HBSE Class 10 Mathematics Question Paper 2017 Set D

CLASS : 10th (Secondary) Code No. 1903
Series : Sec. M/2017
Roll No. SET : D
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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 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 : D) P. T. O.

(2) 1903/(Set : D)
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 : D)

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

1. ;fn 124 vkSj 148 dk HCF 4 gS] rks mudk LCM gS % 1
(A) 1147 (B) 18352
(C) 4588 (D) buesa ls dksbZ ugha
If HCF of 124 and 148 is 4, then their LCM is :
(A) 1147 (B) 18352
(C) 4588 (D) None of these

2. 3x 2 + 1 + 4x ds 'kwU;d gSa % 1
1 1
(A) 1, (B) 1,−
3 3
1 1
(C) − 1, (D) − 1,−
3 3
The zeros of 3x 2 + 1 + 4x are :
1 1
(A) 1, (B) 1,−
3 3
1 1
(C) − 1, (D) − 1,−
3 3

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) vf}rh; gy (B) vifjfer gy
(C) dksbZ gy ugha (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 : D) P. T. O.

(4) 1903/(Set : D)
(A) Unique solution (B) Infinite solutions
(C) No solution (D) None of these
1 1
4. A. P. 5, 6 , 8, 9 , ……… dk 15ok¡ in gS % 1
2 2
1 1
(A) 15 (B) 14
2 2
1
(C) 26 (D) 27
2
1 1
15th term of A. P. 5, 6 , 8, 9 , ……… is :
2 2
1 1
(A) 15 (B) 14
2 2
1
(C) 26 (D) 27
2

5. ;fn ,d A. P. dk rhljk in 12 vkSj 10ok¡ in 26 gS] rks mldk 20ok¡ in gS % 1
(A) 46 (B) 52
(C) 50 (D) 44
If the third term of an A. P. is 12 and 10th term is 26, then its 20th
term is :
(A) 46 (B) 52
(C) 50 (D) 44

6. nh xbZ vkÑfr esa DE || BC, rks EC dk eku gS % 1
A
1.5 lseh 1.2 lseh

D E
3 lseh
B C

(A) 2.7 lseh (B) 1.5 lseh

1903/(Set : D)

(5) 1903/(Set : D)
(C) 2.4 lseh (D) 3 lseh

In the given figure DE || BC, then the value of EC is :
A
1.5 cm 1.2 cm

D E
3 cm
B C
(A) 2.7 cm (B) 1.5 cm
(C) 2.4 cm (D) 3 cm

7. nks le:i f=Hkqtksa ds {ks=Qyksa dk vuqikr 5 : 3 gS] rks mldh laxr Hkqtkvksa dk vuqikr gS %
1
(A) 5:3 (B) 3:5
(C) 5: 3 (D) 3: 5

Areas of two similar triangles are in the ratio of 5 : 3, then the ratio of
their corresponding sides is :
(A) 5:3 (B) 3:5
(C) 5: 3 (D) 3: 5

8. ,d fcUnq A ls tks o`Ùk ds dsUnz ls 5 lseh dh nwjh ij gS o`Ùk dh Li'kZ js[kk dh yEckbZ 4
lseh gSA o`Ùk dh f=T;k dh yEckbZ gS % 1
(A) 3 lseh (B) 4 lseh
(C) 5 lseh (D) 8 lseh
The length of tangent from a point A at distance 5 cm from the centre of
circle is 4 cm. The radius of the circle is :
(A) 3 cm (B) 4 cm
(C) 5 cm (D) 8 cm

9. o`Ùk ds vUnj fLFkr fdlh fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh la[;k gS % 1

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

(6) 1903/(Set : D)
(A) 1 (B) 2
(C) 4 (D) 0
Number of tangents drawn from a point inside the circle is :
(A) 1 (B) 2
(C) 4 (D) 0

10. fcUnq (3, –4) dh ewy fcUnq ls nwjh gS % 1
(A) –1 (B) 1
(C) 5 (D) 7

The distance of point (3, –4) from origin is :
(A) –1 (B) 1
(C) 5 (D) 7

11. (2, 3), (–1, 0) vkSj (2, –4) dks feykus ls cuus okys f=Hkqt dk {ks=Qy gS % 1
(A) 21 (B) 10.5
(C) 0 (D) buesa ls dksbZ ugha
The area of triangle formed by the joining (2, 3), (–1, 0) and (2, –4) is :
(A) 21 (B) 10.5
(C) 0 (D) None of these

