Mathematics · Class 11 Science

Madhya Pradesh Mpbse 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.

2020–2026
Years of papers: 6
Total Papers: 6
Real Board Papers: 0
Sample papers: 295
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

50 Q2026complete

50 Q2025complete

50 Q2024complete

50 Q2023complete

49 Q2022complete

—2021Exam cancelled (COVID-19)

46 Q2020complete

—2019Paper not yet available

—2018Paper not yet available

2021 — Exam cancelled (COVID-19): The Madhya Pradesh School Education Department cancelled the Class-11 annual examination statewide in 2021 due to COVID-19 (decision of 16 April 2021) — students were evaluated through a half-yearly test and internal assessment instead. No question paper exists because no annual exam was ever administered that year.

2019 — Paper not yet available: The MPBSE Class-11 exam was presumably held this year, but no verified question paper for this subject has been found from the sources we check — the official mpbse.nic.in and related state portals (which keep no browsable past-paper archive) plus the public past-paper archives, which otherwise cover this subject for every other year. We publish only a paper we can verify against a real printed original — it will appear here once it is.

2018 — Paper not yet available: The MPBSE Class-11 exam was presumably held this year, but no verified question paper for this subject has been found from the sources we check — the official mpbse.nic.in and related state portals (which keep no browsable past-paper archive) plus the public past-paper archives, which otherwise cover this subject for every other year. We publish only a paper we can verify against a real printed original — it will appear here once it is.

MP Board Higher Secondary (Class 11) 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 50 of this paper’s questions (100% of the full paper), with 50 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)Section Section A (Objective)	Objective -- all compulsory, 1 mark each	32	1	32
Section B (Very Short Answer)Section Section B (Very Short Answer)	Very short answer, internal choice within each question	10	2	20
Section C (Short Answer)Section Section C (Short Answer)	Short answer, internal choice within each question	4	3	12
Section D (Long Answer)Section Section D (Long Answer)	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 (Class 11) 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), Section B (Very Short Answer), Section C (Short Answer), Section D (Long Answer).
Section Section A (Objective) comprises 32 questions of 1 mark each (Objective -- all compulsory, 1 mark each).
Section Section B (Very Short Answer) comprises 10 questions of 2 marks each (Very short answer, internal choice within each question).
Section Section C (Short Answer) comprises 4 questions of 3 marks each (Short answer, internal choice within each question).
Section Section D (Long Answer) 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 A

Q1.

The number of all non-empty subsets of the set

\{1, 2, 3\}

is:

(a) 8
(b) 7
(c) 3
(d) 9

[1]

Q2.

Let

A = \{1, 2\}

and

B = \{3, 4\}

, then the number of relations from set A to set B will be:

(a) 4
(b) $2^4$
(c) 2
(d) 1

[1]

Q3.

Conjugate of

3 + 5i

is:

(a) $-3+5i$
(b) $-3-5i$
(c) $3-5i$
(d) $3+i$

[1]

Q4.

The relation between arithmetic mean and geometric mean of two numbers always be:

(a) $A \ge G$
(b) $A = G$
(c) $G > A$
(d) $A = \dfrac{G}{2}$

[1]

Q5.

The slope of x-axis is:

(a) $90^\circ$
(b) 1
(c) 0
(d) $45^\circ$

[1]

Q6.

Number of elements in sample space when a coin is tossed three times will be:

(a) 3
(b) 4
(c) 8
(d) 2

[1]

Q7.

Fill in the blank: The complementary set of universal set will be a ______ set.

[1]

Page 1 of 7

Q8.

Fill in the blank: If (x+1, y-2) = (3, 1), then the value of y is ___.

[1]

Q9.

Fill in the blank: If -(2)/(7), x, -(7)/(2) are consecutive terms of a geometric progression, then the value of x will be ___.

[1]

Q10.

Fill in the blank: Equation of a line making intercepts a and b on the x and y axis respectively is ___.

[1]

Q11.

Fill in the blank: The co-ordinates of points in the xy-plane are in the form of ___.

[1]

Q12.

Fill in the blank: If variance of given data is 225, then the standard deviation of the same data will be ___.

[1]

Q13.

Write True/False: Sets \2, 6, 10\ and \3, 7, 11\ are disjoint sets.

[1]

Q14.

Write True/False: If Cartesian product of two sets A and B is A × B = \(p, q), (p, r)\, then A = \p, q, r\.

[1]

Q15.

Write True/False: ax² + bx + c ≤ 0 is called linear inequality.

[1]

Q16.

Write True/False: The geometric mean of numbers a and b is (a+b)/(2).

[1]

Q17.

Write True/False: In the expansion of (a+b)ⁿ, the sum of indices of a and b is always n.

[1]

Q18.

Write True/False: The distance between points (1, 0, 0) and (0, 1, 0) is √(2).

[1]

Page 2 of 7

Q19.

Match the columns — Column A: sin(-x). Choose its correct equivalent from Column B. (a) (1-tan² x)/(1+tan² x) (b) (2tan x)/(1-tan² x) (c) (2tan x)/(1+tan² x) (d) -sin x (e) sin x (f) -cos x (g) cos x

[1]

Q20.

Match the columns — Column A: cos((π)/(2) - x). Choose its correct equivalent from Column B. (a) (1-tan² x)/(1+tan² x) (b) (2tan x)/(1-tan² x) (c) (2tan x)/(1+tan² x) (d) -sin x (e) sin x (f) -cos x (g) cos x

[1]

Q21.

