TN 10th Question Paper 2026 Mathematics

FOR TN 10TH EXAM PREPARATION

TN 10th 2026
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

TN 10th 2026 Question Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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!9212Mathematics!
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Part - III
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c. oPou® / MATHEMATICS
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Põ» AÍÄ : 3.00 ©o ÷|µ® ] [ ö©õzu ©v¨ö£sPÒ : 100

Time Allowed : 3.00 Hours ] [Maximum Marks : 100

AÔÄøµPÒ : (1) AøÚzx ÂÚõUPЮ \›¯õP Aa_¨ £vÁõQ EÒÍuõ GߣuøÚ
\›£õºzxU öPõÒÍÄ®. Aa_¨£vÂÀ SøÓ°¸¨¤ß AøÓU
PsPõo¨£õÍ›h® EhÚi¯õP öu›ÂUPÄ®.
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AiU÷PõikÁuØS® £¯ß£kzu ÷Ásk®. £h[PÒ ÁøµÁuØS
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Instructions : (1) ag
Check the question paper for fairness of printing. If there is any lack of fairness,

inform the Hall Supervisor immediately.

(2) Use Blue or Black ink to write and underline and pencil to draw diagrams.

SÔ¨¦ : CÆÂÚõzuõÒ |õßS £SvPøÍU öPõshx.
Note : This question paper contains four parts.

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£Sv & I / PART - I

m s e
s e SÔ¨¦ : (i) AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®.
g la 14x1=14

g la a
öPõkUP¨£mkÒÍ ©õØÖ ÂøhPÎÀ ªPÄ® Hئøh¯ Âøh°øÚz
a
(ii)

÷uº¢öukzxU SÔ±mkhß Âøh°øÚ²® ÷\ºzx GÊuÄ®.
Note : (i) Answer all the questions.

(ii) Choose the most appropriate answer from the given four alternatives and write

the option code and the corresponding answer.

[ v¸¨¦P / Turn over

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1. {(a, 8) (6, b)} BÚx J¸ \©Ûa\õº¦ GÛÀ, a ©ØÖ® b ©v¨¦PÍõÁÚ •øÓ÷¯ :
(A) (8, 6) (B) (8, 8) (C) (6, 8) (D) (6, 6)

If {(a, 8) (6, b)} represents an identity function, then the value of a and b are respectively :

(a) (8, 6) (b) (8, 8) (c) (6, 8) (d) (6, 6)

2.
3
f(x)=(x+1) −(x−1)
3
SÔ¨¤k® \õº£õÚx :
(A) ÷|›¯ \õº¦ (B) J¸ PÚa \õº¦
(C) uø»RÌ \õº¦ (D) C¸£ia \õº¦
3 3
f(x)=(x+1) −(x−1) represents a function which is :

(a) linear (b) cubic

(c) reciprocal (d) quadratic

3. 65©ØÖ® 117 &°ß «.ö£õ.Á &øÁ 65m−117 GßÓ ÁiÂÀ GÊx®÷£õx, m &°ß
©v¨¦ :
(A) 4 (B) 2 (C) 1 (D) 3

If the H.C.F of 65 and 117 is expressible in the form of 65m−117, then the value of m is :

(a) 4 (b) 2 (c) 1 (d) 3

4.
3 3 3 3
(1 +2 +3 +. . . .+15 )−(1+2+3+. . . .+15) &°ß ©v¨¦ :
(A) 14400 (B) 14200

(C) 14280 (D) 14520

3 3 3 3
The value of (1 +2 +3 +. . . .+15 )−(1+2+3+. . . .+15) is :

(a) 14400 (b) 14200

(c) 14280 (d) 14520

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5. x+y−3z=−6, −7y+7z=7, 3z=9 GßÓ öuõS¨¤ß wºÄ :

(A) x=1, y=2, z=3 (B) x=−1, y=2, z=3

(C) x=−1, y=−2, z=3 (D) x=1, y=−2, z=3

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The solution of the system x+y−3z=−6, −7y+7z=7, 3z=9 is :
.co
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(a)

e
x=1, y=2, z=3

s
(b) x=−1, y=2, z=3

l a
(c)
g l a
x=−1, y=−2, z=3 (d) x=1, y=−2, z=3 ag
a
1 3 5 7 

 
6. öPõkUP¨£mh Ao A=

2 4 6 8

&UPõÚ {øµ {µÀ ©õØÖ Ao°ß
 
9 11 13 15
 

Á›ø\ :

