TN 11th Question Paper 2026 Mathematics

FOR TN 11TH EXAM PREPARATION

TN 11th 2026
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

TN 11th 2026 Question Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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No. of Printed Pages : 11
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9112

!9112IstYearMathematics! £vÄ Gs
Register Number

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s e
s em Pou® / MATHEMATICS
l a
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ag uªÌ ©ØÖ® B[Q» ÁÈ
( / Tamil & English Version)

Põ» AÍÄ : 3.00 ©o ÷|µ® ] [ ö©õzu ©v¨ö£sPÒ : 90

Time Allowed : 3.00 Hours ] [Maximum Marks : 90

AÔÄøµPÒ : (1) AøÚzx ÂÚõUPЮ \›¯õP¨ £vÁõQ EÒÍuõ GߣuøÚa
\›£õºzxU öPõÒÍÄ®. Aa_¨£vÂÀ SøÓ°¸¨¤ß, AøÓU
o m
c
PsPõo¨£õÍ›h® EhÚi¯õPz öu›ÂUPÄ®.
. ø©°øÚ ©mk÷© GÊxÁuØS®,
(2) }»® AÀ»x P¸¨¦
e m
AiU÷PõikÁuØS®
l as£¯ß£kzu ÷Ásk®. £h[PÒ ÁøµÁuØS
ag
ö£ß]À £¯ß£kzuÄ®.

Instructions : (1) 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.

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£Sv & I / PART - I

m s e
s e SÔ¨¦ : (i) AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®.
g la 20x1=20

g la a ªPÄ® Hئøh¯
öPõkUP¨£mkÒÍ |õßS ©õØÖ ÂøhPÎÀ
a
(ii)

Âøhø¯z ÷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. 3EÖ¨¦PÒ öPõsh Pnzvß «uõÚ öuõhº¦PÎß GsoUøP :
(A) (B)
512 (C) (D) 9 1024 81

The number of relations on a set containing 3 elements is :

(a) 512 (b) 9 (c) 1024 (d) 81

2. f : [−3, 3] → S GßÓ \õº¦ f (x)=x 2
GÚ Áøµ¯ÖUP¨£mk ÷©Ø÷PõºzuÀ GÛÀ,
SGߣx :
(A) [−3, 3] (B) [−9, 9] (C) [0, 9] (D) R

2
If the function f : [−3, 3] → S defined by f (x)=x is onto, then S is :

(a) [−3, 3] (b) [−9, 9] (c) [0, 9] (d) R

3. ?x+2? ≤ 9 GÛÀ, Aø©²® CøhöÁÎ :
x

(A) (−∞, −7) c (B) [11, ∞) (−∞, −7)

(C) (−11, 7) (D) [−11, 7]

If ?x+2? ≤ 9, then x belongs to :

(a) (−∞, −7) c [11, ∞) (b) (−∞, −7)

(c) (−11, 7) (d) [−11, 7]

4. log
3
11 ⋅ log
11
13 ⋅ log
13
15 ⋅ log
15
27 &ß ©v¨¦ :
(A) 3 (B) 1 (C) 4 (D) 2

The value of log 11 ⋅ log 13 ⋅ log 15 ⋅ log 27 is :
3 11 13 15

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

5. cos18+cos28+cos38+. . .+cos1798=

(A) −1 (B) 0 (C) 89 (D) 1

cos18+cos28+cos38+. . .+cos1798=

(a) −1 (b) 0 (c) 89 (d) 1

6. ¤ßÁ¸ÁÚÁØÔÀ Gx \›¯õÚuÀ» ?
3
(A) tanθ=25 (B) sinθ =−
4

1
(C) sec θ =
4
(D) cosθ=−1

Which of the following is not true ?

3
(a) tanθ=25 (b) sin θ =−
4

1
(c) sec θ = (d) cosθ=−1
4

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7. 44‰ø»Âmh[PÒ EÒÍ J¸ £»÷Põnzvß £UP[PÎß GsoUøP :
(A) 11 (B) (C) (D) 4 22 4!

Number of sides of a polygon having 44 diagonals is :

(a) 11 (b) 4 (c) 22 (d) 4!