Match the columns — Column A: cos(π - x). Choose its correct equivalent from Column B. (a) (1-tan² x)/(1+tan² x) (b) (2tan x)/(1-tan² x) (c) (2tan x)/(1+tan² x) (d) -sin x (e) sin x (f) -cos x (g) cos x

[1]

Q22.

Match the columns — Column A: sin 2x. Choose its correct equivalent from Column B. (a) (1-tan² x)/(1+tan² x) (b) (2tan x)/(1-tan² x) (c) (2tan x)/(1+tan² x) (d) -sin x (e) sin x (f) -cos x (g) cos x

[1]

Q23.

Match the columns — Column A: cos 2x. Choose its correct equivalent from Column B. (a) (1-tan² x)/(1+tan² x) (b) (2tan x)/(1-tan² x) (c) (2tan x)/(1+tan² x) (d) -sin x (e) sin x (f) -cos x (g) cos x

[1]

Q24.

Match the columns — Column A: tan 2x. Choose its correct equivalent from Column B. (a) (1-tan² x)/(1+tan² x) (b) (2tan x)/(1-tan² x) (c) (2tan x)/(1+tan² x) (d) -sin x (e) sin x (f) -cos x (g) cos x

[1]

Q25.

Match the columns — Column A: (d)/(dx)sin x. Choose its correct equivalent from Column B. (a) (1-tan² x)/(1+tan² x) (b) (2tan x)/(1-tan² x) (c) (2tan x)/(1+tan² x) (d) -sin x (e) sin x (f) -cos x (g) cos x

[1]

Q26.

Define subset.

[1]

Q27.

Evaluate i⁹ + i¹⁹.

[1]

Page 3 of 7

Q28.

Write modulus of 5 - 3i.

[1]

Q29.

Find distance between the points (4, 0, 0) and (-4, 0, 0).

[1]

Q30.

Write value of limx→ 0 (sin x)/(x).

[1]

Q31.

Write derivative of cos x.

[1]

Q32.

Define "Mutually Exclusive Event".

[1]

Section B

Q1.

If U = \1, 2, 3, 4, 5, 6\, A = \2, 3\ and B = \3, 4, 5\, then find A' and B'. **OR** If A = \1, 2, 3, 4, 5, 6\, B = \2, 4, 6, 8\, then find A - B and B - A.

[2]

Q2.

If A = \-1, 1\, then find the value of A × A × A. **OR** Write domain and range of function f(x) = -|x|.

[2]

Q3.

Write dfrac(3+i√(5))(3-i√(5))(√(3)+√(2)i)-(√(3)-i√(2)) in the form of a+ib. **OR** Find the multiplicative inverse of the complex number 4 - 3i.

[2]

Page 4 of 7

Q4.

If ⁿC₈ = ⁿC₂, then find the value of ⁿC₂. **OR** How many 3-digit numbers can be formed by using the digits from 1 to 9, if no digit is repeated?

[2]

Q5.

How many chords can be drawn through 21 points on a circle? **OR** If ⁿPr = 720 · ⁿCr, then find the value of r.

[2]

Q6.

Which term of geometric progression 2, 8, 32, … is 2048? **OR** Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

[2]

Q7.

Find the co-ordinate of the focus and the equation of directrix for equation y² = 12x. **OR** Find the centre and radius of the circle for the given equation (x+5)² + (y-3)² = 36.

[2]

Q8.

Find the distance between points (2, 3, 5) and (4, 3, 1). **OR** Show that the points (0, 0, 0), (1, 1, 0) and (2, 2, 0) are collinear.

[2]

Q9.

Compute the derivative of f(x) = sin² x. **OR** Evaluate limx→ 0 (sin 4x)/(sin 2x).

[2]

Q10.

One card is drawn from a well-shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will not be an ace. **OR** If P(A) = (1)/(3), P(B) = (1)/(5), P(A ∩ B) = (1)/(15), then find the value of P(A ∪ B).

[2]

Page 5 of 7

Section C

Q1.

Find all pairs of consecutive odd natural numbers, in which both the numbers are larger than 10 and their sum is less than 40. **OR** Solve the inequality (2x-1)/(3) ≥ (3x-2)/(4) - (2-x)/(5) for real number x.

[3]

Q2.

Expand (1-2x)⁵. **OR** Which is larger, (1.01)¹⁰⁰⁰⁰⁰⁰ or 10,000? (using binomial theorem)

[3]

Q3.

Find the sum of n terms of the sequence 8, 88, 888, 8888, … **OR** If the A.M. and G.M. of two positive numbers "a" and "b" are 10 and 8 respectively, then find the numbers.

[3]

Q4.

Find the derivative of cos x from first principle. **OR** Evaluate limx→ 0 dfrac√(1+x)-1x.

[3]

Section D

Q1.

Prove that (sin x - sin y)/(cos x + cos y) = tan(x-y)/(2). **OR** Show that tan 3x tan 2x tan x = tan 3x - tan 2x - tan x.

[4]

Page 6 of 7

Q2.

If x + iy = (a+ib)/(a-ib), then prove that x² + y² = 1. **OR** If ((1+i)/(1-i))m = 1, then find the least positive integral value of m.

[4]

Q3.

Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0. **OR** Line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

[4]

Q4.

Find the standard deviation for the following data: xᵢ: 3, 8, 13, 18, 23; fᵢ: 7, 10, 15, 10, 6. **OR** Find mean deviation about the mean for the following data: xᵢ: 2, 5, 6, 8, 10, 12; fᵢ: 2, 8, 10, 7, 8, 5.

[4]

Page 7 of 7