Mathematics · Class 11 Science

Puducherry Tnboard Class 11 Mathematics — Real Previous-Year Papers

with complete answers

Real previous-year board papers, year by year — the official exam pattern, the full question paper, and every question solved the concept-first way. Distinct from the chapter-wise textbook bank.

2018–2026
Years of papers: 8
Total Papers: 8
Real Board Papers: 0
Sample papers: 379
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

47 Q2026complete

47 Q2025complete

47 Q2024complete

50 Q2023complete

47 Q2022complete

—2021No regular exam held this year

47 Q2020complete

47 Q2019complete

47 Q2018complete

2021 — No regular exam held this year: Tamil Nadu cancelled the March 2021 Class 9/10/11 Public Examinations outright (COVID-19 2nd wave) — students were promoted using their quarterly/half-yearly marks, so no genuine full-cohort exam was ever sat. The single "September 2021" paper on DGE’s own archive that year is a private-candidate/improvement sitting, not the regular annual exam, so it is not published here (mirrors this platform’s standing "main sitting only" convention, applied identically to TN-DGE’s Class-12 2021 papers).

Tamil Nadu HSC First Year (DGE) Board 2026 · Set ANNUAL

Real board examination

About this paper

The real Class-12 board examination held in 2026. Every question below is solved the concept-first way. Sample papers are labelled honestly — never shown as a past exam.

Total marks: 90
Questions: 47
Duration: 180 min
Sections: 4

The marks / questions / duration above are the official exam pattern. We currently have 47 of this paper’s questions (100% of the full paper), with 47 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

Section	Type	Questions	Marks each	Total
ISection I	mcq	20	1	20
IISection II	short_answer_choice	7	2	14
IIISection III	short_answer_choice	7	3	21
IVSection IV	long_answer_or	7	5	35
Total		47		90

The question paper

The questions we hold for this paper, laid out by section. Solutions are on the Answers tab.

Board Examination

Mathematics

Tamil Nadu HSC First Year (DGE) Board 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 90

General Instructions

This question paper contains 47 questions divided into 4 sections — I, II, III, IV.
Section I comprises 20 questions of 1 mark each (mcq).
Section II comprises 7 questions of 2 marks each (short_answer_choice).
Section III comprises 7 questions of 3 marks each (short_answer_choice).
Section IV comprises 7 questions of 5 marks each (long_answer_or).

Above is the official exam pattern. The questions printed below are those we currently hold for this paper.

Section A

Q1.

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

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

[1]

Q2.

If the function

f : [-3, 3] \to S

defined by

f(x) = x^2

is onto, then

S

is:

(a) $[-3, 3]$
(b) $[-9, 9]$
(c) $[0, 9]$
(d) $\mathbb{R}$

[1]

Q3.

|x + 2| \le 9

, then

x

belongs to:

(a) $(-\infty, -7) \cup [11, \infty)$
(b) $(-\infty, -7)$
(c) $(-11, 7)$
(d) $[-11, 7]$

[1]

Q4.

The value of

\log_3 11 \cdot \log_{11} 13 \cdot \log_{13} 15 \cdot \log_{15} 27

is:

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

[1]

Q5.

\cos 1^\circ + \cos 2^\circ + \cos 3^\circ + \ldots + \cos 179^\circ =

(a) $-1$
(b) $0$
(c) $89$
(d) $1$

[1]

Q6.

Which of the following is not true?

(a) $\tan\theta = 25$
(b) $\sin\theta = -\dfrac{3}{4}$
(c) $\sec\theta = \dfrac{1}{4}$
(d) $\cos\theta = -1$

[1]

Q7.

Number of sides of a polygon having 44 diagonals is:

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

[1]

Page 1 of 7

Q8.

The HM of two positive numbers whose AM and GM are 16, 8 respectively is: (a) 5 (b) 10 (c) 4 (d) 6

[1]

Q9.

Which of the following equations is the locus of (acosθ, bsinθ)? (a) x²+y²=a² (b) (x²)/(a²)-(y²)/(b²)=1 (c) y²=4ax (d) (x²)/(a²)+(y²)/(b²)=1

[1]

Q10.

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)

[1]

Q11.

If A = λ 1\-1 -λ , then for what value of λ, A²=0? (a) -1 (b) 0 (c) 1 (d) ± 1

[1]

Q12.

The value of overrightarrowAB+overrightarrowBC+overrightarrowDA+overrightarrowCD is: (a) vec0 (b) overrightarrowAD (c) -overrightarrowAD (d) overrightarrowCA

[1]

Q13.

[1]

Q14.

f(x)=(1)/(x) is continuous at: (a) (-∞, 0] (b) mathbbR (c) [0, ∞) (d) mathbbR-\0\

[1]

Q15.

If y = mx + c and f(0) = f'(0) = 1, then f(2) is: (a) 3 (b) 1 (c) -3 (d) 2

[1]

Q16.

Find f'(7) if f(x) = |x - 5| (a) -1 (b) 1 (c) 5 (d) 7

[1]

Q17.

