Mathematics · Class 12 Science

Madhya Pradesh Mpbse 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.

2018–2026
Years of papers: 8
Total Papers: 8
Real Board Papers: 0
Sample papers: 378
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

—2026Paper not yet available

50 Q2025complete

50 Q2024complete

50 Q2023complete

50 Q2022complete

—2021Exam cancelled (COVID-19)

46 Q2020complete

46 Q2019complete

42 Q2018complete

2026 — Paper not yet available: This year’s exam was held, but no source we check has published a verified question paper yet. 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): The MP Board (MPBSE) cancelled the Class-12 Higher Secondary 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 internal-assessment formula.

MP Board Higher Secondary 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: 80
Questions: 50
Duration: 180 min
Sections: 4

The marks / questions / duration above are the official exam pattern. We currently have 44 of this paper’s questions (88% of the full paper), with 44 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

Section	Type	Questions	Marks each	Total
Section A (Objective, Q1-5 sub-items)Section Section A (Objective, Q1-5 sub-items)	Objective -- all compulsory, 1 mark each	32	1	32
Section B -- Very Short Answer (Q6-15)Section Section B -- Very Short Answer (Q6-15)	Very short answer, internal choice within each question	10	2	20
Section B -- Short Answer (Q16-19)Section Section B -- Short Answer (Q16-19)	Short answer, internal choice within each question	4	3	12
Section B -- Long Answer (Q20-23)Section Section B -- Long Answer (Q20-23)	Long answer, internal choice within each question	4	4	16
Total		50		80

The question paper

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

Board Examination

Mathematics

MP Board Higher Secondary 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

This question paper contains 50 questions divided into 4 sections — Section A (Objective, Q1-5 sub-items), Section B -- Very Short Answer (Q6-15), Section B -- Short Answer (Q16-19), Section B -- Long Answer (Q20-23).
Section Section A (Objective, Q1-5 sub-items) comprises 32 questions of 1 mark each (Objective -- all compulsory, 1 mark each).
Section Section B -- Very Short Answer (Q6-15) comprises 10 questions of 2 marks each (Very short answer, internal choice within each question).
Section Section B -- Short Answer (Q16-19) comprises 4 questions of 3 marks each (Short answer, internal choice within each question).
Section Section B -- Long Answer (Q20-23) comprises 4 questions of 4 marks each (Long answer, internal choice within each question).

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

Section Section A (Objective, Q1-5 sub-items)

Objective -- all compulsory, 1 mark each · 1 mark each · 25 of 32 shown

Q1.

R

be the relation in the set

N

given by

R = \{(a,b): a = b - 2, b > 6\}

, then

(a) $(2, 4) \in R$
(b) $(3, 8) \in R$
(c) $(6, 8) \in R$
(d) $(8, 7) \in R$

[1]

Q2.

A

and

B

are symmetric matrices of same order, then

AB - BA

is a:

(a) Skew symmetric matrix
(b) Symmetric matrix
(c) Zero matrix
(d) Identity matrix

[1]

Q3.

The number of arbitrary constants in the general solution of a differential equation of fourth order are:

(a) $0$
(b) $2$
(c) $3$
(d) $4$

[1]

Q4.

The principal value of

\sin^{-1}\left(\frac{1}{\sqrt{2}}\right)

(a) $-\frac{\pi}{4}$
(b) $\frac{\pi}{3}$
(c) $\frac{\pi}{6}$
(d) $\frac{\pi}{4}$

[1]

Q5.

A

is an invertible matrix of order 2, then

\det(A^{-1})

is equal to:

(a) $\det(A)$
(b) $\frac{1}{\det(A)}$
(c) $1$
(d) $0$

[1]

Q6.

The value of

\hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{i} \times \hat{k}) + \hat{k} \cdot (\hat{i} \times \hat{j})

is:

(a) $0$
(b) $-1$
(c) $1$
(d) $3$

[1]

Page 1 of 6

Q7.

Fill in the blank: The derivative of ex with respect to x, is ___.

[1]

Q8.

Fill in the blank: Unique solution of equation AX = B is given by X = ___, where |A| ≠ 0.

[1]

Q9.

Fill in the blank: The degree of the differential equation xy(d²y)/(dx²) + x((dy)/(dx))² - y((dy)/(dx)) = 0 is ___.

[1]

Q10.

Fill in the blank: Minimum value of function f is ___ given by f(x) = x², x ∈ R.

[1]

Q11.

Fill in the blank: A quantity that has magnitude as well as direction is called a ___.

[1]

Q12.

Fill in the blank: A matrix is said to be a column matrix if it has only ___.

[1]

Q13.

Write True or False: Multiplication of diagonal matrices of same order will be commutative.

[1]

Q14.

Write True or False: Two collinear vectors are always equal in magnitude.

[1]

Q15.

Write True or False: Every differentiable function is continuous, but the converse is not true.

[1]

Q16.

Write True or False: If A and B are two events such that P(A) ≠ 0 and P(B/A) = 1, then A = φ.

[1]

Q17.

