HP Board 10th Class Model Question Paper 2025 Math

HPBOSE
MODEL QUESTION
PAPERS

Model Question Paper
10th Class
Mathematics
2024-25
Time : 3Hrs M.M: 80
General Instruction :

1. Question No.1 to 16 are of MCQ type and carry 1 mark for each question.
2. Question No. 17 to 25 are of short type questions and each carry 2 marks.
3. Question No. 26 to 32 are of long type questions and each carry 3 marks.
4. Question No. 33 to 37 are application based question and each carry 5 marks.

Section-A (1 x 16 = 16)
M.C.Q (Choose the right option)
1. HCF of 17,23 and 29 is
17, 23, 29 dk HCF gS
(a) 17 (b) 23 (c) 1 (d) 0
2. Product of two numbers = _____________
nks la[;kvksa dk xq.kuQy = _____________
(a) LCM + HCF (b) LCM X HCF (c) LCM ÷ HCF (d) None of above
(a) y0l0o0$ x0l0o0 (b) y0l0o0 X x0l0o0 (c) y0l0o0 ÷ x0l0o0 (d) buesa ls dksbZ ugha
3. How many zeroes will quadratic equation 4x2-4x-1= 0 have:
f}?kkr llhdj.k 4x2-4x-1= 0 esa “kwU;dksa dh la[;k fdruh gS\
(a) 1 (b) 2 (c) 3 (d) 4
4. P(E) + P(E) = …………..
(a) 0 (b) -1 (c) 1 (d) 2
5. The roots of quadratic equation will be equal if
f}?kkr lehdj.k ds ewy cjkcj gksx
a s ;fn
(a) b2=4ac<0 (b) b2-4ac=0 (c) b2-4ac>0 (d) b2-4ac<0
6. Next term in the A.P -5, -1,3 ………..
A.P Eksa -5, -1,3 ……….. vxyk in dksSu lk gksxk\
(a) 2 (b) 7 (c) 6 (d) -7
2
7. In Trigonometric Identify: 1 + tan 𝜃 = …………
f+=dks.kkferh esa% 1 + tan2𝜃 = …………
(a)Sin2 𝜃 (b)Sec2 𝜃 (c)Cot2 𝜃 (d)None of these.
8. According to Pythagoras theorm (8)2 + (15)2 = ………….
ikbFkkxksjl ize; s ds vuqlkj (8)2 + (15)2 = ………….
(a) (16)2 (b) (17)2 (c) (18)2 (d) (19)2
9. A Line intersecting a circle in two points is called a ……………..
o`r dks nks fcanqvksa ij izfrPNsn djus okyh js[kk dks ----------- dgrs gSaA
(a) Chord (pki) (b) Secant line (Nsnd js[kk) (c) Tangent line (LIk”kZ js[kk) (d) Radius (f=T;k)
10. Volume of cylinder
csyu dk vk;ru
(a) 𝜋rh (b) 𝜋r2h (c) 2𝜋rh (d) 𝜋 r2h
11. nthTerm of an A.P.
A.P.dk nthin
(a) a+(n-1)d (b) a-(n-1)d (c) (n-1)d (d) (n+1)d

12. If Sin A = then value of Cosec A?
;fn Sin A = rks Cosec A dk eku\
(a) (b) (c) (d)
13. All Squares are ………….
lHkh oxZ ----------- gksrs gSaA
(a) Similar (le:i) (b) Congruent (lokZxle)
(c) Always equal(cjkcj) (d) all of above (mijksDr lHkh)
14. Tangent to circle make an angle of …………. With the radius of circle.
o`r dh Li”kZ js[kk o`r dh f=T;k ds lkFk ----------- dk dks.k cukrh gSA
(a) 600 (b) 700 (c) 900 (d) 1800
15. Volume of two spheres are in ratio 64 : 27 then the ratio of their surface area is
nks xksyksa ds vk;ru dk vuqikr 64%27 gS rks muds i`’Bh; {ks=Qyksa dk vuqikr gksxk\
(a) 3:4 (b) 16:9 (c) 9:16 (d) 27:64
2
16. Sum of zeroes in the polynomial 5y - 14y + 8 is
cgqin 5y2- 14y + 8 esa “kwU;dksa dk ;ksx gS\
(a) (b) (c) (d)