(A) 2× 3 (B) 3×2

m
(C) 3× 4 (D) 4×3

m .co
s e
1 3 5

g la 7 

For the given matrix A =



2 4 6a 8



the order of the matrix A
T
is :

9 11 13 15
 

(a) 2× 3 (b) 3×2

(c) 3× 4 (d) 4×3

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« ©ØÖ® « E¯µ•ÒÍ C¸ P®£[PÒ \©uÍz uøµ°À ö\[SzuõP EÒÍÚ.
11
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s e m
s e Cøh÷¯ EÒÍ öuõø»Ä GßÚ ?
g l a
g la (A) « (B) « (C) « a (D) «
a
13 14 15 12.8

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance

between their feet is 12 m, what is the distance between their tops ?

(a) 13 m (b) 14 m (c) 15 m (d) 12.8 m

[ v¸¨¦P / Turn over

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9212 4

8. 3x−y=4 ©ØÖ® x+y=8 BQ¯ ÷|ºU÷PõkPÒ \¢vUS® ¦ÒÎ :
(A) (5, 3) (B) (2, 4) (C) (3, 5) (D) (4, 4)

The point of intersection of the straight lines 3x−y=4 and x+y=8 is :

(a) (5, 3) (b) (2, 4) (c) (3, 5) (d) (4, 4)

9. x=11 GÚU öPõkUP¨£mh ÷|ºU÷Põmiß \©ß£õhõÚx :
(A) X - Aa_US Cøn
(B) Y - Aa_US Cøn
(C) Bv¨¦ÒÎ ÁÈa ö\À¾®
(D) (0, 11) GßÓ ¦ÒÎ ÁÈaö\À¾®
The straight line given by the equation x=11 is :

(a) Parallel to X axis

(b) Parallel to Y axis

(c) Passing through the origin

(d) Passing through the point (0, 11)

10. tan θ+cot θ=2 GÛÀ tan
2
θ+cot
2
θ &ß ©v¨¦ :
(A) 2 (B) 4 (C) 2 (D) 0

2 2
If tan θ+cot θ=2, then tan θ+cot θ is equal to :

(a) 2 (b) 4 (c) 2 (d) 0

11. xö\.« Bµ•ÒÍ J¸ vs©U÷PõÍ® E¸UP¨£mk A÷u Bµ•ÒÍ J¸ T®£õP
©õØÓ¨£kQÓx GÛÀ, T®¤ß E¯µ® :
(A) 3x ö\.« (B) ö\.« x (C) 4x ö\.« (D) 2x ö\.«
A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius.

The height of the cone is :

(a) 3x cm (b) x cm (c) 4x cm (d) 2x cm

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12. r
1
A»SPÒ Bµ•ÒÍ J¸ ÷Põͨ£¢x E¸UP¨£mk, r
2
A»SPÒ Bµ•øh¯
8 \©÷PõÍ £¢xPÍõP BUP¨£kQÓx GÛÀ, r
1
: r
2

(A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4

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A spherical ball of radius r units is melted to make 8 new identical balls each of radius

m 1

.co m
r units. Then r : r is :

e
2 1 2

e m l as
s
(a) 2 : 1 (b) 1 : 2 (c) 4 : 1 (d) 1 : 4

g l a ag
a
13. J¸ ¦ÒÎ ÂÁµz öuõS¨¤ß, 2
Σx =140, Σx=28 ©ØÖ® n=7 GÛÀ, Auß vmh
»UP® :

(A) 4 (B) 2 (C) 16 (D) 8

2
For a collection of data, Σx =140, Σx=28 and n=7, the standard deviation is :

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(a) 4 (b) 2 (c) 16 (d) 8

s em
g laTÇõ[PØPÒ EÒÍ J¸ SkøÁ°À C¸¢x
14. p
a
]Á¨¦, }» ©ØÖ® £aø\ {ÓU
q

J¸ ]Á¨¦ TÇõ[PÀ Gk¨£uØPõÚ {PÌuPÁõÚx :
r

q p
(A) p+q+r
(B) p+q+r

p+q p+r
(C) (D)
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p+q+r p+q+r

m
m .coThe probability of a red marble selected at random from a jar containing p red, q blue and

s e m
s e r green marbles is :

g l a
g la a
a (a)
p+q+r
q
(b)
p

p+q+r

p+q p+r
(c) (d)
p+q+r p+q+r

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£Sv & II / PART - II

SÔ¨¦ : GøÁ- ÷ ¯Ý® ÂÚõU- P - Ð US Âøh- ¯ - Î U- P - Ä ®. ÂÚõ Gs
10 28 &US
Pm-hõ-¯-©õP Âøh-¯-ÎU-PÄ®. 10x2=20

Note : Answer any ten questions. Question No. 28 is Compulsory.

