HBSE Class 10 Question Paper 2025 Math Basic

CLASS : 10th (Secondary) Code No. 2104
Series : Sec/Annual Exam.-2025
Roll No. SET : A

xf.kr ¼vk/kkj½
MATHEMATICS (Basic)
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear/Improvement/Additional Candidates)

le; : 3 ?k.Vs ] [ iw.kk±d : 80
Time allowed : 3 hours ] [ Maximum Marks : 80

• Ñi;k tk¡p dj ysa fd bl iz'u&i= esa eqfnzr i`"B 24 rFkk iz'u 38 gSaA
Please make sure that the printed pages in this question paper are 24 in number
and it contains 38 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.

2104/(Set : A) P. T. O.

(2) 2104/(Set : A)
• 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 jksy ua0 ds vfrfjDr iz'u&i= ij vU; dqN Hkh u
fy[ksa vkSj oSdfYid iz'uksa ds mÙkjksa ij fdlh izdkj dk fu'kku u yxk,¡A
Candidates must write their Roll No. on the question paper. Except Roll No. do not
write anything on question paper and don't make any mark on answers of objective
type questions.
• d`i;k iz'uksa ds 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 Instructions :
(i) bl ç'u-i= esa dqy 38 ç'u gSa tksfd ik¡p [k.Mksa % v] c] l] n vkSj ; esa ck¡Vs x;s gSaA
This question paper consists of 38 questions in all which are divided into five
Sections : A, B, C, D and E.
(ii) [k.M – v % bl [k.M esa 1 ls 20 rd dqy 20 ç'u gSa] çR;sd ç'u 1 vad dk gSA
Section – A : There are 20 questions from 1 to 20, each of 1 mark.
(iii) [k.M – c % bl [k.M esa 21 ls 25 rd dqy 5 ç'u gSa] çR;sd ç'u 2 vad dk gSA
Section – B : There are 5 questions from 21 to 25, each of 2 marks.
(iv) [k.M – l % bl [k.M esa 26 ls 31 rd dqy 6 ç'u gSa] çR;sd ç'u 3 vad dk gSA
Section – C : There are 6 questions from 26 to 31, each of 3 marks.

2104/(Set : A)

(3) 2104/(Set : A)
(v) [k.M – n % bl [k.M esa 32 ls 35 rd dqy 4 ç'u gSa] çR;sd ç'u 5 vad dk gSA
Section – D : There are 4 questions from 32 to 35, each of 5 marks.

(vi) [k.M – ; % bl [k.M esa 36 ls 38 rd dqy 3 ç'u gSa] çR;sd ç'u 4 vad dk gSA
Section – E : There are 3 questions from 36 to 38, each of 4 marks.

(vii) lHkh iz'u vfuok;Z gSaA gkykafd [k.M&c ds 2 iz'u es]a [k.M
[k.M&l
&l ds nks iz'uksa es]a [k.M&n ds lHkh
iz'uksa esa vkSj [k.M&; ds lHkh ç'uksa esa vkUrfjd fodYi fn;s x;s gSaA muesa ls vkidks ,d ç'u dks
pquuk gSA
All questions are compulsory. However provision of internal choice has
been made in 2 questions of Section-B, 2 questions of Section-C, all
questions of Section-D and all questions of Section-E. You have to choose
one question of them.

[k.M – v
SECTION – A

1. la[;k 7 × 11 × 13 × 15 + 15 gS] ,d % 1

(A) vHkkT; la[;k (B) HkkT; la[;k

(C) u HkkT; u vHkkT; (D) buesa ls dksbZ ugha

Number 7 × 11 × 13 × 15 + 15 is a :

(A) Prime number (B) Composite number

(C) Neither prime nor composite (D) None of these
2104/(Set : A) P. T. O.

