HBSE Class 10 Mathematics Question Paper 2018 Set B

CLASS : 10th (Secondary) Code No. 3503
Series : Sec. M/2018
Roll No. SET : B

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MATHEMATICS
(Academic/Open)
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[ 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 iz'u 32 gSaA
Please make sure that the printed question paper are 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.
• 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.

3503/(Set : B) P. T. O.

(2) 3503/(Set : B)
• 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 :
[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.
[k.M & v
SECTION – A

1. ;fn a vkSj b nks /kukRed iw.kk±d gSa] rks muds LCM vkSj HCF esa lEcU/k gksxk % 1
(A) LCM > HCF (B) HCF > LCM
(C) HCF = LCM (D) buesa ls dksbZ ugha
3503/(Set : B)

(3) 3503/(Set : B)
If a and b are two positive integers, then the relation between their LCM
and HCF will be :
(A) LCM > HCF (B) HCF > LCM
(C) HCF = LCM (D) None of these

2. buesa ls dkSu-lk cgqin (Polynomial) gS \ 1
1
1
(A) (B) x3 +2
x +1
1
(C) (D) x+ 2
x2 +1
Which one is polynomial ?
1
1
(A) (B) x3 +2
x +1
1
(C) (D) x+ 2
x2 +1

3. lehdj.kksa a1x + b1y + c1 = 0 vkSj a 2x + b2y + c 2 = 0 esa ;fn a1 = b1 = c1 , rks
a2 b2 c2
fuEufyf[kr esa dkSu-lk lR; gS \ 1
(A) çfrPNsfnr js[kk,¡ (B) laikrh js[kk,¡
(C) lekarj js[kk,¡ (D) buesa ls dksbZ ugha
a1 b1 c1
If in equations a1x + b1y + c1 = 0 and a 2 x + b2y + c 2 = 0 , = = ,
a 2 b2 c 2
then which of the following is true ?
(A) Intersecting lines (B) Coincident lines
(C) Parallel lines (D) None of these

4. buesa ls dkSu-lh A. P. Js.kh 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 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, ……

3503/(Set : B) P. T. O.

(4) 3503/(Set : B)
5. A. P. −10, −6, −2, 2, …. dk 20ok¡ in gS % 1

(A) 66 (B) −66

(C) 77 (D) buesa ls dksbZ ugha
In an A. P. −10, −6, −2, 2, …., 20th term is :

(A) 66 (B) −66

(C) 77 (D) None of these

6. f=Hkqtksa ds ;qXeksa esa ls dkSu-lk ;qXe le:i ugha gS \ 1
A P

(A) 60° 60°

80° 40° C 80° 40°
B Q R
P

A
(B) 6 5
2 3

B C Q R
2.5 4

L D
(C)
2.7 3 4 6
M P
2 E F
5

P
M
(D) 2.5 70° 5 5

N L 70°
Q R
10

3503/(Set : B)

(5) 3503/(Set : B)
Which one pair of the triangles is not similar triangles ?
A P
(A) 60°
60°
80° 40° C 80° 40°
B Q R
P

A
(B)
2 6 5
3

B C Q R
2.5 4

L D
(C)
2.7 3 4 6
M P
2 E F
5

P
M
(D) 5
2.5 70° 5

N L 70°
Q R
10
7. ;fn nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 3 : 2 gS] rks muds {ks=Qyksa dk vuqikr gS %
1

(A) 3: 2 (B) 2:3

(C) 9:4 (D) buesa ls dksbZ ugha
If the ratio of the sides of two similar triangles is
3 : 2, then the ratio of their areas is :

(A) 3: 2 (B) 2:3

(C) 9:4 (D) None of these

3503/(Set : B) P. T. O.

(6) 3503/(Set : B)
8. o`Ùk ds vUnj fLFkr fdlh fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh la[;k gS % 1

(A) 1 (B) 2

(C) 0 (D) buesa ls dksbZ ugha
Number of tangents drawn from a point inside the circle is :

(A) 1 (B) 2

(C) 0 (D) None of these

9. ,d o`Ùk dh fdruh Li'kZ js[kk,¡ gks ldrh gSa \ 1

(A) 1 (B) 2

(C) vifjfer :i ls vusd (D) 0

How many tangents can a circle have ?

(A) 1 (B) 2

(C) Infinitely many (D) 0

10. fcUnq Q(−3, –4) fdl prqFkk±'k esa fLFkr gS \ 1

(A) çFke (B) r`rh;
(C) f}rh; (D) prqFkZ
Point Q(−3, –4) lies in which quadrant ?