8. C¸ ªøP GsPÎß Tmka \µõ\› ©ØÖ® ö£¸USa \µõ\› •øÓ÷¯ 16 ©ØÖ®
m
8GÛÀ, AÁØÔß Cø\a\µõ\› :
m .co
(A) 5 (B) (C)
.co (D) 10 4 6

s e m
em a
The HM of two positive numbers whose AM and GM are 16, 8 respectively is :

s l
la GßÓ ¦Ò롧 {¯©¨£õøu : ag
(a) 5 (b) 10 (c) 4 (d) 6

9.

ag
(a cosθ, b sinθ)

2 2
x y
(A) 2
x +y =a
2 2
(B) 2
−
2
=1
a b

2 2
x y
(C) 2
y =4ax (D) 2
+
2
=1
a b

Which of the following equations is the locus of (a cosθ, b sinθ) ?

m
2 2

c. o
x y
2 2 2 =1
(a) x +y =a (b) −
2 2
a b

s em 2 2

la
x y
2 =1
(c) y =4ax (d) +

g
2 2
a b

10. y=−xGßÓ ÷PõmiØS (2, 3)
a ¦Ò롧 ¤®£¨¦ÒÎ :
GßÓ
(A) (B)
(−2, −3) (−3, −2) (C) (3, 2) (D) (−3, 2)

The image of the point (2, 3) in the line y=−x is :

(a) (−2, −3) (b) (−3, −2) (c) (3, 2) (d) (−3, 2)

 λ 1 
11. A=
 
GÛÀ, λ &ß G®©v¨¦PÐUS 2
A =0 ?
−1 −λ
 

m
.co
(A) −1 (B) 0 (C) 1 (D) ±1

m
.co m
 λ 1 

e
2
If A = , then for what value of λ, A =0 ?
 

e m 
−1 −λ


l as
las (a) −1 (b) 0 (c) 1

ag (d) ±1

ag 12. Gߣx :
→
(A) 0 (B) (C) (D)
The value of is :

→
(a) 0 (b) (c) (d)

[ v¸¨¦P / Turn over

m .
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→ → → → → →
13. a = 13, b =5 ©ØÖ® a ⋅ b = 60 GÛÀ, a × b &ß ©v¨¦ :
(A) 45 (B) 15 (C) 25 (D) 35

→ → → → → →
If a = 13, b =5 and a ⋅ b = 60 , then a × b is :

(a) 45 (b) 15 (c) 25 (d) 35

1
14. f (x) = GÝ® \õº¦ G[S öuõhºa]¯õÚx ?
x

(A) (−∞, 0] (B) R (C) [0, ∞) (D) R−{0}

1
f (x) = is continuous at :
x

(a) (−∞, 0] (b) R (c) [0, ∞) (d) R−{0}

15. y=mx+c ©ØÖ® f (0)=f '(0)=1 GÛÀ, f (2) Gߣx :
(A) 3 (B) 1 (C) −3 (D) 2

If y=mx+c and f (0)=f '(0)=1, then f (2) is :

(a) 3 (b) 1 (c) −3 (d) 2

16. f (x)=?x−5? GÛÀ, &ß ©v¨¦ :
f '(7)

(A) −1 (B) 1 (C) 5 (D) 7

Find f '(7) if f (x)=?x−5?

(a) −1 (b) 1 (c) 5 (d) 7

17.
∫ f ( x )dx = g(x ) + c GÛÀ, ∫ f ( x ) g'(x )dx Gߣx :
2
(A) ∫ f '( x ) g(x )dx (B) ∫ ( f (x ) ) dx

2
(C) ∫ ( g(x ) ) dx (D) ∫ f ( x ) g(x )dx

If
∫ f ( x )dx = g(x ) + c , then ∫ f ( x ) g'(x )dx is :

2
(a)
∫ f '( x ) g(x )dx (b)
∫ ( f (x ) ) dx

2
(c)
∫ g(x )
( ) dx (d)
∫ f ( x ) g(x )dx

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∫e
x
18. dx =

(A) 2e
x
( 1− x ) +c
(B) 2 x ( 1−e
x
) +c

(C) (D) ( )
m
2e
x
( x −1 ) +c 2 x e
x
−1 +c

m .co
.co
∫e
m
x
dx =

s e
s em) ( ) l a
ag
x
(a) ( (b) 2 1−e +c

l(a )
x
2e 1− x +c x

(c) 2e
ag x
x −1 +c (d)
2 x ( e
x
−1 ) +c

19. GßÓ Pnzv¼¸¢x J¸ Gs ÷uº¢öukUP¨£kQÓx. A¢u Gs
{1, 2, 3, . . ., 20}

3 AÀ»x BÀ ÁS£kÁuØPõÚ {PÌuPÄ :
4

1 2 2 1
(A) 2
(B) 5
(C) 3
(D) 8

A number is selected from the set{1, 2, 3, . . ., 20}. The Probability that the selected number is