12. ;fn cot A = 7 , rks sin A dk eku gS % 1
24
24 24
(A) (B)
7 25
25 7
(C) (D)
24 25

7
If cot A = , then the value of sin A is :
24

1903/(Set : D)

(7) 1903/(Set : D)
24 24
(A) (B)
7 25
25 7
(C) (D)
24 25

13. 3 sin 30° − 4 sin3 30° dk eku gS % 1
(A) sin 60° (B) sin 90°
(C) 0 (D) buesa ls dksbZ ugha
The value of 3 sin 30° − 4 sin3 30° is :

(A) sin 60° (B) sin 90°

(C) 0 (D) None of these

14. o`Ùk ds O;kl vkSj ifjf/k dk vuqikr gS % 1

(A) 2π : 1 (B) 1 : 2π

(C) 1:π (D) π:1

The ratio of the diameter is to circumference is :

(A) 2π : 1 (B) 1 : 2π

(C) 1:π (D) π:1

15. ,d csyu ds vk/kkj dh f=T;k 2.1 lseh vkSj Å¡pkbZ 5 lseh gS] rks mldk vk;ru gS % 1

(A) 22.05 π (B) 7.35 π

(C) 21 π (D) buesa ls dksbZ ugha
The radius of the base of a cylinder is 2.1 cm and height 5 cm, then its
volume is :

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

(8) 1903/(Set : D)
(A) 22.05 π (B) 7.35 π

(C) 21 π (D) None of these

16. ;fn P(A ugha) = 0.04 rks P(A) dk eku gS % 1
(A) 0.04 (B) 0
(C) 0.96 (D) 0.6
If P (not A) = 0.04 then P (A) is :
(A) 0.04 (B) 0
(C) 0.96 (D) 0.6
[k.M & c
SECTION – B

17. fl) dhft, fd 3 + 2 5 ,d vifjes; la[;k gSA 3

Prove that 3 + 2 5 is an irrational number.

18. ,d f}?kkr cgqin Kkr dhft, ftlds 'kwU;d 3 vkSj –2 gksaA 3
Find a quadratic polynomial whose zeros are 3 and –2.

19. 10 eh yEch ,d lh<+h nhokj ds lgkjs bl izdkj [kM+h gS fd og 8 eh Å¡ph ,d f[kM+dh
rd igq¡prh gSA lh<+h ds fupys fljs dh nhokj ls nwjh Kkr dhft,A 3
A ladder 10 m long reaches a window 8 m above the ground. Find the
foot distance of the foot of the ladder from the wall.

20. ;fn tan 2A = cot (A – 18°), tgk¡ 2A ,d U;wudks.k gS] rks A dk eku Kkr dhft,A 3
If tan 2A = cot (A – 18°), where 2A is an acute angle, then find the value
of A.

21. 6 lseh f=T;k vkSj 60° dks.k okys o`Ùk ds f=T;k[kaM dk {ks=Qy Kkr dhft,A 3
Find the area of a sector of a circle with radius 6 cm and angle of
sector 60°.

1903/(Set : D)

(9) 1903/(Set : D)
[k.M & l
SECTION – C

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

2x 3y
− = −2
3 2
x 4y 25
+ =
2 3 3

Solve the following equations :

2x 3y
− = −2
3 2
x 4y 25
+ =
2 3 3

23. ,d vk;rkdkj [ksr dk {ks=Qy 528 eh2 gSA ;fn [ksr dh yEckbZ pkSM+kbZ ds nqxqus ls 1 eh
vf/kd gS] rks [ksr dh yEckbZ vkSj pkSM+kbZ Kkr dhft,A 4

The area of a rectangular plot is 528 m2. The length of the plot is one
meter more than twice its breadth. Find the length and breadth of the
plot.

24. ;fn A. P. ds igys 10 inksa dk ;ksx –60 vkSj igys 15 inksa dk ;ksx –165 gS] rks mlds
igys n inksa dk ;ksx Kkr dhft,A 4

If the sum of first 10 terms of an A. P. is –60 and sum of first 15 terms
is –165, then find the sum of its n terms.

25. fdlh cká fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh yEckb;k¡ cjkcj gksrh gSa] fl) dhft,A
4

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

( 10 ) 1903/(Set : D)
Prove that the length of tangents drawn from an external point to a
circle are equal.

26. ,d rk'k dh vPNh rjg QsaVh xbZ xìh ls ,d iÙkk fudkyk tkrk gSA ml iÙks ds iku dk iÙkk
gksus dh izkf;drk Kkr dhft,A ml iÙks ds bDdk u gksus dh izkf;drk Hkh Kkr dhft,A
4

A card is drawn from a well shuffled pack of playing cards. Find the
probability that card drawn is a heart card. Also find the probability
that card is not an ace.

