (7, 6) and (–3, –4).

(xi) ;fn tan A = 4 gS] rks cos A dk eku Kkr dhft,A 1
3

4
If tan A = , then find cos A.
3

(xii) sin 60° – cos 30° dk eku Kkr dhft,A 1

Find the value of sin 60° – cos 30°.

(xiii) ;fn f=T;k[k.M dk dks.k θ gks rks] y?kq f=T;k[k.M dk

{ks=Qy dk lw= gksxk % 1

θ
(A) πr 2 (B) 2πr
360
θ
(C) πr 2 (D)
× 2πr
360
If the angle of the sector is θ then the
formula for area of minor sector will be :

θ
(A) πr 2 (B) 2πr
360
θ
(C) πr 2 (D) × 2πr
360
4804 P. T. O.

(8) 4804
(xiv) ,d 'kadq dk oØ i`"Bh; {ks=Qy Kkr dhft, ftldh
f=T;k o fr;Zd Å¡pkbZ Øe'k% 4 lseh rFkk 3 lseh gSaA 1
Find the curved surface area of a cone
whose radius and slant height are 4 cm and
3 cm respectively.

(xv) ;fn P (E) = 0.01 gS] rks P (E ) dk eku Kkr dhft,A 1

If P (E) = 0.01, then find P (E ) .

(xvi) ikls dks ,d ckj mNkyus ij la[;k 8 izkIr djus dh
izkf;drk Kkr dhft,A 1

A die is thrown once, find the probability of
getting a number 8.

[k.M & c

SECTION – B

2. 867 o 255 dk ;wfDyM foHkktu izesf;dk }kjk e0l0v0

(H.C.F.) Kkr dhft,A 3

Use Euclid's division algorithm to find the H.C.F.
of 867 and 255.
4804

(9) 4804
3. f}?kkr cgqin t 2 − 15 ds 'kwU;d Kkr dhft, vkSj 'kwU;dksa rFkk
xq.kkadksa ds chp ds laca/k dh lR;rk dh tk¡p dhft,A 3
Find the zeroes of quadratic polynomial t 2 − 15
and verify the relationship between the zeroes
and the coefficients.

4. rhu vadksa okyh fdruh la[;k,¡ 7 ls foHkkT; gSa \ 3
How many three digit numbers are divisible by 7 ?

5. fn[kkb, fd % tan 48° tan 23° tan 42° tan 67° = 1 3
Show that : tan 48° tan 23° tan 42° tan 67° = 1

6. 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 % 3

vk;q ¼o"kksZa esa½ 5-15 15-25 25-35 35-45 45-55 55-65

jksfx;ksa dh la[;k 6 11 21 23 14 5

mi;qZDr vk¡dM+ksa dk ek/; Kkr dhft,A

The following table shows the ages of the patients
admitted in a hospital during a year :

Age (In Years) 5-15 15-25 25-35 35-45 45-55 55-65

No. of Patients 6 11 21 23 14 5

Find the mean of data given above.

4804 P. T. O.

( 10 ) 4804
[k.M & l

SECTION – C

7. lehdj.kksa ds fuEu ;qXe dks gy dhft, % 4

2 3 5 4
+ = 13 vkSj − = −2
x y x y

Solve the following pair of equations :

2 3 5 4
+ = 13 and − = −2
x y x y

8. nks la[;kvksa dk varj 26 gS vkSj ,d la[;k nwljh la[;k dh
rhu xquh gSA mUgsa Kkr dhft,A 4

The difference between two numbers is 26 and
one number is three times the other. Find them.

9. x-v{k ij og fcUnq Kkr dhft, tks (2, –5) vkSj (–2, 9) ls

lenwjLFk gSA 4

Find the point on the x-axis which is equidistant
from (2, –5) and (–2, 9).

4804

( 11 ) 4804
10. k dk eku Kkr dhft, ;fn fcUnq (7, –2), (5, 1), (3, k)

lajs[kh gSaA 4

Find the value of k if the points (7, –2), (5, 1), (3, k)
are collinear.