15. R GßÓ EÓÄ {(x, y)/y=x+3, x e {0, 1, 2, 3, 4, 5}} GÚU öPõkUP¨£mkÒÍx. Cuß
\õº£Pzøu²®, Ãa\Pzøu²® PshÔP.
A relation R is given by the set {(x, y)/y=x+3, x e {0, 1, 2, 3, 4, 5}}. Determine its domain

and range.

16. X={−5, 1, 3, 4} ©ØÖ® GßP.
Y={a, b, c} R={(−5, a) (1, a) (3, b)} GßÓ EÓÁõÚx
X ¼¸¢x Y &US J¸ \õº£õS©õ ?
Let X={−5, 1, 3, 4} and Y={a, b, c}.

Determine whether the relation R={(−5, a) (1, a) (3, b)} is a function from X to Y ?

17. 71 ≡ x (©mk 8) GßÓ \©ß£õmøh {øÓÄ ö\´¯UTi¯ SøÓ¢u£m\ ªøP •Ê
x&ß ©v¨ø£U PõsP.
Find the least positive value of x such that 71 ≡ x (mod 8)

18. 9+3+1+. . . . . GßÓ •iÄÓõ öuõh›ß TkuÀ PõsP.
Find the sum to infinity of 9+3+1+. . . . .

2
x −16
19.
2
GÝ® ÂQu•Ö ÷PõøÁø¯ Gί ÁiÂÀ _¸USP.
x +8x+16

2
x −16
Reduce the rational expression to its lowest form.
2
x +8x+16

24
20. Kº Gs ©ØÖ® Auß uø»RÈ BQ¯ÁØÔß Âzv¯õ\® GÛÀ, A¢u
5

GsønU PõsP.
24
If the difference between a number and its reciprocal is , find the number.
5

21. a =?i−2j?
ij
GßÓ Aø©¨ø£U öPõsh 3×3 Á›ø\²øh¯ Ao°øÚU PõsP.
Construct a 3×3 matrix whose elements are given by a =?i−2j?
ij

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22. ∆ABC&°ß £UP[PÒ AB ©ØÖ® &À Aø©¢u ¦ÒÎPÒ •øÓ÷¯ ©ØÖ® .
AC D E

÷©¾® ö\.«,
AB=5.6 ö\.«,
AD=1.4 ö\.« ©ØÖ®
AC=7.2 ö\.« GÛÀ, AE=1.8

GÚU PõmkP.
DE ?? BC

D and E are respectively the points on the sides AB and AC of a ∆ABC such that AB=5.6 cm,

AD=1.4 cm, AC=7.2 cm and AE=1.8 cm, show that DE ?? BC.
m
m
c. −o BQ¯ ¦ÒÎPøÍ CønUS® ÷|ºU÷Põmiß \õ´øÁU sem .co
em
23. (14, 10) ©ØÖ® (14, 6)

PõsP.
s g l a
g la a
a
Find the slope of a line joining the points (14, 10) and (14, −6).

24. 4©ØÖ® − &I •øÓ÷¯ ©ØÖ® Aa_PÎß öÁmkzxskPÍõP öPõsh
6 x y

÷|ºU÷Põmiß \©ß£õmøhU PõsP.
Find the equation of a straight line whose intercepts on the x and y axes are 4 and −6

respectively.

o m
1 + cos θ
. c
m
25. = cosec θ + cot θ Gߣøu {¹¤UPÄ®.
1 − cos θ

s e
1 + cos θ
g la
Prove that
1 − cos θ a
= cosec θ + cot θ

26. •uÀ 21 C¯À GsPÎß vmh »UPzøuU PõsP.
Find the Standard Deviation of first 21 natural numbers.