divisible by 3 or 4 is :

m
1 2
.co 2 1

em
(a) (b) (c) (d)
2 5 3 8

s
la SøÓ¢ux
20.
ag
£zx |õn¯[PøÍa _sk®÷£õx 8 uø»PÒ Qøh¨£uØPõÚ
{PÌuPÄ :
7 7 7 7
(A) 16
(B) 64
(C) 128
(D) 32

Ten coins are tossed. The Probability of getting at least 8 heads is :

7 7 7 7
(a) (b) (c) (d)
16 64 128 32

m
c o m mGs
£Sv & II / PART - II
.co
. s e
em
SÔ¨¦ : GøÁ÷¯Ý® HÊ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ 30 &US
s Pmhõ¯©õP Âøh¯ÎUPÄ®.
g l a 7x2=14

la a
ag
Note : Answer any seven questions. Question No. 30 is compulsory.

21.
3
x −x −17x=22
2
&ß J¸ ‰»® x=−2 GÛÀ, ¤Ó ‰»[PøÍU PõsP.
3 2
If x=−2 is one root of x −x −17x=22, then find the other roots of the equation.

22.
n
C
12
= C
n
9
GÛÀ, 21
C
n
&IU PõsP.
n n 21
If C = C , find C .
12 9 n

[ v¸¨¦P / Turn over

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23. (x+y)
7
&ß Â›ÂÀ ø©¯ EÖ¨¦PøÍU PõsP.
7
Find the middle terms in the expansion of (x+y) .

24. 5x+12y−3=0 GßÓ ÷PõmiØS® (1, 2) GßÓ ¦ÒÎUS® Cøh÷¯ EÒÍ yµ®
PõsP.
Find the distance from a point (1, 2) to the line 5x+12y−3=0.

0 c b

 
25. A=

c 0 a

GÛÀ, A
2
&IU PõsP.
b a 0
 

0 c b

  2
If A = c 0 a , compute A
 
b a 0
 

2026 2023 0

26. ©v¨¦ PõsP : 2025 2022 1

2024 2021 0

2026 2023 0

Evaluate 2025 2022 1

2024 2021 0

→ ∧ ∧ → ∧ ∧ ∧ → →
27. a =3 i +4 j ©ØÖ® b = i + j + k GÛÀ a × b &ß ©v¨ø£U PõsP.
→ → → ∧ ∧ → ∧ ∧ ∧
Find a × b , where a =3 i +4 j and b = i + j + k

28. f (x)=2x +3x−5
2
BÚx R &ß GÀ»õ ¦ÒÎPξ® öuõhºa]¯õÚx GÚ {ÖÄP.
2
Prove that f (x)=2x +3x−5 is continuous at all points in R.

29. (i) J¸ \õuõµn Á¸hzvÀ J¸ ½¨ Á¸hzvÀ (ii)

53 bõ°ØÖU QÇø©PÒ Á¸ÁuØPõÚ {PÌuPÄPøÍU PõsP.
What is the Probability that (i) non-leap year (ii) leap year should have 53 Sundays ?

11
lim x −1
30. PnUQkP : x →1 x −1

11
lim x −1
Calculate
x →1 x −1

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£Sv & III / PART - III

SÔ¨¦ : GøÁ÷¯Ý® HÊ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 40 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 7x3=21

Note : Answer any seven questions. Question No. 40 is compulsory.

m
m
1 B)=3 ©ØÖ® n(A c B)=10 GÛÀ, n(P(A∆B)) PõsP.
.co
.co
31. n(A

1 B)=3 and n(A c B)=10, then find n(P(A∆B)).
e m
s
If n(A

e m l a
las
£Sv ¤ßÚ[PÍõP¨ ¤›UPÄ® :
1

ag
g
32.

a
2 2
x −7

1
Resolve into Partial fractions :
2 2
x −7

33. 5 ö\.«. Bµ®, ø©¯U ÷Põn® 158 &I öPõsh Ámh ÂÀ¼ß }Í® PõsP.
Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring 158.