Section-B (9 x 2 = 18)
17. Express 336 as a product of its prime factor
336 dks vHkkT; xq.ku[kaMksa ds xq.kuQy ds :Ik esa O;Dr dhft,A
18. The coordinates of Ram’s house are (6,0) and coordinates of shyam’s house are (0,8)
find the distance between houses of Ram and shyam.
jke ds ?kj ds funsZ”kkad ¼6]0½ gSa rFkk “;ke ds ?kj ds funsZ”kkad ¼0]8½ gSaA jke vkSj “;ke ds
?kj ds chp nwjh Kkr djksA
19. Find the Value of : Sin 600 Cos300 + Sin600 Cos600
Sin 600 Cos300 + Sin600 Cos600 dk eku crkbZ,%
20. Solve the pair of linear equation by the substitution method
izfrLFkkiu fof| }kjk gy dhft,A
x + y = 14
x–y=4
21. Find the roots of the equation
Lkehdj.k ds ewy Kkr djksA
2
√2 x + 7x + 5√2 = 0

22. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag.
What is the probability that ball drawn is red?
,d FkSys esa 3 yky vkSj 5 dkyh xsans gSaA bl FkSys esa ls ,d xsan ;kn`PN;k fudkyh tkrh
gSA bldh izkf;drk D;k gS fd fudkyh xbZ xsan yky gSA
23. Prove that the perpendicular at the point of contact to the tangent of circle passes
through the centre .
fl) dhft, fd Li”kZ fcanq ls Li”kZ js[kk ij [khapk x;k yac o`r ds dsnz ls gksdj tkrk gSA
OR
The length of the minute hand of a clock is 6cm. Find the area swept by it when it
moves from 9:10 a.m. to 9:20a.m.
?kM+h dh feuV dh lqbZ dh yackbZ 6cm gS] bl lqbZ }kjk 9%10 am ls ysdj 9%20 am rd
jfpr {ks= dk {ks=Qy Kkr djksA

24. Show that 5 - √3 is irrational
fl) dhft, fd 5 - √3 ,d vifjes; la[;k gSA
25. Determine the A.P whose third term is 16 and 7th term exceeds the 5th term by 12
og A.P Kkr dhft, ftldk rhljk in 16 gS vkSj 7oka in 5csa in ls 12 vf/kd gS
Section-C (7 x 3 = 21)
26. Solve the pair of linear equations graphically.
jSf[kd lehdj.kksa ds ;qXe dks xzkQh; fof| }kjk gy djksA
2x + y = 6
4x – 2y = 4
27. Find a relation between x and y such that the point (x,y) is equidistant from the point
(3,6) and (-3,4)
x vkSj y esa ,d ,slk laca/k Kkr dhft, fd fcanq (x,y) fcanqvksa (3,6) vkSj (-3,4) ls lenwjLFk gksA
OR
A cottage industry produces a certain number of pottery articles in a day. It was
observed that on a particular day the cost of production of each article (In was 3
more than twice the number of articles produced on that day. If the total cost of
production on that day was , find the number of articles produced and the cost of
each article.
,d dqVhj m|ksx ,d fnu esa dqN crZuksa dk fuekZ.k djrk gSA ,d fo”ks’k fnu ;g ns[kk
x;k fd izR;sd ux ds fuekZ.k ykxr :i;s esa ml fnu ds fuekZ.k fd;s crZuksa dh la[;k ds
nks xq.ks ls rhu vf/kd FkhA ;fn ml fnu mRiknu dh dqy ykxr 90 :i;s Fkh] rks
mRikfnr oLrqvksa dh la[;k vkSj izR;sd oLrq dh ykxr Kkr dhft,A
28. Prove that
fl) dhft,
=