(A) First (B) Third

(C) Second (D) Fourth

11. fcUnqvksa (−5, 7) vkSj (5, –7) dks feykus okys js[kk[kaM ds e/; fcUnq ds funs'Z kkad gSa % 1

(A) (5, 7) (B) (0, 0)
(C) (0, 7) (D) (5, 0)

3503/(Set : B)

(7) 3503/(Set : B)
Coordinate of mid point of line joining two points (−5, 7) and (5, −7) are
:

(A) (5, 7) (B) (0, 0)
(C) (0, 7) (D) (5, 0)

12. crkb, fd fuEu dFku lR; gS ;k vlR; % 1

^^tan A dk eku lnSo −1 vkSj 1 ds chp gksrk gS**
State whether the following statement is true or false :

"The value of tan A is always lies in between −1 and 1"

13. crkb, fd fuEu dFku lR; gS ;k vlR; % 1

^^A = 0° ij cot A ifjHkkf"kr ugha gS**
State whether the following statement is true or false :

"cot A is not defined for A = 0°"
14. f=T;k r okys o`Ùk ds ml f=T;[kaM ds laxr pki dh yackbZ ftldk dks.k θ° gS] gksxh % 1
θ θ
(A) × πr 2 (B) × 2πr
360 360
θ
(C) × 2πr (D) buesa ls dksbZ ugha
180
Length of an arc of a sector of angle θ° of a circle with radius r will be :
θ θ
(A) × πr 2 (B) × 2πr
360 360
θ
(C) × 2πr (D) None of these
180

3503/(Set : B) P. T. O.

(8) 3503/(Set : B)
15. ,d 'kadq ds vk/kkj dh f=T;k 4 lseh vkSj fr;Zd Å¡pkbZ 5 lseh gS] rks mldk i`"Bh; {ks=Qy
gksxk % 1
20 lseh 20π lseh
2 2
(A) (B)

30π lseh 80π lseh
2 2
(C) (D)
The radius of the base of a cone is 4 cm and slant height is 5 cm. Its
CSA is :
2 2
(A) 20 cm (B) 20π cm
2 2
(C) 30π cm (D) 80π cm

16. ikls dks ,d ckj Qsadus ij] la[;k 6 vkus dh çkf;drk gksxh % 1
(A) 1 (B) 0
1
(C) (D) buesa ls dksbZ ugha
6
Probability of getting 6 in a single throw of a die is :
(A) 1 (B) 0
1
(C) (D) None of these
6

[k.M & c

SECTION – B

17. fl) dhft, fd 7 ,d vifjes; la[;k gSA 3

Prove that 7 is an irrational number.

18. ,d f}?kkr cgqin Kkr dhft, ftlds 'kwU;dksa ds ;ksx rFkk xq.kuQy Øe'k% 1 vkSj 4 gSaA3
4

3503/(Set : B)

(9) 3503/(Set : B)
Find a quadratic polynomial with the given number as the sum and
1
product of its zeroes respectively are and 4.
4

19. CM vkSj RN Øe'k% ∆ABC vkSj ∆PQR dh ekf/;dk,¡ gSa ;fn ∆ABC ~ ∆PQR gS] rks
fl) dhft, fd ∆AMC ~ ∆PNRA 3

CM and RN are respectively the medians of ∆ABC and ∆PQR. If ∆ABC ~
∆PQR, prove that ∆AMC ~ ∆PNR.

tan 65°
20. dk eku fudkfy,A 3
cot 25°
Find the value of :
tan 65°
cot 25°

21. ,d o`Ùkkdkj [ksr ftldk O;kl 10 ehVj gS dh 1.50 #0 çfr oxZ ehVj dh nj ls tqrkbZ
djkbZ tkuh gSA [ksr dh tqrkbZ djkus dk [kpkZ Kkr dhft,A 3
Find the cost of ploughing the circular field having diameter 10 meter
and rate of ploughing is Rs. 1.50 per square meter.

[k.M & l
SECTION – C

22. fuEufyf[kr lehdj.kksa dks gy dhft, % 4

3x − y = 3

x−y=4

3503/(Set : B) P. T. O.

( 10 ) 3503/(Set : B)
Solve the following equations :

3x − y = 3

x−y=4

23. ,slh nks la[;k,¡ Kkr dhft, ftudk ;ksx 27 gks vkSj xq.kuQy 182 gksA 4
Find two numbers whose sum is 27 and product is 182.

24. 10 vkSj 250 ds chp esa 4 ds fdrus xq.kt gSa \ 4

How many multiples of 4 lie between 10 and 250 ?

25. fl) dhft, fd nks ladsUæh; o`Ùkksa esa cM+s o`Ùk dh thok tks NksVs o`Ùk dks Li'kZ djrh gS] Li'kZ
fcanq ij lef}Hkkftr gksrh gSA 4

Prove that in two concentric circles, the chord of the larger circle, which
touches the smaller circle, is bisected at the point of contact.