27. J¸ £Pøh E¸mh¨£k® A÷u ÷|µzvÀ J¸ |õn¯•® _sh¨£kQÓx.
m
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£Pøh°À JØøÓ¨£øh Gs Qøh¨£uØS®, |õn¯zvÀ uø» Qøh¨£uØS©õÚ
m
.co m
{PÌuPøÁU PõsP.
m s e
s e l a
A die is rolled and a coin is tossed simultaneously. Find the Probability that the die shows an

g
la a
odd number and the coin shows a head.

ag
28. J¸ PÚa\xµzvß PÚ AÍÂØS®, AUPÚa\xµzvÝÒ \›¯õP ö£õ¸¢x® J¸
ªP¨ö£›¯ ÷PõÍzvß PÚ AÍÂØS® EÒÍ ÂQu® PõsP.
Find the ratio of the volume of a cube to that of a largest sphere which exactly fits into the

cube.

[ v¸¨¦P / Turn over

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9212 8

£Sv & III / PART - III

SÔ¨¦ : GøÁ÷¯Ý® ÂÚõU- P - Ð US Âøh- ¯ - Î U- P - Ä ®. ÂÚõ Gs
10 42 &US
Pm-hõ-¯©õ-P Âøh-¯-ÎU-P-Ä®. 10x5=50

Note : Answer any ten questions. Question No. 42 is Compulsory.

29. A={x e W/x < 2} B={x e N/1 < x ≤ 4} ©ØÖ® C={3, 5} GÛÀ, A×(B 1 C)=(A×B)1(A×C)
Gߣøua \›£õºUPÄ®.
Let A={x e W/x < 2} B={x e N/1 < x ≤ 4} and C={3, 5}. Verify that A×(B 1 C)=(A×B)1(A×C)

30. f (x)=x−1, g(x)=3x+1 ©ØÖ® h(x)=x
2
GÛÀ, (fog)oh=fo(goh) GÚ {ÖÄP.
2
If f (x)=x−1, g(x)=3x+1 and h(x)=x , then prove that (fog)oh=fo(goh).

31. &US®
300 600 &US® Cøh÷¯ &BÀ ÁS£k® AøÚzx C¯À GsPÎß TkuÀ
7

PõsP.
Find the sum of all natural numbers between 300 and 600 which are divisible by 7.

32. 3+33+333+. . . . . . GßÓ öuõhº Á›ø\°ß n - EÖ¨¦PÎß TkuÀ PõsP.
Find the sum to n terms of the series.

3+33+333+. . . . . .

1 7 
5 2 9
 
33. A=
 
B=

1 2

GÛÀ, (AB)
T
=B
T
A
T
Gߣøua \›£õºUPÄ®.
1 2 8
   
5 −1
 

1 7 
5 2 9
  T T T
If A = B= 1 2 verify that (AB) =B A .
   
1 2 8
   
5 −1
 

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34. J¸ •U÷Põnzvß ÷Põn C¸\©öÁmiPÒ J¸ ¦Ò롧 ÁȯõPa ö\À¾®
GÚU PõmkP.
Show that the angle bisectors of a triangle are concurrent.

m
35. ©ØÖ®
(8, 6), (5, 11), (−5, 12)
m (−4, 3) BQ¯ ¦ÒÎPøÍ •øÚPÍõPU öPõsh
.co
|õØPµzvß £µ¨ø£U PõsP.
.co s e m
s em l a
ag
Find the area of the quadrilateral formed by the points (8, 6), (5, 11), (−5, 12) and (−4, 3).

g la
36. ∆ABC
a
&°ß •øÚPÒ ©ØÖ® GÛÀ, •øÚ &°¼¸¢x
A(−3, 0), B(10, −2) C(12, 3) A

Áøµ¯¨£k® SzxU÷Põmiß \©ß£õmøhU PõsP.
A(−3, 0), B(10, −2) and C(12, 3) are the vertices of ∆ABC. Find the equation of the altitude

through A.

