Mathematics · Class 11 Science

Haryana Bseh 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: 331
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

46 Q2026complete

38 Q2025complete

38 Q2024complete

35 Q2023complete

52 Q2022complete

52 Q2021complete

—2020Exam not held (COVID-19 lockdown)

35 Q2019complete

35 Q2018complete

2020 — Exam not held (COVID-19 lockdown): Haryana postponed its March 2020 board exams starting 19 March 2020 (COVID-19 lockdown). BSEH Class-11 papers already sat before the cutoff (incl. Physics, Chemistry, Biology) are archived for 2020, but Mathematics — scheduled later in the cycle — was never conducted that year. No question paper exists because none was ever administered.

Board of School Education Haryana (Senior Secondary Part-I / 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: 38
Duration: 180 min
Sections: 5

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	compulsory	20	1	20
BSection B	compulsory	5	2	10
CSection C	compulsory	6	3	18
DSection D	compulsory	4	5	20
ESection E	compulsory	3	4	12
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

Board of School Education Haryana (Senior Secondary Part-I / Class 11) 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

This question paper contains 38 questions divided into 5 sections — A, B, C, D, E.
Section A comprises 20 questions of 1 mark each (compulsory).
Section B comprises 5 questions of 2 marks each (compulsory).
Section C comprises 6 questions of 3 marks each (compulsory).
Section D comprises 4 questions of 5 marks each (compulsory).
Section E comprises 3 questions of 4 marks each (compulsory).

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

Section A

compulsory · 1 mark each · 30 of 20 shown

Q1.

The shaded region in the given Venn-diagram represents:

(a) A ∪ B
(b) A ∩ B
(c) (A ∪ B)'
(d) (A ∩ B)'

[1]

Q2.

If x = -3.45, then the value of x - [x] is (where [x] represents the greatest integer function):

(a) -0.45
(b) 0
(c) 6.90
(d) 0.55

[1]

Q3.

If tan x = -5/12 and x lies in 2nd quadrant, then the value of sin x is:

(a) 5/13
(b) 12/13
(c) -5/13
(d) -12/13

[1]

Q4.

Multiplicative inverse of 1 + √3i is:

(a) 1 - √3i
(b) (1 - √3i)/2
(c) (1 + √3i)/4
(d) None of these

[1]

Q5.

If ⁿC₈ = ⁿC₂, then the value of ⁿC₃ is:

(a) 720
(b) 360
(c) 120
(d) None of these

[1]

Q6.

If a_(n+1) = 3a_n + 2, n ≥ 1, a₁ = 3, then the value of a₄ is:

(a) 107
(b) 35
(c) 29
(d) 53

[1]

Q7.

The number of terms in the expansion of (1 + x)⁴ + (1 - x)⁴ after simplification is:

(a) 2
(b) 3
(c) 4
(d) 5

[1]

Page 1 of 6

Q8.

The value of x for which the progression 2/7, x, 14 is in G.P., is: (a) 4 (b) 2 (c) 1 (d) None of these

[1]

Q9.

The centre of the circle given by the equation x² + y² - 8x + 12y - 12 = 0 has the coordinates: (a) (8, -12) (b) (-8, 12) (c) (4, -6) (d) (-4, 6)

[1]

Q10.

lim (x→1) (x³ - 1)/(x - 1) is: (a) 0 (b) 2 (c) 3 (d) Not defined

[1]

Q11.

Mean of first 50 natural numbers is: (a) 25 (b) 25.5 (c) 26 (d) 26.5

[1]

Q12.

If P(A) = 0.35, P(A ∩ B) = 0.25, P(A ∪ B) = 0.75, then P(B) is: (a) 0.65 (b) 0.40 (c) 0.10 (d) None of these

[1]

Q13.

cos (x - y) - cos (x + y) = ..............

[1]

Q14.

If U = 1, 2, 3, 4, 5, 6, 7, 8, 9, A = 2, 4, 6, 8 and B = 2, 3, 6, 7, then (A ∪ B)' = ..............

[1]

Q15.

The modulus of (1 + i)/(1 - i) is ..............

[1]

Q16.

Find the slope of the line perpendicular to 3x - 4y + 10 = 0.

[1]

Q17.

Find: d/dx (sin x cos x + 5x + 3)

[1]

Q18.

A fair coin is tossed 3 times. Find the probability of getting 2 heads and 1 tail.

[1]

Page 2 of 6

Q19.

Assertion (A): If n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, then n(X ∩ Y) = 38. Reason (R): n(A ∪ B) = n(A) + n(B) - n(A ∩ B). (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true.

[1]

Q20.

Assertion (A): The eccentricity of ellipse x²/16 + y²/9 = 1 is 5/4. Reason (R): The eccentricity of ellipse x²/a² + y²/b² = 1 is given by b² = a²(1 - e²). (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true.

[1]

Q21.

Case study: In our country there are nearly 950 million people who are voters and the voter turn up for voting is nearly 65%. Let A be the set of all citizens of India who are eligible to vote. A relation R is defined on A as follows: R = (V1, V2) : V1, V2 ∈ A and V1 and V2 both casted their votes in election. Let X and Y ∈ A, X casted his vote but Y did not cast his vote. Wife of X is W ∈ A and she casted her vote. F1, F2 and F3 are three friends who are voters and all casted their votes in election; F1, F2, F3 ∈ A. Now which of the following is true? (a) (X, Y) ∈ R (b) (Y, X) ∈ R (c) (Y, Y) ∈ R (d) (X, Y) ∉ R

[1]

Q22.

