Mathematics · Class 12 Science

Kerala Dhse 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.

2013–2026
Years of papers: 13
Total Papers: 13
Real Board Papers: 0
Sample papers: 283
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

20 Q2026complete

25 Q2025complete

20 Q2024complete

20 Q2023complete

36 Q2022complete

29 Q2021complete

—2020Paper not available

24 Q2019complete

24 Q2018complete

16 Q2017complete

16 Q2016complete

18 Q2015complete

18 Q2014complete

17 Q2013complete

2020 — Paper not available: The Kerala DHSE exam was held this year — COVID-19 disrupted the 2020 timetable but never cancelled it — but no verified question paper for this subject has been found from the sources we check. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

Kerala DHSE Plus Two 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: 60
Questions: 20
Duration: 120 min
Sections: 3

The marks / questions / duration above are the official exam pattern. We currently have 20 of this paper’s questions (100% of the full paper), with 20 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	choice	8	3	24
BSection B	choice	8	4	32
CSection C	choice	4	6	24
Total		20		60

The question paper

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

Board Examination

Mathematics

Kerala DHSE Plus Two Board 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 2 hoursMaximum Marks: 60

General Instructions

This question paper contains 20 questions divided into 3 sections — A, B, C.
Section A comprises 8 questions of 3 marks each (choice).
Section B comprises 8 questions of 4 marks each (choice).
Section C comprises 4 questions of 6 marks each (choice).

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

Section A

choice · 3 marks each · 8 of 8 shown

Q1.

Consider the matrices P = [[3, -1, 2], [-2, 1, 4]], Q = [[4, -2, 1], [-5, 3, 1]] and R = [[3, 0, 0], [0, 3, 0], [0, 0, 3]].

(i) The order of the matrix PR is ______.
(1)
(ii) Show that PR = 3P.
(1)
(iii) Find 3P + Q. (1)

[3]

Q2.

Consider the relation R = {(x, y) : x, y ∈ A, x = y} defined on the set A = {1, 2, 3, 4}.

(i) Show that R is an equivalence relation.
(2)
(ii) Hence write the equivalence classes. (1)

[3]

Q3.

(i) Evaluate ∫ (from 0 to π) sin x dx.

(2)
(ii) Hence find the area formed by the curve y = sin x between x = 0 and x = 2π. (1)

[3]

Q4.

Let P(3, -1, 2) and Q(3, 6, 4) be two points in space.

(i) Find the vector PQ→.
(1)
(ii) Which of the following is perpendicular to PQ→?
(a) 5ĵ
(b) î
(c) î − ĵ
(d) ĵ + k̂
(1)
(iii) Hence find the angle between vector PQ→ and the vector 3î + 4ĵ. (1)

[3]

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Q5.

(i) Find the principal value of cos⁻¹(−1/2). (1) (ii) Express tan⁻¹(cos x / (1 − sin x)) in the simplest form. (2)

[3]

Q6.

(i) Check the continuity of the function f(x) = x², x < 2; 4, x > 2. (2) (ii) Find dy/dx if y = √(sin(2x + 1)). (1)

[3]

Q7.

Consider the function f(x) = x, x ≤ 2; x − 1, x > 2 defined on set of natural numbers ℕ. Check whether f(x) is one-one and onto.

[3]

Q8.

A fair coin and an unbiased die are tossed together. Let A: "Head appears on the coin" and B: "3 appears on the die" be two events. Check whether A and B are independent events.

[3]

Section B

choice · 4 marks each · 8 of 8 shown

Q1.

Consider the matrix A = [[2, -3, 1], [4, -2, 1], [5, 1, 3]]. (i) Find the cofactors C31, C32, C33 of the elements 5, 1, 3. (1) (ii) Which of the following is the value of 5 × C31 + 1 × C32 + 3 × C33? (a) 0 (b) 1 (c) |A| (d) 2|A| (1) (iii) Find a symmetric matrix using A. (2)

[4]

Q2.

Find ∫ (3x + 1) / ((x − 1)(x² + 1)) dx.

[4]

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Q3.

(i) Observe the graph of f'(x) (derivative of the function f(x)) given below and answer the following questions. (a) Write the interval in which the function f(x) is decreasing. (1) (b) Find the local maximum and local minimum points of the function f(x). (1) (ii) Find the absolute maximum and absolute minimum value of the function g(x) = |x| + 2, in the interval [−2, 4]. (2)

[4]

Q4.

(i) The length x of a rectangle is decreasing at the rate of 4 cm/s and the width y is increasing at the rate of 3 cm/s. Find the rate of change of perimeter. (1) (ii) Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone. (3)

[4]

Q5.

(i) If A(x) = ∫ (from 0 to x) x² dx is the area function, then A'(2) is (a) 4 (b) 2 (c) 0 (d) 1 (1) (ii) The figure given below represents the curve y = (x − 1)² − 1. Find the area of the shaded region. (3)

[4]

Q6.

(i) If a directed line has direction ratios l = 1/2, m = √3/2, then which of the following is its direction angle with the positive direction of z-axis? (a) 30° (b) 45° (c) 60° (d) 90° (1) (ii) The adjacent sides of a parallelogram are a→ = 3î − ĵ + 2k̂, b→ = 4î + 2ĵ + 6k̂. (a) Write a vector parallel to its diagonal. (1) (b) Find the area of the parallelogram. (2)

[4]

Q7.

Find the shortest distance between the skew lines (x + 1)/3 = (y − 1)/2 = (z − 9)/1 and (x − 2)/2 = (y + 1)/1 = (z + 1)/1.

[4]

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Q8.

A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike, and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time.

[4]

Section C

choice · 6 marks each · 4 of 4 shown

Q1.

Solve system of linear equations, using matrix method: x + y + 3z = 16 3x + 2y − 5z = 6 2x + y + 2z = 10

[6]

Q2.

(i) Find dy/dx if x = a(θ − sin θ), y = a(1 + sin θ). (1) (ii) If eʸ(x + 1) = 1, show that d²y/dx² = (dy/dx)². (2) (iii) Find ∫ (from 0 to π) x/(1 + sin x) dx. (3)

[6]

Q3.

Consider the linear programming problem: Objective function: Z = 2x + 3y Subject to the constraints: x + 2y ≤ 10, x + y ≤ 8, x ≥ 0, y ≥ 0 (i) Mark the feasible region. (2) (ii) Write the corner points. (2) (iii) Find the maximum value of objective function Z. (2)

[6]

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Q4.

(i) Solve the differential equation dy/dx = xy. (3) (ii) Find the equation of a curve passing through (1, 2), given that the slope of the tangent to the curve at any point (x, y) is x/y². (3)

[6]

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