HBSE Class 10 Question Paper 2018 Maths

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

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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.
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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 : A) P. T. O.

(2) 3503/(Set : A)
• 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. 12 vkSj 20 ds HCF vkSj LCM esa lEcU/k gksxk % 1
(A) HCF > LCM (B) HCF < LCM
(C) HCF = LCM (D) buesa ls dksbZ ugha

3503/(Set : A)

(3) 3503/(Set : A)
The relation between HCF and LCM of 12 and 20 will be :
(A) HCF > LCM (B) HCF < LCM
(C) HCF = LCM (D) None of these

2. buesa ls dkSu-lk cgqin (Polynomial) gS \ 1
1
(A) (B) x +2
x +1
1
(C) (D) x3 +1
2
x + 2x + 7
Which one is polynomial ?
1
(A) (B) x +2
x +1
1
(C) (D) x3 +1
2
x + 2x + 7

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) çfrPNsn djrh gqbZ 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 , = ≠ ,
a2 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 : A) P. T. O.

(4) 3503/(Set : A)
5. A. P. 10, 7, 4, …. dk 30ok¡ in gS % 1
(A) 97 (B) 77
(C) −77 (D) buesa ls dksbZ ugha
In an A. P. 10, 7, 4, …., 30th term is :
(A) 97 (B) 77
(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
2 3 5

B C Q R
2.5 4

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

M
P
(D) 2.5 70° 5
5
N L 70°
Q R
10

Which one pair of the triangulars is not similar triangles ?
(A) A P

60° 60°

3503/(Set : A)B 80° 40° C 80° 40°
Q R

P
A

2 6 5
3

B C Q R
2.5 4

L D

2.7 3 4 6
M P
2 E F

(5) 3503/(Set : A)

(B)

(C)

(D)

7. nks le:i f=Hkqtksa ds {ks=Qyksa dk vuqikr 5 : 3 gS] rks mudh laxr Hkqtkvksa dk vuqikr gS %
1
(A) 5 : 3 (B) 25 : 9
(C) 9 : 25 (D) 5 : 3
Area of two similar triangles are in the ratio of 5 : 3, then the ratio of their
corresponding sides is :
(A) 5 : 3 (B) 25 : 9
(C) 9 : 25 (D) 5: 3

8. o`Ùk ds ckgj fLFkr fdlh fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh la[;k gSa % 1
(A) 1 (B) 2

(C) 0 (D) 4

Number of tangents drawn from a point outside the circle are :

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

(6) 3503/(Set : A)
(A) 1 (B) 2

(C) 0 (D) 4

9. fjDr LFkku Hkjsa % 1

,d o`Ùk dh ------------ lekarj Li'kZ js[kk,¡ gks ldrh gSaA
Fill in the blank :

A circle can have ……….. parallel tangents at the most.

10. fcUnq P(6, – 4) fdl prqFkk±'k esa fLFkr gS \ 1

(A) çFke (B) f}rh;
(C) r`rh; (D) prqFkZ
Point P(6, – 4) lies in which quadrant ?

(A) First (B) Second

(C) Third (D) Fourth

11. fcUnqvksa (−1, 7) vkSj (4, –3) dks feykus okys js[kk[kaM ds e/; fcUnq ds funs'Z kkad gSa % 1

 3  3 
(A)  − , 2 (B)  , 2
 2  2 
3   3
(C)  , − 2 (D)  2, 
2   2
Coordinate of mid point of line joining two points (−1, 7) and (4, −3) are
:

 3  3 
(A)  − , 2 (B)  , 2
 2  2 

3503/(Set : A)

(7) 3503/(Set : A)
3   3
(C)  , − 2 (D)  2, 
2   2

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

^^fdlh Hkh dks.k θ ds fy, cos θ = 3 **
2
State whether the following statement is true or false %
3
" cos θ = for some angle θ"
2

13. crkb, fd fuEu dFku lR; gS ;k vlR; % 1
^^sin θ = cos θ lHkh θ ds ekuksa ij**
State whether the following statement is true or false :
"sin θ = cos θ for all values of θ"
14. f=T;k R okys o`Ùk ds ml f=T;[kaM dk {ks=Qy ftldk dks.k θ° gS] gksxk %1
θ θ
(A) × 2πR (B) × πR 2
180 180
θ θ
(C) × 2πR (D) × πR 2
360 360
Area of a sector of angle θ° of a circle with radius R will be :
θ θ
(A) × 2πR (B) × πR 2
180 180
θ θ
(C) × 2πR (D) × πR 2
360 360

15. ,d 'kadq ds vk/kkj dh f=T;k 4 lseh vkSj Å¡pkbZ 3 lseh gS] rks mldk i`"Bh; {ks=Qy gksxk %
 22 
π =  1
 7 

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

(8) 3503/(Set : A)
20 lseh 20π lseh
2 2
(A) (B)

30π lseh buesa ls dksbZ ugha
2
(C) (D)
The radius of the base of a cone is 4 cm and the height is 3 cm. Its
 22 
CSA is  π =  :
 7 

2 2
(A) 20 cm (B) 20π cm
2
(C) 30π cm (D) None of these
16. ikls dks ,d ckj Qsadus ij] la[;k 8 vkus dh çkf;drk gksxh % 1
1 1
(A) 1 (B) 0 (C)(D)
6 2
Probability of getting 8 in a single throw of a die is :
1 1
(A) 1 (B) 0 (C) (D)
6 2

[k.M & c

SECTION – B

17. fl) dhft, fd 5 ,d vifjes; la[;k gSA 3

Prove that 5 is an irrational number.