(4) 2104/(Set : A)
2. ;fn HCF (a, 8) =4 rFkk LCM (a, 8) = 24] rc a gS % 1
(A) 6 (B) 8
(C) 10 (D) 12
If HCF (a, 8) = 4 and LCM (a, 8) = 24] then a is :
(A) 6 (B) 8
(C) 10 (D) 12

3. la[;k ( 3 + 5 )2 gS] ,d % 1

(A) vokLrfod la[;k (B) ifjes; la[;k
(C) vifjes; la[;k (D) iw.kk±d
2
The number ( 3 + 5 ) is a/an :
(A) Not a real number (B) Rational number
(C) Irrational number (D) Integer

4. 'kwU;d −7 vkSj 3 okys cgqin dh ?kkr gS % 1

(A) 0 (B) 1

(C) 2 (D) 3

The degree of polynomial having zeroes −7 and 3 is :

(A) 0 (B) 1

(C) 2 (D) 3

5. f}?kkr lehdj.k x 2 + 2x − 143 = 0 dk fofoDrdj gksxk % 1
(A) 24 (B) 26
(C) 28 (D) 29

2104/(Set : A)

(5) 2104/(Set : A)
The discriminant of quadratic equation x 2 + 2x − 143 = 0 is :

(A) 24 (B) 26
(C) 28 (D) 29

6. vkÑfr esa ∆ABC ~ ∆QPR, rks ∠R + ∠P gS % 1
A R

60°°

Q
70°°
B C P

(A) 110° (B) 120°
(C) 130° (D) buesa ls dksbZ ugha

In figure, ∆ABC ~ ∆QPR, then ∠R + ∠P is :
A R

60°°

Q
70°°
B C P

(A) 110° (B) 120°
(C) 130° (D) None of these

7. fcUnqvksa  − 8 , − 2  rFkk  7 , 3  ds chp dh nwjh gS .............A 1
 5  5 
 8  7 
The distance between the points  − , − 2  and  , 3  is ………… .
 5  5 
2104/(Set : A) P. T. O.

(6) 2104/(Set : A)
8. lR; ;k vlR; crkb,] ;fn sec θ = 4 , θ ds fdlh eku ds fy,A 1
3
4
State true or false, whether sec θ = for some angle θ.
3

9. 2 2 cos 45°. cos 60° + 2 3 sin 30° tan 60° − cos 0° dk eku gS % 1
3
(A) 3 (B)
2
1
(C) (D) 1
2
The value of 2 2 cos 45°. cos 60° + 2 3 sin 30° tan 60° − cos 0° is :
3
(A) 3 (B)
2
1
(C) (D) 1
2

10. [kkyh LFkku Hkjsa % 1

7 cot 2 A − 7 cos ec 2 A = .............

Fill in the blanks :

7 cot 2 A − 7 cos ec 2 A = .............

11. ,d 6 eh0 Å¡pk [kEHkk lw;Z ds 60° mUu;u dks.k ds lkFk Hkwfe ij Nk;k cukrk gSA ml Nk;k dh yackbZ
gS % 1

(A) 3 m (B) 2 3m

(C) 3 3 m (D) 6 m

2104/(Set : A)

(7) 2104/(Set : A)
A pole 6 m high casts a shadow on ground with Sun's elevation 60°. The length
of shadow is :

(A) 3 m (B) 2 3m

(C) 3 3 m (D) 6 m

12. ;fn ,d fcUnq P ls O dsUæ okys fdlh o`Ùk ij PA, PB Li'kZ js[kk,¡ ijLij 70° ds dks.k ij >qdh gks]
rks |POA cjkcj gS % 1
(A) 45° (B) 50°
(C) 55° (D) 60°
If tangents PA and PB from a point P to a circle with centre O are inclined to
each other at angle of 70°, then |POA is equal to :
(A) 45° (B) 50°
(C) 55° (D) 60°

13. o`Ùk rFkk mldh Li'kZ js[kk ds mHk;fu"B fcUnq dks ----------- dgrs gSaA 1

The common point of a tangent to a circle and the circle is called …………. .

14. 28 cm O;kl okys o`Ùk ds ,d f=T;[kaM dk {ks=Qy D;k gksxk] ftldk dks.k 72° gSA 1
Find the area of a sector of a circle with diameter 28 cm, if angle of the sector is
72°.

15. O;kl r okys o`Ùk ds dks.k θ okys pki dh yEckbZ gS % 1

θ θ
(A) × πr 2 (B) × 2πr
360° 360°

θ θ
(C) × πr (D) × 2π r 2
360° 360°

2104/(Set : A) P. T. O.