37. C¸ P¨£ÀPÒ P»[Pøµ ÂÍUPzvß C¸ £UP[Pξ® Ph¼À £¯n®
m
ö\´QßÓÚ. C¸ P¨£ÀPμ¸¢x P»[Pøµ ÂÍUPzvß Ea]°ß HØÓU
.co
÷Põn[PÒ •øÓ÷¯ ©ØÖ® BS®. P»[Pøµ ÂÍUPzvß E¯µ®
308 458

s em
« 200

GÛÀ, C¸ P¨£ÀPÐUS Cøh÷¯ EÒÍ öuõø»øÁU PõsP. (
g la) 3 = 1.732

a
Two ships are sailing in the sea on either sides of a lighthouse. The angle of elevation of the

top of the lighthouse as observed from the ships are 308 and 458 respectively. If the lighthouse

is 200 m high, find the distance between two ships. ( 3 = 1.732 )

38. }Í® « ©ØÖ® Âmh®
3 « Eøh¯ J¸ \©ß£kzx® E¸øÍø¯U öPõsk
2.8

J¸ ÷uõmh® \©ß£kzu¨£kQÓx. _ØÖPÎÀ GÆÁÍÄ £µ¨ø£ E¸øÍ \©ß8

m
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ö\´²® ?
m
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e m
long and whose diameter is 2.8 m is rolled to level a

s
s e
garden. How much area will it cover in 8 revolutions ?

g l a
g la a
a 39. Âmh® ö\.«, E¯µ® ö\.« Eøh¯ J¸ vs© ÷|ºÁmhU T®¦ Kº EÒÏhØÓ
14 8

÷PõÍ©õP E¸©õØÓ¨£kQÓx. ÷PõÍzvß öÁÎÂmh® ö\.« GÛÀ, 10

EÒÂmhzøuU PõsP.
A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow

sphere. If the external diameter of the sphere is 10 cm, find the internal diameter.

[ v¸¨¦P / Turn over

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9212 10

40. 24, 26, 33, 37, 29, 31 BQ¯ÁØÔß ©õÖ£õmkU öPÊøÁU PõsP.
Find the coefficient of variation of 24, 26, 33, 37, 29, 31.

41. Cµsk £PøhPÒ E¸mh¨£kQßÓÚ. Cµsk •P ©v¨¦PЮ \©©õP C¸UP
AÀ»x •P ©v¨¦PÎß TkuÀ BP C¸¨£uØPõÚ {PÌuPøÁU PõsP. 4

Two dice are rolled together. Find the Probability of getting a doublet or sum of faces as 4.

42. α ©ØÖ® β Gß£Ú 2
2x −3x+1=0 GÝ® C¸£ia\©ß£õmiß ‰»[PÒ GÛÀ,
1 1

2 ©ØÖ® β
2 BQ¯ÁØøÓ ‰»[PÍõPU öPõsh C¸£ia\©ß£õmøhU PõsP.
α

2
If α and β are the roots of the equation 2x −3x+1=0, then form a quadratic equation

1 1
whose roots are 2
and .
2
α β

£Sv & IV / PART - IV

SÔ¨¦ : AøÚzx ÂÚõU-P-ÐU-S® Âøh-¯-ÎU-P-Ä®. 2x8=16

Note : Answer all the questions.

3
43. (A) öPõkUP¨£mh •U÷Põn® PQR &US Jzu £UP[PÎß ÂQu® 5
GÚ
3
Aø©²©õÖ J¸ ÁiöÁõzu •U÷Põn® ÁøµP. (AÍÄ Põµo 5
< 1 )

AÀ»x
(B) ö\.« Âmh•ÒÍ Ámh® Áøµ¢x Ámhzvß ø©¯zv¼¸¢x ö\.«
6 8

öuõø»ÂÀ GßÓ ¦ÒÎø¯U SÔUPÄ®. A¨¦Òΰ¼¸¢x
P ©ØÖ® PA PB

GßÓ C¸ öuõk÷PõkPÒ Áøµ¢x AÁØÔß }Í[PøÍ AÍÂkP.
3
(a) Construct a triangle similar to a given triangle PQR with its sides equal to of the
5

3
corresponding sides of the triangle PQR. (Scale factor < 1).
5

OR

(b) Draw a circle of diameter 6 cm from a point P, which is 8 cm away from its centre.

Draw two tangents PA and PB to the circle and measure their lengths.

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44. (A) 2
GßÓ C¸£i\©ß£õmiß Áøµ£h® ÁøµP. Auß wºÄPÎß
x −6x+9=0

ußø©ø¯U PõsP.
AÀ»x

m
1
(B) GßÓ ÷|›¯ \õº¤ß Áøµ£h® ÁøµP. ÂQu\© ©õÔ¼ø¯
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y = x

m
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(b) Graph the following linear function y = x. Identify the constant of variation and
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verify it with the graph. Also (i) find y when x=9 (ii) find x when y=7.5.

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For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 12