27. (3, 4) vkSj (–4, 7) 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 (3, 4) and (–4, 7) is divided by y-
axis. Also find the coordinates of the point of intersection.

[k.M & n
SECTION – D

28. nks LVs'kuksa ds chp 168 fdeh ;k=k djus esa ,d ,Dlizsl jsyxkM+h] lokjh xkM+h ls 1 ?kaVk de
le; ysrh gS ¼LVs'kuksa ij Bgjus dk le; /;ku esa u fy;k tk,½ ;fn ,Dlizsl xkM+h dh pky
lokjh xkM+h ls 14 fdeh/?k.Vk vf/kd gS] rks nksuksa jsyxkfM+;ksa dh vkSlr pky Kkr dhft,A
5

An express train takes 1 hour less than a passenger train to travel 168
km between two stations (Stoppage time between two stations is not

1903/(Set : D)

( 11 ) 1903/(Set : D)
considered). If the average speed of the express train is 14 km/hour
more than the passenger train, find the average speeds of two trains.

29. fl) dhft, % 5

tan θ cot θ
+ = 1 + sec θ cos ec θ
1 − cot θ 1 − tan θ

Prove that :

tan θ cot θ
+ = 1 + sec θ cos ec θ
1 − cot θ 1 − tan θ

vFkok
OR

Hkwfe ds fcUnq P ls ,d 10 eh Å¡ps Hkou ds f'k[kj dk mUu;u dks.k 30° gSA Hkou ds
f'k[kj ij ,d /ot ds f'k[kj dk mUu;u dks.k 45° gSA /ot dh yEckbZ vkSj fcUnq P ls
Hkou dh nwjh Kkr dhft,A

From the point P on the ground the angle of elevation of the top of a 10
m building is 30°. A flag is hoisted at the top of building and the angle
of elevation of the top of flagstaff from P is 45°. Find the length of
flagstaff and distance of building from P.

30. 5 lseh, 6 lseh vkSj 7 lseh Hkqtkvksa okys ,d f=Hkqt dh jpuk dhft,A bl f=Hkqt ds le:i
nwljs f=Hkqt dh jpuk dhft,] ftldh Hkqtk,¡ bl f=Hkqt dh 7 gksaA 5
5

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

( 12 ) 1903/(Set : D)
Construct a triangle with sides 5 cm, 6 cm and 7 cm. Consider
7
another similar triangle whose sides are of the corresponding sides
5
of first triangle.

31. 6 lseh f=T;k okys ,d xksys dks fi?kykdj 24 lseh Å¡pkbZ okys ,d 'kadq esa <kyk tkrk gSA
'kadq ds vk/kkj dh f=T;k Kkr dhft,A 5
A metallic sphere of radius 6 cm is melted and recast into the shape of
cone of height 24 cm. Find the radius of the base of the cone.

32. fuEufyf[kr lkj.kh esa ,d Ldwy ds fo|kfFkZ;ksa dk nSfud tsc [kpZ fn;k x;k gS % 5
nSfud tsc [kpZ ¼#i;s esa½ 11-13 13-15 15-17 17-19 19-21 21-23 23-25

fo|kfFkZ;ksa dh la[;k 7 6 9 13 20 5 4

bl Ldwy ds cPpksa dk vkSlr tsc [kpZ Kkr dhft,A
The following distribution shows the daily pocket money of children of a
school :
Daily Pocket Money (Rs.) 11-13 13-15 15-17 17-19 19-21 21-23 23-25
Number of Children 7 6 9 13 20 5 4

Find the average daily pocket money of children.

vFkok
OR

,d ikS/ks dh 40 ifÙk;ksa dh yEckb;k¡ fuEu lkj.kh esa feeh esa nh xbZ gS %
yEckb;k¡ ¼feeh esa½ 18-27 27-36 36-45 45-54 54-63 63-72

ifÙk;ksa dh la[;k
[;k 3 5 10 13 5 4

ifÙk;ksa dh ek/;d yEckbZ Kkr dhft,A

1903/(Set : D)

( 13 ) 1903/(Set : D)
The length of 40 leaves of a plant are measured in mm and are given in
the following table :
Length in (mm) 18-27 27-36 36-45 45-54 54-63 63-72
Number of Leaves 3 5 10 13 5 4

Find the median length of the leaves

S

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