(8) 2104/(Set : A)
The length of an arc of angle θ of a circle with diameter r is :

θ θ
(A) × πr 2 (B) × 2πr
360° 360°
θ θ
(C) × πr (D) × 2π r 2
360° 360°

16. ;fn ,d xksys dk vk;ru 12 π cm3 gS] rks xksys dh f=T;k gksxh % 1
(A) 31/ 3 cm (B) 32 / 3 cm

(C) 3 3 cm (D) 3 cm

The radius of a sphere whose volume is 12 π cm3 will be :
(A) 31/ 3 cm (B) 32 / 3 cm

(C) 3 3 cm (D) 3 cm

17. ;fn P(A), ?kVuk A dh çkf;drk O;Dr djrk gS] rks % 1
(A) P(A) < 0 (B) P(A) > 1
(C) −1 ≤ P(A) ≤ 1 (D) 0 ≤ P(A) ≤ 1
If P(A) denotes the probability of an event A, then :
(A) P(A) < 0 (B) P(A) > 1
(C) −1 ≤ P(A) ≤ 1 (D) 0 ≤ P(A) ≤ 1

18. fuEufyf[kr ckjackjrk caVu esa cgqyd oxZ dh mPp oxZ lhek gS % 1
oxZ vUrjky 0-5 6-11 12-17 18-23 24-29
ckjackjrk 13 10 15 8 11
(A) 16.5 (B) 17
(C) 17.5 (D) 18

2104/(Set : A)

(9) 2104/(Set : A)
The upper limit of the modal class of following frequency distribution is :

Class Interval 0-5 6-11 12-17 18-23 24-29

Frequency 13 10 15 8 11

(A) 16.5 (B) 17
(C) 17.5 (D) 18

ç'u la[;k 19 vkSj 20 ds fy, fn'kkfunsZ'k % ç'u la[;k 19 vkSj 20 eas vfHkdFku (A) ds ckn rdZ (R) dk
dFku gSA (A), (B), (C) vkSj (D) esa ls lgh fodYi pqusa tSlk fd uhps fn;k x;k gS %
Direction for Question Nos. 19 and 20 : In Question Nos. 19 and 20, a statement
of Assertion (A) is followed by a statement of Reason (R). Choose the correct option
from (A), (B), (C) and (D) as given below :

19. vfHkdFku (A) % ;fn ,d A. P. dk nok¡ in (2n + 1) gS] rks mlds igys rhu inksa dk ;ksx 15 gSA 1

rdZ (R) % igyh n çkÑfrd la[;kvksa dk ;ksx n (n + 1) gSA
2

fodYi %
(A) vfHkdFku (A) vkSj rdZ (R) nksukas lgh gSa vkSj rdZ (R) vfHkdFku (A) dh lgh O;k[;k djrk gSA

(B) vfHkdFku (A) vkSj rdZ (R) nksukas lgh gS]a ysfdu rdZ (R) vfHkdFku (A) dh lgh O;k[;k ugha djrk gSA
(C) vfHkdFku (A) lgh gS] ysfdu rdZ (R) xyr gSA
(D) vfHkdFku (A) xyr gS] ysfdu rdZ (R) lgh gSA

2104/(Set : A) P. T. O.

( 10 ) 2104/(Set : A)
Assertion (A) : If nth term of an A. P. is (2n + 1), then the sum of its first three
terms is 15.

n (n + 1)
Reason (R) : The sum of first n natural numbers is .
2

Option :

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is correct
explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct
explanation of Assertion (A).

(C) Assertion (A) is true, but Reason (R) is false.

(D) Assertion (A) is false, but Reason (R) is true.