If ∫ f(x)dx = g(x) + c, then ∫ f(x) g'(x)dx is: (a) ∫ f'(x) g(x)dx (b) ∫ (f(x))² dx (c) ∫ (g(x))² dx (d) ∫ f(x) g(x)dx

[1]

Page 2 of 7

Q18.

∫ e√(x) dx = (a) 2e√(x)(1-√(x))+c (b) 2√(x)(1-e√(x))+c (c) 2e√(x)(√(x)-1)+c (d) 2√(x)(e√(x)-1)+c

[1]

Q19.

A number is selected from the set \1, 2, 3, …, 20\. The Probability that the selected number is divisible by 3 or 4 is: (a) (1)/(2) (b) (2)/(5) (c) (2)/(3) (d) (1)/(8)

[1]

Q20.

Ten coins are tossed. The Probability of getting at least 8 heads is: (a) (7)/(16) (b) (7)/(64) (c) (7)/(128) (d) (7)/(32)

[1]

Section B

Q1.

If x = -2 is one root of x³ - x² - 17x = 22, then find the other roots of the equation.

[2]

Q2.

If ⁿC₁₂ = ⁿC₉, find ²¹Cₙ.

[2]

Q3.

Find the middle terms in the expansion of (x+y)⁷.

[2]

Q4.

Find the distance from a point (1, 2) to the line 5x + 12y - 3 = 0.

[2]

Q5.

If A = 0 c bc 0 ab a 0 , compute A²

[2]

Page 3 of 7

Q6.

Evaluate 2026 2023 0\2025 2022 1\2024 2021 0

[2]

Q7.

Find |veca×vecb|, where veca = 3hati+4hatj and vecb = hati+hatj+hatk

[2]

Q8.

Prove that f(x)=2x²+3x-5 is continuous at all points in mathbbR.

[2]

Q9.

What is the Probability that (i) non-leap year (ii) leap year should have 53 Sundays?

[2]

Q10.

Calculate limlimitsx→ 1 dfracx¹¹-1x-1

[2]

Section C

Q1.

If n(A∩ B)=3 and n(A∪ B)=10, then find n(P(AΔ B)).

[3]

Q2.

Resolve into Partial fractions: (1)/(x²-7²)

[3]

Page 4 of 7

Q3.

Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring 15^°.

[3]

Q4.

Prove that ((2n)!)/(n!) = 2ⁿ(1.3.5…(2n-1))

[3]

Q5.

Find the value of √[3]65

[3]

Q6.

Rewrite √(3)x + y + 4 = 0 into normal form.

[3]

Q7.

Show that the vectors -hati-2hatj-6hatk, 2hati-hatj+hatk and -hati+3hatj+5hatk form a right angled triangle.

[3]

Q8.

Find (dy)/(dx) if x=a(t-sin t), y=a(1-cos t)

[3]

Q9.

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?

[3]

Page 5 of 7

Q10.

Evaluate: ∫ (2x+3)/(x²+3x+7) dx

[3]

Section D

Q1.

Write the values of f at -4, 1, -2, 7, 0 if f(x)= -x+4 ; -∞<x≤ -3x+4 ; -3<x<-2x²-x ; -2≤ x<1x-x² ; 1≤ x<7\0 ; otherwise **OR** Find the value of k, if the following equation 12x²+7xy-12y²-x+7y+k=0 represents a pair of straight lines. Further, find whether these lines are parallel or intersecting.

[5]

Q2.

In the set mathbbZ of integers, define mRn if m-n is divisible by 11. Prove that R is an equivalence relation. **OR** Prove that (cos(180^°-θ)sin(90^°+θ)sec(-θ))/(sin(270^°-θ)cot(-θ)tan(360^°-θ)) = 1

[5]

Q3.

If y=e^tan⁻¹x, show that (1+x²)y''+(2x-1)y'=0 **OR** Show that b+c a-c a-bb-c c+a b-ac-b c-a a+b = 8abc

[5]

Q4.

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then prove that overrightarrowAB+overrightarrowAD+overrightarrowCB+overrightarrowCD=4overrightarrowEF **OR** Evaluate: ∫ (x+3)/((x+2)²(x+1)) dx

[5]

Page 6 of 7

Q5.

Prove that log(75)/(16)-2log(5)/(9)+log(32)/(243)=log 2 **OR** By the principle of mathematical induction, prove that, for all integers n≥ 1, 1²+2²+3²+…+n²=(n(n+1)(2n+1))/(6)

[5]

Q6.

If θ+φ=α and tanθ=ktanφ, then prove that sin(θ-φ)=(k-1)/(k+1)sinα **OR** Prove that √[3]x³+6-√[3]x³+3 is approximately equal to (1)/(x²) when x is sufficiently large.

[5]

Q7.

Show that: limx→ 0^+ x[lfloor(1)/(x)rfloor+lfloor(2)/(x)rfloor+…+lfloor(15)/(x)rfloor]=120 **OR** 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. (i) Find the probability that the ball is black. (ii) If the ball is black, what is the probability that it is from the first urn?

[5]

Page 7 of 7