(Continuing the same case study on relation R defined on the set of voters A — see 36(i) for full context.) Which of the following is true? (a) (X, W) ∈ R and (W, X) ∈ R (b) (X, W) ∈ R but (W, X) ∉ R (c) (X, W) ∉ R and (W, X) ∉ R (d) (W, X) ∈ R but (X, W) ∉ R

[1]

Q23.

(Continuing the same case study on relation R defined on the set of voters A — see 36(i) for full context.) Which of the following is true? (a) (F1, F2) ∈ R, (F2, F3) ∈ R, (F1, F3) ∈ R (b) (F1, F2) ∈ R, (F2, F3) ∈ R but (F1, F3) ∉ R (c) (F1, F2) ∈ R, (F2, F2) ∈ R but (F3, F3) ∉ R (d) (F1, F2) ∉ R, (F2, F3) ∉ R and (F1, F3) ∉ R

[1]

Q24.

(Continuing the same case study on relation R defined on the set of voters A — see 36(i) for full context.) Relation R is: (a) Symmetric only (b) Reflexive only (c) Transitive only (d) Equivalence relation

[1]

Q25.

(Same parabolic-reflector case study as 37(i).) Find the coordinates of the focus F.

[1]

Q26.

(Same parabolic-reflector case study as 37(i).) What is the length of the latus rectum?

[1]

Q27.

Case study: In Bhiwani zoo the lioness Geeta gave birth to three cubs. Their gender was not known at the time of the birth. The probability of male or female cub is equal. Probability of all female cubs.

[1]

Page 3 of 6

Q28.

(Same lioness-cubs case study as 38(i).) Probability of two male and one female cub.

[1]

Q29.

(Same lioness-cubs case study as 38(i).) Probability of one male and two female cubs.

[1]

Q30.

(Same lioness-cubs case study as 38(i).) Probability of all male cubs.

[1]

Section B

compulsory · 2 marks each · 6 of 5 shown

Q1.

Prove that: cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x) sin(π/4 - y) = sin(x + y) **OR** In a circle of diameter 40 cm, the length of chord is 20 cm. Find the length of minor arc of the chord.

[2]

Q2.

Solve the inequality -15 < 3(x - 2)/5 ≤ 0.

[2]

Q3.

Which term of the sequence √3, 3, 3√3, ........... is 2187?

[2]

Q4.

Find the angle between the lines √3x + y = 1 and x + √3y = 1. **OR** Find the equation of line parallel to 3x - 4y + 2 = 0 and passing through (-2, 3).

[2]

Q5.

Find the equation of parabola with focus at (6, 0) and directrix x = -6.

[2]

Page 4 of 6

Q6.

Case study: A parabolic reflector is 20 cm in diameter and 5 cm deep. A bulb is placed at its focus F, so that rays after striking with boundary become parallel to the axis. Find the equation of the parabola.

[2]

Section C

compulsory · 3 marks each · 6 of 6 shown

Q1.

If f(x) is a linear function defined from Z → Z and is given by f = (1, 1), (2, 3), (0, -1), (-1, -3), find f(x).

[3]

Q2.

Find the general and principal solution of the equation cos 4x = cos 2x.

[3]

Q3.

How many words with or without meaning can be made from the letters of the word MONDAY? (i) When all the letters are used (ii) How many of them will start from the letter M

[3]

Q4.

Find the middle term in the expansion of (3 - x/2)⁸.

[3]

Q5.

If sum of 3 numbers in A.P. is 24 and their product is 440, find the numbers. **OR** The ratio of Arithmetic mean and Geometric mean of two numbers is 5 : 3. Find the numbers.

[3]

Page 5 of 6

Q6.

Differentiate (px² + qx + r)/(ax + b) w.r.t. x. **OR** Find the derivative of x³ - 3x from first principles w.r.t. x.

[3]

Section D

compulsory · 5 marks each · 4 of 4 shown

Q1.

Prove that: sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x **OR** A market research group conducted a survey of 1000 consumers. It is reported that 720 persons like product A and 450 persons like product B. What is the minimum number of persons must have liked both products A and B?

[5]

Q2.

Find the term independent of x in the expansion of (3x²/2 - 1/3x)⁶. **OR** The ratio of the sum of m and n terms of an A.P. is m² : n². Show that the ratio of mth and nth term is (2m - 1) : (2n - 1).

[5]

Q3.

A point R with x-coordinate 4 lies on the line joining the points P(2, -3, 4) and Q(8, 0, 10). Find the ratio PR : RQ and the coordinates of R. **OR** Find the area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the end of the latus rectum.

[5]

Q4.

Find the mean and the variance of the following data: Class-interval: 0-30 | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 Frequency: 2 | 3 | 5 | 10 | 3 | 5 | 2 **OR** The Mean of 5 observations is 4.4 and their variance is 8.24. If three observations are 1, 2 and 6, find the other two observations.

[5]

Page 6 of 6