Write True or False: Order and degree (if defined) of a differential equation are always positive integers.

[1]

Page 2 of 6

Q18.

Write True or False: f: X → Y is onto if and only if range of f = Y.

[1]

Q19.

Write the answer in one word/sentence: Write the principal value branches (Range) of sin⁻¹ x.

[1]

Q20.

Write the answer in one word/sentence: Define equivalence relation.

[1]

Q21.

Write the answer in one word/sentence: Write the minimum value of (1-x+x²)/(1+x+x²), for all real values of x.

[1]

Q22.

Write the answer in one word/sentence: Write the general solution of a differential equation of the type (dx)/(dy) + P₁ x = Q₁.

[1]

Q23.

Write the answer in one word/sentence: If E and F are independent events then write the value of P(E ∩ F).

[1]

Q24.

Write the answer in one word/sentence: Write the equation of a line in Cartesian form which passes through a point (x₁, y₁, z₁) and whose direction cosines are l, m, n.

[1]

Q25.

Write the answer in one word/sentence: Write the value of ∫₁³ dx.

[1]

Section Section B -- Very Short Answer (Q6-15)

Very short answer, internal choice within each question · 2 marks each · 10 of 10 shown

Q1.

T be the set of all triangles in a plane with R a relation in T given by R = \(T₁, T₂): T₁ is congruent to T₂\. Show that R is an equivalence relation.

[2]

Page 3 of 6

Q2.

Find the derivative of the function f(x) = sin(cos x) with respect to x.

[2]

Q3.

Find the value of tan⁻¹[2cos(2sin⁻¹(1)/(2))].

[2]

Q4.

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference when r = 4.9 cm?

[2]

Q5.

Find a vector in the direction of vector veca = hati - 2hatj that has magnitude 7 units.

[2]

Q6.

If a line makes angle 90^°, 60^° and 30^° with the positive direction of x, y and z-axis respectively, find its direction cosines.

[2]

Q7.

Show that sin⁻¹(2x√(1-x²)) = 2sin⁻¹x, -frac1√(2) ≤ x ≤ frac1√(2).

[2]

Q8.

Find the general solution of the differential equation (dy)/(dx) = (1+y²)/(1+x²).

[2]

Q9.

Find |veca × vecb|, if veca = 2hati + hatj + 3hatk and vecb = 3hati + 5hatj - 2hatk.

[2]

Q10.

The length x of a rectangle is decreasing at the rate of 3 cm/min. and the width y is increasing at the rate of 2 cm/min. When x = 10 cm and y = 16 cm, find the rate of change of the perimeter of the rectangle.

[2]

Page 4 of 6

Section Section B -- Short Answer (Q16-19)

Short answer, internal choice within each question · 3 marks each · 4 of 4 shown

Q1.

If A = 2 4 \3 2 and B = 1 3 \-2 5 , then find the values of (i) A + B (ii) A - B (iii) AB.

[3]

Q2.

Using integration, find the area enclosed by the ellipse (x²)/(a²) + (y²)/(b²) = 1.

[3]

Q3.

Solve the following linear programming problem graphically: Maximise Z = 4x + y Subject to the constraints: x + y ≤ 50, 3x + y ≤ 90, x ≥ 0, y ≥ 0.

[3]

Q4.

In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that the chosen student is a girl?

[3]

Section Section B -- Long Answer (Q20-23)

Long answer, internal choice within each question · 4 marks each · 4 of 4 shown

Q1.

If y = (tan⁻¹x)², then show that (x²+1)²(d²y)/(dx²) + 2x(x²+1)(dy)/(dx) = 2.

[4]

Page 5 of 6

Q2.

If A = 2 3 \1 -4 and B = 1 -2 \-1 3 , then verify that (AB)⁻¹ = B⁻¹A⁻¹.

[4]

Q3.

Find the shortest distance between the lines ell₁ and ell₂ whose vector equations are vecr = hati + 3hatj + λ(2hati - hatj + hatk) and vecr = 2hati + 3hatj - hatk + μ(3hati - 5hatj + 2hatk).

[4]

Q4.

Find the value of I = ∫π/6π/3 fracdx1 + √(tan x).

[4]

Section Other

Other / unmarked

Q1.

Match the correct pair. Column 'A': (i) ∫ sin 2xdx; (ii) ∫ fracdx√(1-x²); (iii) ∫ (dx)/(1+x²); (iv) ∫ (dx)/(x²-a²); (v) ∫ (dx)/(a²-x²); (vi) ∫ cos 2xdx; (vii) ∫ √(a²-x²)dx. Column 'B': (a) (1)/(2a)log|(x-a)/(x+a)| + c; (b) (sin 2x)/(2) + c; (c) (1)/(2)x√(a²-x²) + (a²)/(2)sin⁻¹(x)/(a) + c; (d) -(cos 2x)/(2) + c; (e) sin⁻¹x + c; (f) (1)/(2a)log|(a+x)/(a-x)| + c; (g) tan⁻¹x + c.

[7]

Page 6 of 6