HBSE Class 10 Question Paper 2017 Maths

CLASS : 10th (Secondary) Code No. 1903
Series : Sec. M/2017
Roll No. SET : A
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh Candidates)
(Morning Session)
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 this question paper are 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.
• 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

1903/(Set : A) P. T. O.

(2) 1903/(Set : A)
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 :
[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.

1903/(Set : A)

(3) 1903/(Set : A)
[k.M & v
SECTION – A

1. ;fn 306 vkSj 657 dk HCF 9 gS] rks mldk LCM gS % 1
(A) 2482 (B) 22338
(C) 2754 (D) 5913

If HCF of 306 and 657 is 9, then its LCM is :
(A) 2482 (B) 22338
(C) 2754 (D) 5913

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

a1 b1 c1
3. lehdj.kksa a1x + b1y + c1 = 0 vkSj a 2x + b2y + c 2 = 0 esa = = , rks
a 2 b2 c 2
fuEufyf[kr esa dkSu-lk lR; gS \ 1
(A) vf}rh; gy (B) dksbZ gy ugha
(C) vifjfer gy (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 ?

1903/(Set : A) P. T. O.

(4) 1903/(Set : A)
(A) Unique solution (B) No solution

(C) Infinite solutions (D) None of these

1 5 9 13
4. A. P. , , , ……… dk 15ok¡ in gS % 1
3 3 3 3

61
(A) (B) 6
3

(C) 5 (D) 19

1 5 9 13
15th term of A. P. , , , is :
3 3 3 3

61
(A) (B) 6
3

(C) 5 (D) 19

5. ;fn A. P. dk rhljk in 5 vkSj 7ok¡ in 13 gS] rks mldk lkoZ varj (common
difference) gS % 1

(A) 1 (B) 2

(C) 3 (D) 4

If 3rd term of an A. P. is 5 and 7th term is 13, then its common
difference is :

(A) 1 (B) 2

(C) 3 (D) 4

6. nh xbZ vkÑfr esa ∆ODC ~ ∆OAB, ∠BOC = 100°, ∠ODC = 60°, rks
∠OAB dk eku gS % 1

1903/(Set : A)

D C (5) 1903/(Set : A)
60°
O 100°

A B
(A) 20° (B) 80°
(C) 60° (D) 40°
In the given figure ∆ODC ~ ∆OAB, ∠BOC = 100°, ∠ODC = 60°,
then ∠OAB is equal to :

D C
60°
O 100°

A B

(A) 20° (B) 80°
(C) 60° (D) 40°

7. ;fn nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 2 : 3 gS] rks muds {ks=Qyksa dk vuqikr gS %
1
(A) 2: 3 (B) 2:3
(C) 4:9 (D) bues ls dksbZ ugha
If ratio of the sides of two similar, triangles is 2 : 3, then the ratio of
their areas is :
(A) 2: 3 (B) 2:3
(C) 4:9 (D) None of these

8. ;fn fdlh fcUnq P ls o`Ùk ds Åij [khaph xbZ] Li'kZ js[kk dh yEckbZ 24 lseh gS vkSj fcUnq dh
dsUnz ls nwjh 25 lseh gS] rks o`Ùk dh f=T;k dh yEckbZ gS % 1
(A) 12 lseh (B) 12.5 lseh
(C) 1 lseh (D) 7 lseh

1903/(Set : A) P. T. O.

(6) 1903/(Set : A)
From a point P, the length of tangent to a circle is 24 cm and distance
of P from the centre is 25 cm. The radius of the circle is :
(A) 12 cm (B) 12.5 cm
(C) 1 cm (D) 7 cm

9. ,d o`Ùk ij lekarj Li'kZ js[kkvksa dh vf/kdre la[;k gS % 1
(A) 1 (B) 2
(C) 3 (D) 4
The maximum number of parallel tangents to a circle is :
(A) 1 (B) 2
(C) 3 (D) 4

10. ewy fcUnq ls (5, –7) dh nwjh gS % 1

(A) 74 (B) –2
(C) 2 (D) 12
The distance of point (5, –7) from origin is :
(A) 74 (B) –2
(C) 2 (D) 12

11. f=Hkqt ftlds 'kh"kZ (1, –1), (–4, 6) vkSj (–3, –5) gS] mldk {ks=Qy gS % 1

43
(A) (B) 8
2
(C) 24 (D) buesa ls dksbZ ugha
The area of triangle whose vertices are (1, –1), (–4, 6) and (–3, –5)
is :

