HBSE Class 10 Mathematics Question Paper 2018 Set D

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

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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 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 : D) P. T. O.

(2) 3503/(Set : D)
• 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 g vkSj l LCM vkSj HCF nks /kukRed iw.kk±dksa ds gSa] rks muesa lEcU/k gksxk % 1
(A) g>l (B) g<l
(C) g=l (D) buesa ls dksbZ ugha

3503/(Set : D)

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

2. buesa ls dkSu-lk cgqin (Polynomial) gS \ 1
2
(A) 1+ x (B) x +1
1 1
(C) (D)
x3 + x2 +1 x3
Which one is polynomial ?
(A) 1+ x (B) x2 +1
1 1
(C) (D)
x3 + x2 +1 x3
a1 b1
3. lehdj.kksa a1x + b1y + c1 = 0 vkSj a 2x + b2y + c 2 = 0 esa ;fn ≠ , rks
a 2 b2
fuEufyf[kr esa ls dkSu-lk lR; gS \ 1
(A) lekarj js[kk,¡ (B) çfrPNsfnr js[kk,¡
(C) laikrh js[kk,¡ (D) buesa ls dksbZ ugha
a1 b1
If in equations a1x + b1y + c1 = 0 and a 2 x + b2y + c 2 = 0 , ≠ , then
a 2 b2
which of the following is true ?
(A) Parallel lines (B) Intersecting lines
(C) Coincident lines (D) None of these

4. buesa ls dkSu-lh A. P. Js.kh gS \ 1

(A) a, a 2 , a 3 , …. (B) 12 , 32 , 5 2 , 7 2 ….
(C) 1, 3, 32 , 33 , …… (D) a, 2a, 3a, 4a, ……
Which one is an A. P. series ?
(A) a, a 2 , a 3 , …. (B) 12 , 32 , 5 2 , 7 2 ….
(C) 1, 3, 32 , 33 , …… (D) a, 2a, 3a, 4a, ……

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

(4) 3503/(Set : D)
5. A. P. 2, 7, 12, …. dk 20ok¡ in gS % 1

(A) −47 (B) 47

(C) 57 (D) 97

In an A. P. 2, 7, 12, …. 20th term is :

(A) −47 (B) 47

(C) 57 (D) 97

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

(A) 70°

80° C 80° 30°
B Q R

P
A
(B) 60°
60°

80° 40° C
B 80° 40° R
Q

A P

2 3 6 5
(C)
B C
2.5 Q R
4

L D

2.7 3 4 6

(D) M 2 N
E 9
F

3503/(Set : D)

(5) 3503/(Set : D)
Which one pair of the triangles is not similar triangles ?
P
A
(A) 70°

80° C 80° 30°
B Q R

P
A
(B) 60°
60°

80° 40° C
B 80° 40° R
Q

A P

(C) 2 3 6 5
B C
2.5 Q R
4

L D

2.7 3 4 6
(D) M 2 N
E 9
F

7. nks le:i f=Hkqtksa dh laxr ekf/;dkvksa dk vuqikr 4 : 9 gS] rks f=Hkqtksa ds {ks=Qyksa dk
vuqikr gS % 1

(A) 2:3 (B) 4:9

(C) 16 : 81 (D) 81 :16

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

(6) 3503/(Set : D)
Ratio of corresponding median of two similar triangles are 4 : 9. Then areas
of these triangles are in the ratio :
(A) 2:3 (B) 4:9
(C) 16 : 81 (D) 81 :16

8. o`Ùk ds Åij fLFkr fcUnq ls o`Ùk ij fdruh Li'kZ js[kk,¡ [khap ldrs gSa \ 1
(A) 1 (B) 2

(C) vifjfer :i ls vusd (D) buesa ls dksbZ ugha
How many tangents are drawn from a point on the circle ?

(A) 1 (B) 2

(C) Infinitely many (D) None of these

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

(A) 1 (B) 2

(C) 3 (D) buesa ls dksbZ ugha
How many parallel tangents are drawn on a circle at the most ?