20. vfHkdFku (A) % fdlh o`Ùk ds ,d O;kl ds fljksa ij [khaph xbZ Li'kZ js[kk,¡ lekUrj gksrh gSaA 1

rdZ (R) % o`Ùk dk O;kl mldh lcls cM+h thok gksrh gSA
fodYi %
(A) vfHkdFku (A) vkSj rdZ (R) nksukas lgh gSa vkSj rdZ (R) vfHkdFku (A) dh lgh O;k[;k djrk gSA

(B) vfHkdFku (A) vkSj rdZ (R) nksukas lgh gS]a ysfdu rdZ (R) vfHkdFku (A) dh lgh O;k[;k ugha djrk gSA
(C) vfHkdFku (A) lgh gS] ysfdu rdZ (R) xyr gSA

(D) vfHkdFku (A) xyr gS] ysfdu rdZ (R) lgh gSA

2104/(Set : A)

( 11 ) 2104/(Set : A)
Assertion (A) : The tangents drawn at the end points of a diameter of a circle
are parallel.

Reason (R) : Diameter of a circle is its longest chord.

Option :

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is correct
explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct
explanation of Assertion (A).

(C) Assertion (A) is true, but Reason (R) is false.

(D) Assertion (A) is false, but Reason (R) is true.

[k.M – c
SECTION – B

21. fuEufyf[kr jSf[kd lehdj.kksa ds ;qXe dks gy djsa % 2
0.2x + 0.3y = 1.3

0.4x + 0.5y = 2.3

Solve the following pair of linear equations :
0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
vFkok
OR

2104/(Set : A) P. T. O.

( 12 ) 2104/(Set : A)
fuEufyf[kr jSf[kd lehdj.kksa ds ;qXe dks gy djsa %
3x 5y x y 13
− = −2 vkSj + =
2 3 3 2 6
Solve the following pair of linear equations :
3x 5y x y 13
− = −2 and + =
2 3 3 2 6

22. ;fn dksbZ js[kk ,d ∆ABC dh Hkqtkvksa AB vkSj AC dks Øe'k% D vkSj E ij çfrPNsn djs rFkk Hkqtk
AD AE
BC ds lekarj gks] rks fl) dhft, fd = gksxkA 2
AB AC
A

D E

B C

If a line intersects sides AB and AC of a ∆ABC at points D and E respectively
AD AE
and is parallel to BC, prove that = .
AB AC
A

D E

B C

23. m dk og eku Kkr dhft, ftlds fy, fcUnqvksa A(−3, −14) rFkk B(m, −5) dh nwjh 9 bdkbZ gSA 2

Find the value of m, if the distance between the points A(−3, −14) and B(m, −5)
is 9 units.

2104/(Set : A)

( 13 ) 2104/(Set : A)
24. ;fn cot θ = 7 , rks (1 + cos θ)(1 − cos θ) dk eku Kkr dhft,A 2
8 (1 − sin θ)(1 + sin θ)
7 (1 + cos θ)(1 − cos θ)
If cot θ = , then evaluate .
8 (1 − sin θ)(1 + sin θ)

vFkok
OR

fl) dhft, %
sec θ (1 − sin θ) (sec θ + tan θ) = 1

Prove that :

sec θ (1 − sin θ) (sec θ + tan θ) = 1

25. ,d o`Ùkkdkj czwp (brooch) dks pk¡nh ds rkj ls cuk;k tkuk gS ftldk O;kl 42 mm gSA rkj dks o`Ùk
ds rhu O;klksa dks cukus esa Hkh ç;qDr fd;k x;k gS tks mls 6 cjkcj f=T;[kaMksa esa foHkkftr djrk gSA dqy
okafNr pk¡nh dh rkj dh yackbZ Kkr dhft,A 2

A brooch is made with silver wire in the form of a circle with diameter 42 mm.
The wire is also used in making 3 diameters which divide the circle into 6 equal
sectors. Find the total length of silver wire.

[k.M – l
SECTION – C

26. fl) dhft, 2 − 3 5 ,d vifjes; la[;k gS] ;fn 5 ,d vifjes; la[;k gSA 3

Prove that 2 − 3 5 is an irrational number, if 5 is an irrational number.

2104/(Set : A) P. T. O.