18. ,d f}?kkr cgqin Kkr dhft, ftlds 'kwU;dksa ds ;ksx rFkk xq.kuQy Øe'k% 1 vkSj −1 gSaA
4
3

Find a quadratic polynomial with the given number as the sum and
1
product of its zeroes respectively are and –1.
4

3503/(Set : A)

(9) 3503/(Set : A)
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. ;fn A, B vkSj C f=Hkqt ABC ds var%dks.k gks]a rks fn[kkb, fd %
3
B +C  A
sin  = cos
 2  2
If A, B and C are interior angles of a triangle ABC, then show that :
B +C  A
sin  = cos
 2  2

21. ,d o`Ùkkdkj [ksr ij 25 #0 çfr ehVj dh nj ls ckM+ yxkus dk [kpkZ 5,275 #0 gS] rks
[ksr dk O;kl fudkfy,A 3

The cost of fencing a circular field at the rate of Rs. 25 per meter is, Rs.
5,275. Find the diameter of the field.

[k.M & l
SECTION – C

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

0.2x + 0.3y = 1.3

0.4x + 0.5y = 2.3

Solve the following equations :

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

( 10 ) 3503/(Set : A)
0.2x + 0.3y = 1.3

0.4x + 0.5y = 2.3

23. nks Øekxr /kukRed iw.kk±d Kkr dhft, ftuds oxks± dk ;ksx 365 gksA 4

Find two consecutive positive integers, sum of whose squares is 365.

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

How many three digit numbers are divisible by 7 ?

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 that point of contact.

26. rk'k ds 52 iÙkksa dks vPNh rjg ls QasVh xbZ ,d xM~Mh esa ls ,d iÙkk fudkyk tkrk gSA yky
jax dk ckn'kkg 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 king of red colour.

27. k dk eku Kkr dhft,] ;fn fcanq A(2, 3), B(4, k) vkSj C(6, −3) lajs[kh gSaA 4

Find the value of k if the points A(2, 3), B(4, k) and C(6, −3) are
collinear.

[k.M & n
SECTION – D

28. D;k ,d ,slh vk;rkdkj vke dh cfx;k cukuk laHko gS ftldh yEckbZ] pkSM+kbZ ls nqxquh gks
vkSj mldk {ks=Qy 800 eh2 gks] rks mldh yEckbZ vkSj pkSM+kbZ Kkr dhft,A 5
3503/(Set : A)

( 11 ) 3503/(Set : A)
Is it possible to design a rectangular mango grove whose length is twice
2
its breadth and area is 800 m ? If so, find its length and breadth.

29. loZlfedk sec 2 θ − tan2 θ = 1 dk ç;ksx djds] fl) dhft, fd % 5

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

sin θ + cos θ − 1 1
Prove that = , using the identity
sin θ − cos θ + 1 sec θ + tan θ
sec 2 θ − tan2 θ = 1 .

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.

30. 7.6 lseh yack ,d js[kk[kaM [khafp, vkSj bls 5 : 8 vuqikr esa foHkkftr dhft,A nksuksa Hkkxksa dks
ekfi, vkSj jpuk dk vkSfpR; Hkh nhft,A 5
Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8.
Measure the two parts. Give the justification of the construction also.

31. foekvksa 5.5 lseh × 10 lseh × 3.5 lseh okyk ,d ?kukHk cukus ds fy, 1.75 lseh O;kl
vkSj 2 feeh eksVkbZ okys fdrus pk¡nh ds flDdksa dks fi?kykuk iM+sxk \ 5

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

( 12 ) 3503/(Set : A)
How many silver coins 1.75 cm in diameter and of thickness 2 mm must
be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm ?

32. fdlh Ldwy dh d{kk X dh 51 yM+fd;ksa dh Å¡pkb;ksa dk ,d losZ{k.k fd;k x;k vkSj
fuEufyf[kr vk¡dMs+ çkIr fd, x, % 5

Å¡pkbZ ¼lseh esa½ 140 ls 145 ls 150 ls 155 ls 160 ls 165 ls
de de de de de de
yM+fd;ksa dh la[;k 4 11 29 40 46 51

ek/;d Å¡pkbZ Kkr dhft,A
A survey regarding the heights (in cm) of 51 girls of class X of a school
was conducted and the following data was :

Obtained height Less Less Less Less Less Less

(in cm) than140 than145 than150 than155 than160 than165

Number of girls 4 11 29 40 46 51

Find the median height.

vFkok
OR

fuEufyf[kr lkj.kh fdlh eksgYys ds 25 ifjokjksa esa Hkkstu ij gq, nSfud O;; dks n'kkZrh gS %
nSfud O;; ¼#i;s es½a 100-150 150-200 200-250 250-300 300-350
ifjokjksa dh la[;k 4 5 12 2 2

mi;qDr fof/k }kjk Hkkstu ij gqvk ek/; O;; Kkr dhft,A
The table below shows daily expenditure on food of 25 households in a
locality :

3503/(Set : A)

( 13 ) 3503/(Set : A)
Daily Expenditure (in Rs.) 100-150 150-200 200-250 250-300 300-350

No. of households 4 5 12 2 2

Find the mean daily expenditure on food by suitable method.

S

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