(A) 1 (B) 2

(C) 3 (D) None of these

10. fcUnq P(−3, –4) fdl prqFkk±'k esa fLFkr gS \ 1
(A) çFke (B) f}rh;
(C) r`rh; (D) prqFkZ
Point P(−3, –4) lies in which quadrant ?
(A) First (B) Second
(C) Third (D) Fourth

3503/(Set : D)

(7) 3503/(Set : D)
11. ml fcUnq ds funsZ'kkad tks fcUnqvksa (−1, 7) vkSj (4, –3) dks feykus okys js[kk[kaM dks 2 : 3

ds vuqikr esa foHkkftr djrk gS % 1

(A) (1, 3) (B) (−1, 3)
(C) (1, −3) (D) (−1, −3)
Coordinates of point which divide the line joining two points (−1, 7) and
(4, –3) in the ratio 2 : 3 are :
(A) (1, 3) (B) (−1, 3)
(C) (1, −3) (D) (−1, −3)

12. crkb, fd fuEu dFku lR; gS ;k vlR; % 1
^^cosec θ dk eku ≥ 1 vkSj ≤ −1 gksrk gS**
State whether the following statement is true or false :
"The value of cosec θ lies ≥ 1 and ≤ −1"
13. crkb, fd fuEu dFku lR; gS ;k vlR; % 1

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

14. f=T;k r okys o`Ùk ds ml f=T;[kaM dk {ks=Qy ftldk dks.k P ° gS] gksxk % 1
P P
(A) × 2πr (B) × πr 2
180 180
P P
(C) × 2πr (D) × 2πr 2
360 720
Area of a sector of angle P ° of a circle with radius r will be :

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

(8) 3503/(Set : D)
P P
(A) × 2πr (B) × πr 2
180 180
P P
(C) × 2πr (D) × 2πr 2
360 720

15. ,d v/kZxksys dh f=T;k r lseh gS] rks mlds vk/kkj dk {ks=Qy gksxk % 1

(A) 2π r 2 (B) πr 2

(C) 2πr (D) 2π r 3

Base area of hemisphere having base radius r cm will be :

(A) 2π r 2 (B) πr 2

(C) 2πr (D) 2π r 3

16. ikls dks ,d ckj Qsadus ij] la[;k 7 vkus dh çkf;drk gksxh % 1
1 2
(A) (B) 1 (C) 0 (D)
6 3
Probability of getting 7 in a single throw of a die will be :
1 2
(A) (B) 1 (C) 0 (D)
6 3

[k.M & c

SECTION – B

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

Prove that 2 is an irrational number.

3503/(Set : D)

(9) 3503/(Set : D)
18. ,d f}?kkr cgqin Kkr dhft, ftlds 'kwU;dksa ds ;ksx rFkk xq.kuQy Øe'k% 5 vkSj 3 gSaA 3

Find a quadratic polynomial with the given number as the sum and
product of its zeroes respectively are 5 and 3.

19. ,d lh<+h fdlh nhokj ij bl çdkj fVdh gqbZ gS fd bldk fupyk fljk nhokj ls 2.5 eh dh
nwjh ij gS rFkk bldk Åijh fljk Hkwfe ls 6 eh dh Å¡pkbZ ij cuh ,d f[kM+dh rd igq¡prk
gSA lh<+h dh yEckbZ Kkr dhft,A 3

A ladder is placed against a wall such that its foot is at a distance of
2.5 m from the wall and its top reaches a window 6 m above the
ground. Find the length of the ladder.

20. cot 85° + cos 75° dks 0° vkSj 17° ds chp ds dks.kksa ds f=dks.kferh; vuqikrksa ds inksa esa
O;Dr dhft,A 3

Express cot 85° + cos 75° in terms of trigonometric ratios of angles
between 0° and 17°.