( 14 ) 2104/(Set : A)
27. ,d f}?kkr cgqin Kkr dhft,] ftlds 'kwU;dksa ds ;ksx rFkk xq.kuQy Øe'k% 2 rFkk 1 gSaA 3
2

Find a quadratic polynomial, where sum and product of its zeroes are
1
respectively 2 and .
2

28. k dk og eku Kkr dhft, ftlds fy, bu jSf[kd lehdj.kksa ds ;qXe ds vifjfer vusd gy gksaxs % 3
kx + 3y − (k − 3) = 0
12x + ky − k = 0
Find the value(s) of k for which the pair of linear equations will have infinitely
many solutions :
kx + 3y − (k − 3) = 0
12x + ky − k = 0

vFkok

OR

,d fHkUu 1 gks tkrh gS] tc mlds va'k ls 1 ?kVk;k tkrk gS vkSj og 1 gks tkrh gS tc gj esa 8
3 4
tksM+ fn;k tkrk gSA og fHkUu Kkr dhft,A

1
A fraction becomes , when 1 is subtracted from the numerator and it becomes
3
1
, when 8 is added to its denominator. Find the fraction.
4

2104/(Set : A)

( 15 ) 2104/(Set : A)
29. fcUnqvksa (2, −1) vkSj (−3, −2) dks tksM+us okys js[kk[k.M dks lef=Hkkftr djus okys fcUnqvksa ds funsZ'kkad
Kkr dhft,A 3

Find the coordinates of the points of trisection of the line segment joining (2, −1)
and (−3, −2).

30. loZlfedk fl) dhft, % 3

1 − cos θ
(cosec θ − cot θ)2 =
1 + cos θ

Prove the identity :
1 − cos θ
(cosec θ − cot θ)2 =
1 + cos θ

vFkok
OR

fl) dhft, %

sec 2 θ + cosec 2θ = tan θ + cot θ

Prove that :

sec 2 θ + cosec 2θ = tan θ + cot θ

2104/(Set : A) P. T. O.

( 16 ) 2104/(Set : A)
31. ,d unh ds iqy ds ,d fcUnq ls unh ds lEeq[k fdukjksa ds voueu dks.k Øe'k% 45° vkSj 30° gSaA ;fn

iqy fdukjksa ls 5 eh0 dh Å¡pkbZ ij gks] rks unh dh pkSM+kbZ Kkr dhft,A 3

From a point on a bridge across a river, the angles of depression of the banks on
opposite sides of the river are 45° and 30° respectively. If the bridge is at a
height of 5 m from the banks, find the width of the river.

[k.M – n
SECTION – D

32. A. P. : 3, 15, 27, 39, ……. dk dkSu-lk in mlds 67osa in ls 132 vf/kd gksxk \ 5

Which term of the A. P. : 3, 15, 27, 39, ……. will be 132 more than its 67th
term ?

vFkok
OR

eksckby lsV dk ,d fuekZrk rhljs o"kZ esa 700 lsV rFkk 7osa o"kZ esa 800 lsVksa dk mRiknu djrk gSA ;g
ekurs gq, fd çR;sd o"kZ mRiknu esa ,dleku :i ls ,d fuf'pr la[;k esa o`f) gksrh gS] Kkr dhft, %
(i) 10osa o"kZ esa mRiknu

(ii) çFke 7 o"kks± esa dqy mRiknu
A manufacturer of Mobile sets produced 700 sets in the third year and 800 sets
in the seventh year. Assuming that the production increases uniformly by a
fixed number every year, find :
(i) the production in the 10th year

(ii) the total production in first 7 years

2104/(Set : A)

( 17 ) 2104/(Set : A)
33. fl) dhft, fd ,d f=Hkqt dh fdUgha nks Hkqtkvksa ds e/; fcUnqvksa dks feykus okyh js[kk rhljh Hkqtk ds
lekarj gksrh gSA 5

Prove that the line joining the mid-points of any two sides of a triangle is parallel
to the third side.

vFkok
OR

lekUrj prqHkqZt ABCD dh c<+kbZ xbZ Hkqtk AD ij fLFkr E ,d fcUnq gS rFkk BE Hkqtk CD dks F ij
çfrPNsn djrh gSA n'kkZb, fd ∆ABE ~ ∆CFB A
E is a point on the side AD produced of a parallelogram ABCD and BE
intersects CD at F. Show that ∆ABE ~ ∆CFB.