11. ,d o`Ùkkdkj [ksr ij 24 #0 izfr ehVj dh nj ls ckM+ yxkus
dk O;; 5280 #0 gSA bl [ksr dh 0.50 #0 izfr oxZ ehVj
dh nj ls tqrkbZ djkbZ tkuh gSA [ksr dh tqrkbZ djkus dk O;;
Kkr dhft,A 4

The cost of fencing a circular field at the rate of
` 24 per meter is ` 5280. The field is to be
ploughed at the rate of ` 0.50 per m2. Find the
cost of ploughing the field.

12. 52 iÙkksa dh vPNh izdkj ls QsVh xbZ ,d xìh esa ls ,d iÙkk
fudkyk tkrk gSA fuEufyf[kr dks izkIr djus dh izkf;drk Kkr
dhft, % 4

(i) iku dk xqyke
(ii) yky jax dh rLohj okyk iÙkk
(iii) gqdqe dk iÙkk
(iv) bZaV dh csxe
4804 P. T. O.

( 12 ) 4804
One card is drawn from a well shuffled deck of

52 cards. Find the probability of getting :

(i) the jack of hearts

(ii) a red face card

(iii) a spade

(iv) the queen of diamonds

[k.M & n
SECTION – D

13. ,sls nks Øekxr fo"ke /kukRed iw.kkZad Kkr dhft, ftuds oxksZa
dk ;ksx 290 gksA 5

Find two consecutive odd positive integers, sum

of whose squares is 290.

14. ml A.P. dk 31ok¡ in Kkr dhft, ftldk 11ok¡ in 38 gS
vkSj 16ok¡ in 73 gSA 5

Find the 31st term of an A.P. whose 11th term is

38 and the 16th term is 73.

4804

( 13 ) 4804
15. ehukj ds vk/kkj ls vkSj ,d ljy js[kk esa 4 ehVj vkSj 9 ehVj
dh nwjh ij fLFkr nks fcUnqvksa ls ehukj ds f'k[kj ds mUu;u
dks.k iwjd dks.k gSaA fl) dhft, fd ehukj dh Å¡pkbZ 6 ehVj
gSA 5

The angles of elevation of the top of a tower from
two points at a distance of 4 m and 9 m from the
base of the tower and in the same straight line
with it are complementary. Prove that the height
of the tower is 6 m.
vFkok
OR
fl) dhft, % 5
1 − cos θ
(cosec θ – cot θ)2 =
1 + cos θ
Prove that :
1 − cos θ
(cosec θ – cot θ)2 =
1 + cos θ
16. ,d 'kadq ds fNUud dh fr;Zd Å¡pkbZ 4 lseh gS rFkk blds o`Ùkh;
fljksa ds ifjeki ¼ifjf/k;k¡½ 18 lseh vkSj 6 lseh gSaA bl fNUud
dk oØ i`"Bh; {ks=Qy Kkr dhft,A 5

The slant height of a frustum of a cone is 4 cm
and the perimeters (circumferences) of its circular
ends are 18 cm and 6 cm. Find the curved surface
area of frustum.

4804 P. T. O.

( 14 ) 4804
17. fuEufyf[kr vk¡dM+ksa dk ek/;d Kkr dhft, % 5

oxZ vUrjky 65-68 68-71 71-74 74-77 77-80 80-83 83-86
ckjackjrk 2 4 3 8 7 4 2

Find the median of the following data :

Class 65-68 68-71 71-74 74-77 77-80 80-83 83-86
Interval

Frequency 2 4 3 8 7 4 2

vFkok
OR

fuEufyf[kr ckjackjrk caVu dk cgqyd Kkr dhft, % 5

oxZ vUrjky ckjackjrk
40-45 2

45-50 3

50-55 8

55-60 6

60-65 6

65-70 3

70-75 2

4804

( 15 ) 4804
Find the mode of the following frequency
distribution :

Class Interval Frequency

40-45 2

45-50 3

50-55 8

55-60 6

60-65 6

65-70 3

70-75 2

S

4804 P. T. O.