43
(A) (B) 8
2

1903/(Set : A)

(7) 1903/(Set : A)
(C) 24 (D) None of these

12. ;fn tan A = 5 , rks cos A dk eku gS % 1
12
5 12 13 12
(A) (B) (C) (D)
13 5 5 13

5
If tan A = , then the value of cos A is :
12
5 12 13 12
(A) (B) (C) (D)
13 5 5 13

1 − tan2 30
13. dk eku gS % 1
1 + tan2 30
(A) cos 60° (B) tan 60°
(C) sin 60° (D) tan 30°

1 − tan2 30
The value of is :
1 + tan2 30
(A) cos 60° (B) tan 60°
(C) sin 60° (D) tan 30°

14. o`Ùk dh ifjf/k vkSj O;kl dk vuqikr gS % 1
(A) 2π : 1 (B) π:1
(C) 1:1 (D) buesa ls dksbZ ugha
The ratio of circumference and diameter of a circle is :

(A) 2π : 1 (B) π:1

(C) 1:1 (D) None of these

1903/(Set : A) P. T. O.

(8) 1903/(Set : A)
 22 
15. ,d 'kadq ds vk/kkj dh f=T;k 7 lseh vkSj Å¡pkbZ 6 lseh gS] rks mldk vk;ru gS  π = 
 7 
% 1

924 lseh 308 lseh
3 3
(A) (B)

1232 lseh buesa ls dksbZ ugha
3
(C) (D)

The radius of the base of a cone is 7 cm and the height is 6 cm. Its
 22 
volume is  π =  :
 7 

(A) 924 cm3 (B) 308 cm3

(C) 1232 cm3 (D) None of these

16. ;fn P(E) = 0.05, rks P (E ugha) gS % 1

(A) 0.05 (B) 0.5

(C) 0.95 (D) buesa ls dksbZ ugha
If P(E) = 0.05, then the P (not E) is :

(A) 0.05 (B) 0.5

(C) 0.95 (D) None of these

[k.M & c
SECTION – B

17. fl) dhft, fd 6 + 2 ,d vifjes; la[;k gSA 3

Prove that 6 + 2 is an irrational number.

18. ,d f}?kkr cgqin Kkr dhft, ftlds 'kwU;d –4 vkSj 2 gksaA 3

1903/(Set : A)

(9) 1903/(Set : A)
Find a quadratic polynomial whose zeros are –4 and 2.

19. nks [kaHks ftldh Å¡pkb;k¡ 7 eh vkSj 12 eh gS ,d lery Hkwfe ij [kM+s gSa ;fn buds fupys
fljksa ds chp dh nwjh 12 eh gS] rks buds Åijh fljksa ds chp dh nwjh Kkr dhft,A 3
Two poles of heights 7 m and 12 m stand on a plane ground. If the
distance between the feet of the poles be 12 m, then find the distance
between their tops.

20. ;fn tan (A + B) = 3 vkSj tan (A – B) = 1 , 0° < A + B ≤ 90°, A
3
> B, rks A vkSj B dk eku Kkr dhft,A 3
1
If tan (A + B) = 3 and tan (A – B) = , 0° < A + B ≤ 90°,
3
A > B, then find the value of A and B.

21. 4 lseh f=T;k okys ,d o`Ùk ds f=T;k[kaM (sector) dk {ks=Qy Kkr dhft, ftldk dsUnz ij
dks.k 45° gksA (π = 3.14) 3
Find the area of the sector of a circle with radius 4 cm and the angle
at the centre is 45°. (π = 3.14)

[k.M & l
SECTION – C

22. fuEufyf[kr lehdj.kksa dks gy dhft, % 4
3x 5y
− = −2
2 3
x y 13
+ =
3 2 6

Solve the following equations :

1903/(Set : A) P. T. O.

( 10 ) 1903/(Set : A)
3x 5y
− = −2
2 3
x y 13
+ =
3 2 6
23. ,d ledks.k f=Hkqt dh ledks.k cukus okyh ,d Hkqtk nwljh ls 17 lseh de gSA ;fn d.kZ dh
yEckbZ 25 lseh gS] rks nksuksa Hkqtkvksa dh yEckbZ Kkr dhft,A 4

The side of a right angle triangle is 17 cm less than the other side. If
length of hypoteneuse is 25 cm, find the length of sides.