34. dksbZ crZu ,d [kks[kys v/kZxksys ds vkdkj dk gS ftlds Åij ,d [kks[kyk csyu v/;kjksfir gSA v/kZxksys
dk O;kl 21 cm gS vkSj bl crZu dh dqy Å¡pkbZ 17 cm gSA bl crZu dk vkarfjd i`"Bh; {ks=Qy
Kkr dhft,A 5

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The
diameter of the hemisphere is 21 cm and the total height of the vessel is 17 cm.
Find the inner surface area of the vessel.

vFkok
OR

2104/(Set : A) P. T. O.

( 18 ) 2104/(Set : A)
,d twl cspus okyk vius xzkgdksa dks vkÑfr esa n'kkZ, fxyklksa ls twl nsrk FkkA csyukdkj fxykl dk
vkarfjd O;kl 7 cm Fkk] ijUrq fxykl ds fupys vk/kkj ¼ryh½ esa ,d mHkjk gqvk v/kZxksyk Fkk ftlls
fxykl dh /kkfjrk de gks tkrh FkhA ;fn ,d fxykl dh Å¡pkbZ 10 cm gS] rks fxykl dh vkHkklh /kkfjrk
rFkk mldh okLrfod /kkfjrk Kkr dhft,A ¼π = 3.14 yhft,½

10 cm

A juice seller was serving his customers using glasses as shown in fig. The inner
diameter of the cylindrical glass was 7 cm, but the bottom of the glass had a
hemispherical raised portion which reduced the capacity of the glass. If the
height of a glass is 10 cm. Find the apparent capacity of the glass and its actual
capacity. (Use π = 3.14)

10 cm

2104/(Set : A)

( 19 ) 2104/(Set : A)
35. fn;k x;k caVu fo'o ds dqN Js"Bre cYyscktksa }kjk ,dfnolh; varjkZ"Vªh; fØdsV eSpksa esa cuk, x, juksa
dks n'kkZrk gS % 5

cuk, x, 3000-4000 4000-5000 5000-6000 6000-7000 7000-8000 8000-9000 9000-10000 10000-11000

ju

cYyscktksa 4 18 9 7 6 3 1 1

dh la[;k

bu vk¡dM+ksa dk cgqyd Kkr dhft,A

The given distribution shows the number of run scored by some top batsmen of

the world in one-day international cricket matches :

Runs 3000-4000 4000-5000 5000-6000 6000-7000 7000-8000 8000-9000 9000-10000 10000-11000

Scored

Number 4 18 9 7 6 3 1 1

of

Batsmen

Find the Mode of the data.

vFkok
OR

2104/(Set : A) P. T. O.

( 20 ) 2104/(Set : A)
uhps fn;k x;k caVu ,d d{kk ds 30 fo|kfFkZ;ksa ds Hkkj dks n'kkZ jgk gSA fo|kfFkZ;ksa dk ek/;d Hkkj Kkr
dhft, %

Hkkj ¼fd0xzk0 esa½ 40-45 45-50 50-55 55-60 60-65 65-70 70-75

fo|kfFkZ;ksa dh la[;k 2 3 8 6 6 3 2

The distribution below gives the weights of 30 students of a class. Find the
median weight of the students :

Weight 40-45 45-50 50-55 55-60 60-65 65-70 70-75
(in kg)

No. of 2 3 8 6 6 3 2
Students

[k.M – ;
SECTION – E

36. uhps fn, x, fp= esa fn[kk, vuqlkj ,d f=dks.kh; [ksy dk eSnku gSA
A

5x m

B (3x − 1) m C

tSlk fd ge ledks.k f=Hkqtkdkj [ksy ds eSnku dh mijksDr vkÑfr esa ns[krs gSa Hkqtkvksa dh yackbZ 5x eh0
rFkk (3x − 1) eh0 gS vkSj f=Hkqt dk {ks=Qy 60 eh02 gSA
2104/(Set : A)

( 21 ) 2104/(Set : A)
mijksDr tkudkjh ds vk/kkj ij fuEufyf[kr ç'uksa ds mÙkj nhft, %
(i) mijksDr ç'u dks ,d f}?kkr lehdj.k ds :i esa O;Dr dhft,A 1
(ii) x dk eku Kkr dhft,A 2

vFkok
AC dh yackbZ Kkr dhft,A 2
(iii) ∆ABC dk ifjeki Kkr dhft,A 1
There is a triangular playground as shown in the figure below :
A

5x m

B (3x − 1) m C

As we see in the above figure of right angled triangular playground, the length of
the sides are 5x m and (3x −1)m and area of the triangle is 60 m2.