21. ,d o`Ùkkdkj [ksr dh 10 #0 çfr oxZ ehVj dh nj ls tqrkbZ dk [kpkZ 1,540 #0 gS] rks
 22 
[ksr dh f=T;k fudkfy,A π = 
 7 

3

Cost of ploughing at the rate of Rs. 10 per m2 is Rs. 1,540. Find the
radius of the circular field.
 22 
π = 
 7 

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

( 10 ) 3503/(Set : D)
[k.M & l
SECTION – C

22. fuEufyf[kr lehdj.kksa dks gy dhft, % 4
2x+ 3y=0
3x− 8y=0

Solve the following equations :
2x+ 3y=0

3x− 8y=0

23. xq.ku[k.M fof/k ls f}?kkr lehdj.k 2x 2 + 7x + 5 2 = 0 ds ewy Kkr dhft,A 4
Find the root of the quadratic equation by factorization method
2x 2 + 7x + 5 2 = 0 .

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

How many two-digit numbers are divisible by 4 ?

25. 5 lseh f=T;k ds o`Ùk dh 8 lseh yEch ,d thok PQ gSA P vkSjQ ij Li'kZ js[kk,¡
ijLij ,d fcUnq T ij çfrPNsn djrh gSA TP dh yEckbZ Kkr dhft,] ;fn o`Ùk dk dsUæ O gSA
4
PQ is a chord of length 8 cm of a circle of radius 5 cm. Tangents at P
and Q intersect at a point T. Find the length TP, if O is the centre of a
circle.

26. rk'k ds 52 iÙkksa dh vPNh rjg ls QsaVh xbZ ,d xM~Mh esa ls ,d iÙkk fudkyk tkrk gSA rks
b±V dh csxe 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 the queen of diamonds.

3503/(Set : D)

( 11 ) 3503/(Set : D)
27. ml f=Hkqt dk {ks=Qy Kkr dhft, ftlds 'kh"kZ (−1.5, 3), (6, −2) vkSj (−3, 4) gSaA 4

Find the area of a triangle whose vertices are (−1.5, 3), (6, −2) and (−3,
4).

[k.M & n
SECTION – D

28. f}?kkr lehdj.k 2x 2 + kx + 3 = 0 esa k dk eku Kkr dhft, fd mlds nks cjkcj ewy gksaA
5

Find the value of k for the quadratic equation 2x 2 + kx + 3 = 0 so that
they have two equal roots.

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

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

vFkok
OR

1.5 eh0 yack ,d vkneh ,d fpeuh ls 28.5 eh dh nwjh ij gSA mldh vk¡[kksa ls fpeuh ds
f'k[kj dk mUu;u dks.k 45° gSA fpeuh dh Å¡pkbZ crkb,A

A man 1.5 m tall is 28.5 m away from a Chimney. The angle of
elevation of the top of the Chimney from her eyes is 45°. What is the
height of the Chimney ?

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

( 12 ) 3503/(Set : D)
30. ,d f=Hkqt ABC cukb, ftlesa BC = 7 lseh] ∠B = 45°, ∠A = 105° gksA fQj ,d
vU; f=Hkqt dh jpuk dhft, ftldh Hkqtk,¡ ∆ABC dh laxr Hkqtkvksa dh 4 xquh gksA jpuk
3
dk vkSfpR; Hkh nhft,A 5

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°,
4
then construct a triangle whose sides are times the corresponding
3
sides of ∆ABC. Give the justification of the construction also.

31. Øe'k% 6 lseh] 8 lseh vkSj 10 lseh f=T;kvksa okys /kkrq ds rhu Bksl xksyksa dks fi?kykdj ,d
cM+k Bksl xksyk cuk;k x;k gSA bl xksys dh f=T;k Kkr dhft,A5
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted
to form a single solid sphere. Find the radius of the resulting sphere.

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

Hkkj ¼fdyksxzke es½a 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 weights 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

3503/(Set : D)

( 13 ) 3503/(Set : D)
vFkok
OR

fuEufyf[kr lkj.kh 35 uxjksa dh lk{kjrk nj ¼çfr'kr esa½ n'kkZrh gSA ek/; lk{kjrk nj Kkr
dhft, %
lk{kjrk nj ¼% esa½ 45-55 55-65 65-75 75-85 85-95

uxjksa dh la[;k 3 10 11 8 3

The following table gives the literacy rate (in percentage) of 35
cities. Find the mean literacy rate :

Literacy rate (in %) 45-55 55-65 65-75 75-85 85-95

Number of cities 3 10 11 8 3

S

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