Mathematics · Class 12 Science

Tripura Tbse Class 12 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.

2023–2025
Years of papers: 2
Total Papers: 2
Real Board Papers: 0
Sample papers: 91
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

—2026Paper not yet available

46 Q2025complete

—2024Paper not yet available

45 Q2023complete

—2022Paper not yet available

—2021Exam cancelled (COVID-19)

2026 — Paper not yet available: This year’s exam was held, but no verified question paper for this subject has been published by any source we check — the official TBSE site and the public past-paper archives. We publish only a paper we can verify against a real printed original — this one will appear here once it is.

2024 — Paper not yet available: This year’s exam was held, but no verified question paper for this subject has been published by any source we check — the official TBSE site and the public past-paper archives. We publish only a paper we can verify against a real printed original — this one will appear here once it is.

2022 — Paper not yet available: This year’s exam was held, but no verified question paper for this subject has been published by any source we check — the official TBSE site and the public past-paper archives. We publish only a paper we can verify against a real printed original — this one will appear here once it is.

2021 — Exam cancelled (COVID-19): TBSE cancelled the Class-12 Higher Secondary (+2 Stage) examination in 2021 due to COVID-19; no annual question paper was conducted or printed that year, so none exists to publish. Results were declared using an expert-committee evaluation formula.

Higher Secondary (+2 Stage) Examination 2025 · Set ANNUAL

Real board examination

About this paper

The real Class-12 board examination held in 2025. Every question below is solved the concept-first way. Sample papers are labelled honestly — never shown as a past exam.

Total marks: 80
Questions: 38
Duration: 195 min
Sections: 6

The marks / questions / duration above are the official exam pattern. We currently have 46 of this paper’s questions (121% of the full paper), with 46 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

Section	Type	Questions	Marks each	Total
ASection A	mcq	10	1	10
BSection B	very_short	10	1	10
CSection C	short	5	2	10
DSection D	short	4	3	12
ESection E	long	7	4	28
FSection F	long	2	5	10
Total		38		80

The question paper

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

Board Examination

Mathematics

Higher Secondary (+2 Stage) Examination 2025 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hr 15 minMaximum Marks: 80

General Instructions

This question paper contains 38 questions divided into 6 sections — A, B, C, D, E, F.
Section A comprises 10 questions of 1 mark each (mcq).
Section B comprises 10 questions of 1 mark each (very_short).
Section C comprises 5 questions of 2 marks each (short).
Section D comprises 4 questions of 3 marks each (short).
Section E comprises 7 questions of 4 marks each (long).
Section F comprises 2 questions of 5 marks each (long).

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

Section A

mcq · 1 mark each · 10 of 10 shown

Q1.

The degree of the differential equation

\dfrac{d^3y}{dx^3}+y=\sqrt{1+\dfrac{dy}{dx}}

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

[1]

Q2.

The area (in square units) of the region bounded by

y=x

y=3

and the

y

-axis is

(a) 2
(b) $\frac{3}{2}$
(c) $\frac{9}{2}$
(d) 4

[1]

Q3.

\vec{a}

is a unit vector and

(\vec{x}-\vec{a})\cdot(\vec{x}+\vec{a})=8

, then the value of

|\vec{x}|

(a) 3
(b) -3
(c) 9
(d) -9

[1]

Q4.

The direction cosines of the line joining the points

(4,3,-5)

and

(-2,1,-8)

are

(a) 2, 4, -13
(b) 6, 2, 3
(c) $\frac{2}{7}, \frac{4}{7}, -\frac{13}{7}$
(d) $\frac{6}{7}, \frac{2}{7}, \frac{3}{7}$

[1]

Q5.

P(A\cap B)=70\%

and

P(B)=85\%

, then

P(A/B)=

(a) $\frac{17}{14}$
(b) $\frac{14}{17}$
(c) $\frac{7}{8}$
(d) $\frac{1}{8}$

[1]

Q6.

If a function

f:R\to R

is defined by

f(x)=x^4

, then

f

(a) one-one and onto
(b) many-one and onto
(c) one-one but not onto
(d) neither one-one nor onto

[1]

Page 1 of 7

Q7.

The principal value of tan⁻¹(-√(3)) is (a) (π)/(3) (b) -(π)/(3) (c) -(π)/(4) (d) (π)/(4)

[1]

Q8.

The value of a b a; a b b; a b c is (a) -1 (b) 1 (c) 0 (d) 2

[1]

Q9.

The interval in which y=x²ex is decreasing is (a) (-∞,∞) (b) (-2,0) (c) (0,2) (d) (2,∞)

[1]

Q10.

∫ (1)/(xlog x)dx= (a) log(log x)+c (b) -(2)/(x³)+c (c) (log x)³+c (d) log x+c

[1]

Section B

very_short · 1 mark each · 10 of 10 shown

Q1.

Find the value: ∫-1¹ xe|x|dx

[1]

Q2.

Find the integrating factor of the differential equation x-(dy)/(dx)-y=x².

[1]

Q3.

Solve the differential equation dy=(1+y²)dx.

[1]

Q4.

If veca=hati+hatj-hatk and vecb=hati-hatj+hatk, find the angle between the two vectors.

[1]

Q5.

A ludo die is rolled. If the outcome is an odd number, what is the probability that it is a prime number?

[1]

Q6.