(2n )!
( 1.3.5. . . ( 2n − 1) ) GÚ {ÖÄP.
m
n
34. =2

.co
n!

(2n )!

e m
s
Prove that =2
n
( 1.3.5. . . ( 2n − 1) )
la
n!

35. 3
65 &ß ©v¨¦ PõsP. ag
3
Find the value of 65

36. 3x + y + 4 = 0 GßÓ ÷Põmøha ö\[Szx ÁiÁzvØS ©õØÖP.
Rewrite 3x + y + 4 = 0 into normal form.

m
.co
∧ ∧ ∧ ∧ ∧ ∧ ∧ ∧ ∧
37. ©ØÖ® BQ¯ öÁUhºPÒ J¸ ö\[÷Põn
m
− i − 2 j − 6 k, 2 i − j + k − i + 3 j +5k

m .co•U÷Põnzøu Aø©US® GÚU PõmkP.
s e m
s e ∧ ∧ ∧ ∧ ∧ ∧ ∧ ∧
g l a ∧

la
Show that the vectors − i − 2 j − 6 k , 2 i − j + k and − i + 3 j + 5 k form a right angled

g a
a
triangle.

dy
38. x=a(t−sint), y=a(1−cost) GÛÀ, PõsP.
dx

dy
Find if x=a(t−sint), y=a(1−cost)
dx

[ v¸¨¦P / Turn over

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39. ‰ßÖ |õn¯[PÒ J÷µ \©¯zvÀ _sh¨£kQßÓÚ. \›¯õP J¸ uø» (i)

SøÓ¢ux J¸ uø»
(ii) AvP£m\©õP J¸ uø» Qøh¨£uØPõÚ (iii)

{PÌuPÄPøÍU PõsP.
Three coins are tossed simultaneously. What is the probability of getting (i) exactly one head

(ii) at least one head (iii) at most one head ?

2x + 3
40. ©v¨¤kP : ∫ 2
dx
x + 3x + 7

2x + 3
Evaluate :
∫ 2
dx
x + 3x + 7

£Sv & IV / PART - IV

SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 7x5=35

Note : Answer all the questions.

41. (A) −x + 4 ; −∞ < x ≤ − 3


x +4 ; − 3 < x <− 2

 2
f (x) = x −x ; − 2≤ x < 1

 2
x −x ; 1 ≤ x < 7



0 ; ©ØÓ Ch[PÎÀ

GÚ Áøµ¯ÖUP¨£iß BQ¯ÁØÔÀ &ß ©v¨¦PøÍU PõsP. −4, 1, −2, 7, 0 f

AÀ»x
(B) 12x
2
GßÓ \©ß£õk Cµmøh ÷|º÷PõmkPÎß
+7 xy −12y
2
−x +7y+ k=0

\©ß£õmøhU SÔzuõÀ &ß ©v¨ø£U PõsP. ÷©¾® AøÁ Cøn¯õ k

AÀ»x öÁmiU öPõÒ£øÁ¯õ GÚU PõsP.
(a) Write the values of f at −4, 1, −2, 7, 0 if

−x + 4 ; −∞ < x ≤ − 3


x +4 ; − 3 < x <− 2

 2
f ( x ) = x −x ; − 2 ≤x < 1

 2
x −x ; 1 ≤x < 7


0 ; otherwise


OR

2 2
(b) Find the value of k, if the following equation 12x +7xy−12y −x+7y+k=0 represents

a pair of straight lines. Further, find whether these lines are parallel or intersecting.