29. A Chord of circle of radius 10cm subtends a right angle at the centre. Find the area of
the cooresponding (i) minor Segment (ii) Major Sector (use 𝜋 = 3.14)
10cm f=T;k okys o`r dh dksbZ thok dsanz ij ledks.k varfjr djrh gSA fuEufyf[kr ds
{ks=Qy Kkr dhft,%
¼i½ laxr y?kq o`r[kaM ¼ii½ laxr nh?kZ f=T;[kaM

( )( )
30. If Cot 𝜃 = , evaluate :
( )( )
( )( )
;fn Cot 𝜃 = rks ( )( )
dk eku Kkr djks
31. Find two numbers whose sum is 27 and product is 182.
nks la[;k,a Kkr dhft, ftudk ;ksx 27 gks vkSj xq.kuQy 182 gksA
32. The length of tangent from a point A at distance 5cm from the centre of the circle is
4cm. Find the radius of circle.
,d A fcanq ls ] tks dsanz ls 5cm nwjh ij gS] o`r dh Li”kZ js[kk dh yackbZ 4cm gSA o`r dh
f=T;k Kkr djksA
Section-D (5 x 5 = 25)

33. Prove that a line is drawn parallel to any one sides of the triangle that intersects the
other two sides in two distinct points, then the line divides those two sides in the same
ratio.

fl) dhft, fd ;fn fdlh f=Hkqt dh ,d Hkqtk ds lekarj ,d js[kk [khaph tk,] tksfd
vU; nks Hkqtkvksa dks vyx&vyx fcanqvksa ij izfrPNsfnr djs rks ;g js[kk mu nks Hkqtkvksa dks
leku vuqikr esa ckaVrh gSA
34. A tree breaks due to storm and the broken part bends so that top of the tree touches
the ground making an angle of 300 with it. The distance between the food of the tree
to the point whose top of tree touches the ground is 8m. Find the height of tree.
vka/kh vkus ls ,d isM+ VwV tkrk gS vkSj VwVk gqvk Hkkx bl rjg eqM+ tkrk gS fd isM+ dk
f”k[kj tehu dks Nwus yxrk gS vkSj blds lkFk 300 dk dks.k cukrk gSA isM+ ds ikn facanq
dh nwjh tgk¡ isM+ dk f”k[kj tehu dks Nwrk gS 8 m gS] isM+ dh ÅapkbZ Kkr djksA
OR
The Taxi charges in a city consist of a fixed charge together with the charge for the
distance covered. For a distance of 10KM, the charge paid is and for a journey
of 15km, the charge paid is What are the fixed charges and charge per KM?
How much does a person have to pay for travelling a distance of 25 KM.
,d uxj esa VSDlh ds HkkM+s esa ,d fu;e HkkM+s ds vfrfjDr pyh xbZ nwjh ij HkkM+k lfEefyr
fd;k tkrk gSA 10 fd0eh0 nwjh ds fy, HkkM+k :Ik;s 105 rFkk 15 fd0eh0 ds fy, HkkM+k
:i;s 155 gSA fu;r HkkM+k rFkk izfr fd0eh0 HkkM+k D;k gS\ ,d O;fDr dks 25 fd0eh0 ;k=k
djus ds fy, fdruk HkkM+k nsuk gksxk\