Find the value of (π)/(3)-sin⁻¹(-(1)/(2)).

[1]

Page 2 of 7

Q7.

If A=[aᵢⱼ] is a matrix of order 2× 3, where aᵢⱼ=((-i+2j)²)/(5), then find a₂₃.

[1]

Q8.

If 0 2; -1 1 A= 1 0; 0 1 , then find the matrix A.

[1]

Q9.

If 3x 7; -2 4 = 8 7; 6 4 , then find the value of x.

[1]

Q10.

Integrate: ∫ fracsin x√(1+cos x)dx

[1]

Section C

short · 2 marks each · 5 of 5 shown

Q1.

Find the value of the constant k such that f(x)= (sin x)/(kx)+k, x≠ 0\2, x=0 is continuous at the point x=0.

[2]

Q2.

The side of a square field is increasing at the rate of 0.3 cm/second. Find the rate of increase of the perimeter of the square.

[2]

Q3.

If P(A)=(1)/(4), P(B)=(1)/(3) and P(A-B)=(1)/(6), then prove that the events A and B are independent.

[2]

Q4.

Let S be the set of all real numbers and let R be a relation defined on S such that R=\(a,b): a≤ b\. Show that the relation R is reflexive but not symmetric.

[2]

Q5.

If the points (a,0), (0,b) and (1,1) are collinear, then prove that (1)/(a)+(1)/(b)=1.

[2]

Page 3 of 7

Section D

short · 3 marks each · 4 of 4 shown

Q1.

If the diagonals of a parallelogram are represented by the vectors vecd₁=2hati-hatj+hatk and vecd₂=3hati+4hatj-hatk, find its area.

[3]

Q2.

If the lines (1-x)/(3)=(7y-14)/(2λ)=(z-3)/(2) and (7-7x)/(3λ)=(y-5)/(1)=(6-z)/(5) are mutually perpendicular, find the value of λ.

[3]

Q3.

Prove that: tan⁻¹(dfrac√(1+x)-√(1-x)√(1+x)+√(1-x))=(π)/(4)-(1)/(2)cos⁻¹x, where -(1)/(√2)≤ x≤ 1.

[3]

Q4.

Find the value of ∫ ex((1)/(x)-(1)/(x²))dx

[3]

Section E

long · 4 marks each · 7 of 7 shown

Q1.

Find the value: ∫₀^π (xsin x)/(1+cos² x)dx **OR** Find the value: ∫₁⁴ dfrac√ x√(5-x)+√ xdx

[4]

Page 4 of 7

Q2.

Using integration, find the area of the region bounded by the curve y=x², x=1, x=2 and the x-axis.

[4]

Q3.

Solve the following differential equation: [xsin²((y)/(x))-y]dx+xdy=0, given that y=(π)/(4) when x=1.

[4]

Q4.

An insurance company has insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of meeting with an accident is 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

[4]

Q5.

Express the matrix 1 5; -1 2 as the sum of a symmetric matrix and a skew-symmetric matrix. **OR** If A= 3 1; -1 2 , then show that A²-5A+7I=0. Hence find A⁻¹.

[4]

Q6.

If x=a(θ-sinθ), y=a(1-cosθ), then find the value of (d²y)/(dx²) at θ=π.

[4]

Q7.

Show that the height of the largest-volume cylinder inscribed in a sphere of radius R is (2R)/(√3). **OR** Show that, among all rectangles of a given area, the square has the least perimeter.

[4]

Page 5 of 7

Section F

long · 5 marks each · 2 of 2 shown

Q1.

Solve the following linear programming problem graphically: Find the maximum and minimum value of Z, where Z=x+2y, subject to the constraints: x+2y≥ 100, 2x-y≤ 0, 2x+y≤ 200, x≥ 0, y≥ 0.

[5]

Q2.

Find the distance of the point (1,0,0) from the line (x-1)/(2)=(y+1)/(-3)=(z+10)/(8). Also find the coordinates of the foot of the perpendicular drawn from the point, and the equation of the perpendicular. **OR** The vector equations of two straight lines are given below. Find the shortest distance between them: vec r=(1-t)hat i+(t-2)hat j+(3-2t)hat k and vec r=(s+1)hat i+(2s-1)hat j-(2s+1)hat k.

[5]

Section G

Q1.

If x=t², y=t³, then find (d²y)/(dx²).

[2]

Q2.

Integrate: ∫ (dx)/(sin²xcos²x)

[2]

Q3.

Find the value of cos⁻¹(1)/(2)+2sin⁻¹(1)/(2).

[2]

Q4.

For what value of k will the matrix k 2; 3 4 have no inverse matrix?

[2]

Page 6 of 7

Section H

Q1.

If P(overlineA)=0.7, P(B)=0.7 and P(B/A)=0.5, then find the value of P(A/B).

[3]

Q2.

Find the value: ∫₀π/2(cos⁵x)/(sin⁵x+cos⁵x)dx **OR** Find the value: ∫₀¹ x(1-x)ⁿdx

[3]

Q3.

Solve: x(dy)/(dx)+y=ex

[3]

Q4.

Prove that (vec a×vec b)²+(vec a·vec b)²=|vec a|²|vec b|² **OR** Show that -hat i+hat j, -4hat i-6hat j and 5hat i+5hat j are the sides of a right-angled triangle.

[3]

Page 7 of 7