24. ,d A. P. ds igys 7 inksa dk ;ksx 49 vkSj igys 17 inksa dk ;ksx 289 gS] rks ml A. P.
ds n inksa dk ;ksx Kkr dhft,A 4

If the sum of first 7 terms of A. P. is 49 and sum of first 17 terms is
289, then find the sum of n terms of A. P.

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. ,d ckWDl esa 5 yky] 8 lQsn vkSj 4 gjh xsansa gSaA ,d xsan ckWDl esa ls fcuk ns[ks fudkyh
tkrh gSA bl xsan ds yky gksus dh izkf;drk Kkr dhft,A bl xsan ds gjh u gksus dh Hkh
izkf;drk Kkr dhft,A 4

A box contains 5 red, 8 white and 4 green balls. A ball is drawn at
random. Find the probability of getting a red ball. Also find the
probability that the ball is not green.

1903/(Set : A)

( 11 ) 1903/(Set : A)
27. (5, –6) vkSj (–1, –4) dks feykus okyh js[kk dks y-v{k fdl vuqikr esa foHkkftr djrk gS

\ foHkkftr djus okys fcUnq ds funsZ'kkad Hkh Kkr dhft,A 4

Find the ratio in which the line joining (5, –6) and (–1, –4) is divided by
y-axis. Also find the coordinates of the point of intersection.

[k.M & n
SECTION – D

28. ,d jsyxkM+h ,dleku pky ls 360 fdeh pyrh gSA ;fn mldh pky 5 fdeh/?k.Vk vf/kd
gks] rks mls bruh nwj tkus esa 1 ?kaVk de yxrk gS \ xkM+h dh pky Kkr dhft,A 5

A train travels 360 km at a uniform speed. If the speed had been 5
km/hour more, it would have taken 1 hour less for the same journey.
Find the speed of the train.

29. fl) dhft, % 5

1 + sec A sin2 A
=
sec A 1 − cos A

Prove that :

1 + sec A sin2 A
=
sec A 1 − cos A

vFkok
OR

1903/(Set : A) P. T. O.

( 12 ) 1903/(Set : A)
,d lery tehu ij [kM+h ehukj dh Nk;k ml fLFkfr esa 40 eh vf/kd yEch

gks tkrh gS tcfd lw;Z dk mUu;u dks.k 60° ls ?kVdj 30° gks tkrk gSA ehukj dh Å¡pkbZ
Kkr dhft,A

The shadow of a tower standing on a level ground is found to be 40 m
longer when the altitude (the angle of elevation) of sun changes from
60° to 30°. Find the height of tower.

30. ,d f=Hkqt dh jpuk dhft, ftldh nks Hkqtk,¡ 6 lseh vkSj 5 lseh gksa vkSj muds chp dk dks.k
60° gks, bl f=Hkqt ds le:i nwljs f=Hkqt dh jpuk dhft,] ftldh Hkqtk,¡ bl f=Hkqt dh

3
gksaA 5
4

Draw a triangle whose two sides are 6 cm and 5 cm and the angle
3
between them is 60°, construct another triangle whose sides are of
4
the corresponding sides of first triangle.

31. f=T;k 4.2 lseh okys /kkrq ds ,d xksys dks fi?kykdj 6 lseh f=T;k okys ,d 'kadq ds :i esa
<kyk tkrk gSA 'kadq dh Å¡pkbZ Kkr dhft,A 5

A metallic sphere of radius 4.2 cm is melted and recast into a shape of
cone of radius 6 cm. Find the height of the cone.

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 ¼fdyksxzke esa½ 40-45 45-50 50-55 55-60 60-65 65-70 70-75

1903/(Set : A)

( 13 ) 1903/(Set : A)
fo|kfFkZ;ksa dh la[;k 2 3 8 6 6 3 2

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

No. of Students 2 3 8 6 6 3 2

vFkok
OR

fdlh eksgYys ds 25 ifjokjksa dk Hkkstu ij O;; fuEufyf[kr gSA Hkkstu ij gqvk ek/; O;;
Kkr dhft, %

[kpZ ¼#i;s esa½ 100-150 150-200 200-250 250-300 300-350

ifjokjksa dh la[;k 4 5 12 2 2

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

S
1903/(Set : A) P. T. O.