35. Radha has a doll in the shape of cone of radius 3.5cm mounted on hemisphere of same
radius the total height of doll is 15.5cm. Radha wants to colour her doll. Find the total
area of doll to be coloured.
jk/kk ds ikl ,d 3-5 cm f=T;k okyh ,d “kaDokdkj xqfM+;k gS] tks mlh f=T;k okys ,d
xksys ij v/;kjksfir gSA bl xqfM+;k dh dqy ÅapkbZ 15-5cm gSA jk/kk xqfM+;k dks jax djuk
pkgrh gSA jax fd, tkus okys dqy {ks= dk {ks=Qy Kkr djksA
OR
A wooden toy rocket is in the shape of a cone mounted on cylinder, as shown in
figure. The height of the entire rocket is 26cm, while the height of the conical part is
6cm. the base of the conical portion has diameter of 5cm, while the base diameter of
cyinderical portion is 3cm if conical portion is to be painted orange and the cylinder
portion yellow, find the area of the rocket painted with each of these colours.
(Take 𝜋 = 3.14)
ydM+h dk ,d f[kykSuk jkdsV ,d “kadq ds vkdkj dk gS tks ,d csyu ij v/;kjksfir gS
tSlk fd fp= esa n”kkZ;k x;k gSA laiw.kZ jkdsV dh ÅapkbZ 26cm gS] tcfd “kaDokdkj Hkkx dh
mapkbZ 6cm gSA “kaDokdkj Hkkx ds vk/kkj dk O;kl 5cm gS vkSj csyukdkj Hkkx ds vk/kkj
dk O;kl 3cm gSA ;fn “kaDokdkj Hkkx ij ukajxh rFkk csyukdkj Hkkx ij ihyk jax fd;k
tkuk gS rks izR;sd jax }kjk jaxs tkus okys jkdsV ds Hkkxksa dk {ks=Qy Kkr djksA ( 𝜋 =
3.14)

36. Five years ago, Nuri was thrice as old as sonu. Ten years later, Nuri will be twice as
old as sonu. How old are Nuri and Sonu?
Ikkap o’kZ iwoZ uwjh dh vk;q lksuw dh vk;q dh rhu xquk FkhA nl o’kZ i”pkr uwjh dh vk;q
lksuw dh vk;q dh nksxquh gks tk,xhA uwjh vkSj lksuw dh vk;q fdruh gS\
37. The following data gives the information on the observed lifetimes (in hours) of 225
electrical components.

Lifetimes 0-20 20-40 40-60 60-80 80-100 100-120
(in Hours)
Frequency 10 35 52 61 38 29

Determine the modal lifetimes of the components.
fuEufyf[kr vkadM+]s 225 fctyh midj.kksa ds izfs {kr thou dky ¼?kaVks es½a dh lwpuk nsrs gSaA
Tkhou dky 0-20 20-40 40-60 60-80 80-100 100-120
¼?kaVksa esa½
ckajckjrk 10 35 52 61 38 29

midj.kksa dk cgqyd thou dky Kkr djksA

*********************************

Blue Print of Model Question Paper (Level wise)
Class-Xth

Question wise Distribution of Marks

Sr. No. Type of Question Marks allotted per Question No. of Question Total Marks
1 MCQ 01 16 16
2 Short Type Question 02 09 18
3 Long Type Question 03 07 21
4 Application based 05 05 25
question
Total 37 80

Unit Wise Distribution marks
Name of Unit MCQ Short Ans. Long Ans. Application Total
Type Type Based
1.Real Numbers 2 Marks 4 Marks - - 6 Marks
2. Polynomials 2 Marks - - - 2 Marks
3. Pair of Linear - 2 Marks 3 Marks 5 Marks 10 Marks
Equations in Two
Variables
4. Quadratic 1 Marks 2 Marks 3 Marks - 6 Marks
Equations
5. Arithmetic 2 Marks 2 Marks - - 4 Marks
Progressions
6. Triangles 2 Marks - - 5 Marks 7 Marks
7. Coordinate - 2 Marks 3 Marks - 5 Marks
Geometry
8. Introduction to 2 Marks 2 Marks 6 Marks - 10 Marks
Trigonometry
9. Some - - - 5 Marks 5 Marks
Applications of
Trigonometry
10. Circles 2 Marks 2 Marks 3 Marks - 7 Marks
11. Areas Related - - 3 Marks - 3 Marks
to Circles
12. Surface Areas 2 Marks - - 5 Marks 7 Marks
and Volumes
13. Statistics - - - 5 Marks 5 Marks
14. Probability 1 Marks 2 Marks - - 3 Marks
Total 16 Marks 18 Marks 21 Marks 25 Marks 80 Marks

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