Based on the above information, answer the following questions :

(i) Represent the above problem in the form of a quadratic equation.

(ii) Find the value of x.

OR

Find the length of AC.

(iii) Find the perimeter of ∆ABC.

2104/(Set : A) P. T. O.

( 22 ) 2104/(Set : A)
37. lkbfdyksa dh psu ;k iqYyh ds pkjksa vksj csYV] o`Ùk dh Li'kZ js[kkvksa ds okLrfod thou ds mnkgj.k gSaA
tSlk fd layXu fp= esa fn[kk;k x;k gSA

mijksDr tkudkjh ds vk/kkj ij fuEufyf[kr ç'uksa ds mÙkj nhft, %
(i) ;fn TP = 39 vkSj AP = x 2 + 3 , rks x dk eku Kkr dhft,A 1
(ii) PT vkSj PA fcUnq P ls o`Ùk ij Li'kZ js[kk,¡ gSaA ;fn pki TMA o`Ùk ds dsUæ ij 120° dk dks.k
vUrfjr djrh gS] rks |TPA Kkr dhft,A 1

(iii) pki TNA vkSj pki TMA ds eki dk vuqikr Kkr dhft,A 2

vFkok
;fn TP = 20 lseh gS] rks AT Kkr dhft,A 2
The chain of bicycles or belt
b lt around pulleys are some real life illustration of
tangents to circle as shown in the adjoining figure.

Based on the given information, answer the following questions :

(i) If TP = 39 and AP = x 2 + 3 , then find value of x.

2104/(Set : A)

( 23 ) 2104/(Set : A)
(ii) PT and PA are tangents to the circle from point P. If arc
ar TMA subtends an
angle 120° at the centre of the circle, then find |TPA .

(iii) Find the ratio of measures of arcs TNA and TMA.

OR
If TP = 20 cm, then find AT.

38. nks lgsfy;ksa lksfu;k vkSj Jqfr ds
ds ikl xqYyd esa dqN cpr gSA mUgksaus vius ikl ekStwn dqy flDdksa dks
fxuus dk QSlyk fd;kA fxuus ds ckn] mUgksaus ik;k fd muds ikl ` 1 ds 60 flDds] ` 2 ds 42 flDds]
` 5 ds 30 flDds] ` 10 ds 35 flDds vkSj ` 20 ds 12 flDds gSaA vc mUgksaus viuh ,d lgsyh
lyksuh ls ;kn`PN;k ,d flDdk pquus dks dgkA

mijksDr tkudkjh ds vk/kkj ij fuEufyf[kr iz'uksa ds mÙkj nhft, %
(i) D;k çkf;drk gS fd pquk x;k flDdk ` 2 dk gS \ 1
(ii) D;k çkf;drk gS fd pquk x;k flDdk ` 5 dk ugha gS \ 1
(iii) D;k çkf;drk gS fd pquk x;k flDdk ` 10 ;k ` 20 dk gS \ 2
vFkok
D;k çkf;drk gS fd pquk x;k flDdk ` 10 ls de #i;s dk gS \ 2

2104/(Set : A) P. T. O.

( 24 ) 2104/(Set : A)
Two friends Soniya and Shruti have some savings in their Piggi Bank. They
decided to count the total coins they both had. After counting, they find that
they have sixty ` 1 coins, forty two ` 2 coins, thirty ` 5 coins,
coins thirty five ` 10
coins, and twelve ` 20
0 coins. Now they said to Saloni,, their another friend, to
choose a coin randomly.

Based on the above information, answer the following questions :

(i) What is the probability that the coin chosen is a ` 2 coin ?
(ii) What is the probability that the coin chosen is not a ` 5 coin ?
(iii) What is the probability that the coin chosen is either of ` 10 or ` 20 coin ?

OR
What is the probability that the coin chosen is less than ` 10 coin ?

2104/(Set : A)
S