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42. (A) Z&À m−n BÚx BÀ ÁS£kö©ÛÀ 11 GÚz öuõhº¦ mRn R Áøµ¯ÖUP¨
£mhõÀ R Gߣx \©õÚz öuõhº¦ GÚ {¹¤UP.
AÀ»x
cos(180
− θ ) sin(90
+ θ ) sec(− θ )
(B) =1 GÚ {ÖÄP.
m
.co
sin(270
− θ ) cot(− θ) tan(360
− θ )

m
(a)

.co
In the set Z of integers, define mRn if m− n is divisible by 11.

m
Prove that R is an

s e m
a
equivalence relation.

s e l
a ag
OR

g l
(b) a
Prove that
cos(180
− θ ) sin(90
+ θ ) sec(− θ )

sin(270
− θ ) cot(− θ ) tan(360
− θ )
=1

−1
43. (A) y=e
tan x
GÛÀ, 2
(1+x )y''+(2x−1)y'=0 GÚU PõmkP.
AÀ»x
b+ c a− c a− b

m
.co
(B) b− c c+ a b − a = 8 abc GÚ {ÖÄP.
c− b c− a a+ b

e m
s
−1

la
tan x 2
(a) If y=e , show that (1+x )y''+(2x−1)y'=0

ag OR

b+ c a− c a− b

(b) Show that b− c c+ a b − a = 8 abc

c− b c− a a+ b

44. (A) ABCD GßÓ |õØPµzvÀ &ß |k¨¦ÒÎPÒ
AC, BD E ©ØÖ® F BP C¸¨¤ß
GÚ {ÖÄP.
m
om
c. (B)
AÀ»x
m .co
m x +3
s e
s e ©v¨¤kP : ∫ 2
dx

g l a
la
(x + 2) (x + 1)

g a
a (a) If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively,

then prove that

OR

x +3
(b) Evaluate :
∫ 2
dx
(x + 2) (x + 1)

[ v¸¨¦P / Turn over

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75 5 32
45. (A) log − 2 log + log = log 2 GÚ {ÖÄP.
16 9 243

AÀ»x

(B) Pouz öuõSzuÔuÀ ‰»®, GÀ»õ •Ê GsPÒ n/1 &US

2 2 2 2
n(n + 1)(2n + 1)
1 +2 +3 + ⋅ ⋅ ⋅ +n = GÚ {ÖÄP.
6

75 5 32
(a) Prove that log − 2 log + log = log 2
16 9 243

OR

(b) By the principle of mathematical induction, prove that, for all integers n / 1,

2 2 2 2 n(n + 1)(2n + 1)
1 +2 +3 + ⋅ ⋅ ⋅ +n =
6

k−1
46. (A) θ+φ=α ©ØÖ® tanθ=k tanφ GÛÀ, sin(θ − φ ) = sin α GÚ {ÖÄP.
k+1

AÀ»x

3 3
(B) x J¸ ÷uøÁ¯õÚ AÍ»õÚ ö£›¯ Gs GÛÀ, x
3
+6 − x
3
+3 &ß
1
©v¨ø£z ÷uõµõ¯©õP 2
GÚ {ÖÄP.
x

k−1
(a) If θ+φ=α and tanθ=k tanφ, then prove that sin(θ − φ ) = sin α
k+1

OR

1
3 3 3 3
(b) Prove that x +6 − x +3 is approximately equal to when x is sufficiently
2
x

large.

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lim  1  2  15  
47. (A) + x
 
+
 
+. . .+
 
= 120 GÚ {ÖÄP.
 x  x  x 
x →0

AÀ»x

m
(B) Jzu C¸ áõiPÎÀ, JßÔÀ P¸¨¦ ©ØÖ® ]Á¨¦ {Ó £¢xPÒ EÒÍÚ. 6 4

m
©ØöÓõ¸ áõi°À P¸¨¦ ©ØÖ® ]Á¨¦ {Ó £¢xPÒ EÒÍÚ. \©Áõ´¨¦
2 2

.co
.co
•øÓ°À J¸ áõi ÷uº¢öukUP¨£mk Av¼¸¢x J¸ £¢x GkUP¨
m s e m
£kQÓx.
s e l a
l a
A¨£¢x P¸¨£õP C¸¨£uØPõÚ {PÌuPøÁU PõsP.
(i)

g ag
a
GkUP¨£mh £¢x P¸¨¦ GÛÀ, •uÀ áõi°¼¸¢x GkUP¨£mh
(ii)

uØPõÚ {PÌuPÄ ¯õx ?
lim  1  2  15  
(a) Show that : + +. . .+ = 120
+ x
     
 x  x  x 
x →0

OR

(b) There are two identical urns containing respectively, 6 black and 4 red balls, 2 black

and 2 red balls. An urn is chosen at random and a ball is drawn from it.

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(i) Find the probability that the ball is black.

(ii)
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If the ball is black, what is the probability that it is from the first urn ?

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