26. rk'k ds 52 iÙkksa dks vPNh rjg ls QsaVh xbZ ,d xM~Mh esa ls ,d iÙkk fudkyk tkrk gSA
rLohj okyk iÙkk çkIr djus dh çkf;drk Kkr dhft,A 4

One card is drawn from a well-shuffled deck of 52 cards. Find the
probability of getting a face card.

27. k dk eku Kkr dhft,] ;fn fcanq A(8, 1), B(k, −4) vkSj C(2, −5) lajs[kh gksaA 4

Find the value of k, if the points A(8, 1), B(k, −4) and C(2, −5) are
collinear.

[k.M & n
SECTION – D

3503/(Set : B)

( 11 ) 3503/(Set : B)
28. D;k fuEu fLFkfr lEHko gS \ ;fn gS rks mudh orZeku vk;q Kkr dhft,A nks fe=ksa dh vk;q dk
;ksx 20 o"kZ gSA pkj o"kZ iwoZ mudh vk;q ¼o"kks± esa½ dk xq.kuQy 48 FkkA 5
Is the following situation possible ? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the
product of their ages in years was 48.

29. loZlfedk cosec 2 A − cot 2 A = 1 dk ç;ksx djds] fl) dhft, fd % 5
cos A − sin A + 1
= cos ec A + cot A
cos A + sin A − 1

cos A − sin A + 1
Prove that = cos ec A + cot A , using the identity
cos A + sin A − 1
cosec 2 A − cot 2 A = 1 .

vFkok
OR

,d unh ds iqy ds ,d fcUnq ls unh ds lEeq[k fdukjksa ds voueu dks.k Øe'k% 30° vkSj
45° gSA ;fn iqy fdukjksa ls 3 eh dh Å¡pkbZ ij gks] rks unh dh pkSM+kbZ Kkr dhft,A
From a point on a bridge across a river, the angles of depression of the
banks on opposite sides of the river are 30° and 45°, respectively. If the
bridge is at a height of 3 m from the banks, find the width of the river.

30. 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, x, f=Hkqt dh laxr Hkqtkvksa dh 2 xquh
3
gksA jpuk dk vkSfpR; Hkh nhft,A 5

3503/(Set : B) P. T. O.

( 12 ) 3503/(Set : B)
Construct triangle of sides 4 cm, 5 cm and 6 cm and then a triangle
2
similar to it whose sides are of the corresponding sides of the first
3
triangle. Give the justification of the construction also.

31. f=T;k 4.2 lseh okys /kkrq ds ,d xksys dks fi?kykdj f=T;k 6 lseh okys ,d csyu ds :i
 22 
esa <kyk tkrk gSA csyu dh Å¡pkbZ Kkr dhft,A π =  5
 7 

A metallic sphere of radius 4.2 cm is melted and recast into the shape of
 22 
a cylinder of radius 6 cm. Find the height of the cylinder. π = 
 7 

32. ,d ikS/ks dh 40 ifÙk;ksa dh yEckbZ fudVre feyhehVjksa esa ekih tkrh gS rFkk çkIr vk¡dM+ksa dks
fuEufyf[kr lkj.kh ds :i esa fu:fir fd;k tkrk gS % 5

yackbZ ¼feeh esa½ 117.5- 126.5- 135.5- 144.5- 153.5- 162.5- 171.5-
126.5 135.5 144.5 153.5 162.5 171.5 180.5

ifÙk;ksa dh la[;k 3 5 9 12 5 4 2

ifÙk;ksa dh ek/;d yEckbZ Kkr dhft,A
The lengths of 40 leaves of a plant are measured correct to the nearest
millimetre and the data obtained is represented in the following table :
Length 117.5- 126.5- 135.5- 144.5- 153.5- 162.5- 171.5-

(in mm) 126.5 135.5 144.5 153.5 162.5 171.5 180.5

Number of 3 5 9 12 5 4 2
Leaves

Find the median length of the leaves.

vFkok
OR

3503/(Set : B)

( 13 ) 3503/(Set : B)
fuEufyf[kr caVu ,d eksgYys ds cPpksa ds nSfud tsc [kpZ n'kkZrk gSA ek/; tsc [kpZ 18 #0
gSA yqIr ckjackjrk f Kkr dhft, %
nSfud tsc HkÙkk ¼#i;ksas es½a 11-13 13-15 15-17 17-19 19-21 21-23 23-25
cPpksa dh la[;k 7 6 9 13 f 5 4

The following distribution shows the daily pocket allowance of children
of a locality. The mean pocket allowance is Rs. 18. Find the missing
frequency f :

Daily Pocket Allowance 11-13 13-15 15-17 17-19 19-21 21-23 23-25
(in Rs.)

Number of Children 7 6 9 13 f 5 4

S

3503/(Set : B) P. T. O.