Mathematics · Class 11 Science

Himachal Hpbose 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.

2024–2026
Years of papers: 2
Total Papers: 2
Real Board Papers: 0
Sample papers: 66
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

31 Q2026complete

—2025Paper not yet available

35 Q2024complete

—2023Paper not yet available

—2022Paper not yet available

—2021Paper could not be verified

—2020Paper not yet available

—2019Paper not yet available

—2018Paper not yet available

2025 — Paper not yet available: The HPBOSE 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 hpbose.org and the public past-paper archives, none of which carry pre-2021 Class-11 content for any subject. We publish only a paper we can verify against a real printed original — it will appear here once it is.

2023 — Paper not yet available: The HPBOSE 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 hpbose.org and the public past-paper archives, none of which carry pre-2021 Class-11 content for any subject. We publish only a paper we can verify against a real printed original — it will appear here once it is.

2022 — Paper not yet available: The HPBOSE 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 hpbose.org and the public past-paper archives, none of which carry pre-2021 Class-11 content for any subject. We publish only a paper we can verify against a real printed original — it will appear here once it is.

2021 — Paper could not be verified: A document claiming to be this year's HPBOSE Class-11 paper was found, but it carries no board identification anywhere — no crest, no "Himachal Pradesh Board" text, no printed paper code, no Series box — so it cannot be authenticated as a genuine board paper. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

2020 — Paper not yet available: The HPBOSE 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 hpbose.org and the public past-paper archives, none of which carry pre-2021 Class-11 content for any subject. We publish only a paper we can verify against a real printed original — it will appear here once it is.

2019 — Paper not yet available: The HPBOSE 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 hpbose.org and the public past-paper archives, none of which carry pre-2021 Class-11 content for any subject. 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 HPBOSE 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 hpbose.org and the public past-paper archives, none of which carry pre-2021 Class-11 content for any subject. We publish only a paper we can verify against a real printed original — it will appear here once it is.

HPBOSE Himachal Pradesh Class 11 Board Exam 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: 34
Duration: 180 min
Sections: 4

The marks / questions / duration above are the official exam pattern. We currently have 31 of this paper’s questions (91% of the full paper), with 31 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	omr	16	1	16
BSection B	compulsory	12	3	36
CSection C	compulsory	2	4	8
DSection D	compulsory	4	5	20
Total		34		80

The question paper

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

Board Examination

Mathematics

HPBOSE Himachal Pradesh Class 11 Board Exam 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

This question paper contains 34 questions divided into 4 sections — A, B, C, D.
Section A comprises 16 questions of 1 mark each (omr).
Section B comprises 12 questions of 3 marks each (compulsory).
Section C comprises 2 questions of 4 marks each (compulsory).
Section D comprises 4 questions of 5 marks each (compulsory).

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

Section A

omr · 1 mark each · 13 of 16 shown

Q1.

A collection of novels written by writer Munshi Prem Chand is:

(a) an empty set
(b) a finite set
(c) an infinite set
(d) Not a well defined collection.

[1]

Q2.

X = \{1, 3, 5\}

and

Y = \{1, 2, 3\}

then

X \cap Y = ?

(a) $\{1, 2, 3, 4, 5\}$
(b) $\{1, 2, 3, 5\}$
(c) $\{1, 3\}$
(d) $\phi$

[1]

Q3.

i^9 \cdot i^{19}

is equal to

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

[1]

Q4.

[PARTIALLY ILLEGIBLE — faded scan; printed stem appears as ". 7 . 5 is equal to" with the operator/notation between the digits not clearly legible, likely a permutation/factorial expression]

(a) 2490
(b) 4920
(c) 5040
(d) 5160

[1]

Q5.

First 3 terms of the sequence

a_n = \dfrac{2n-3}{6}

(a) $\dfrac{1}{6}, \dfrac{1}{6}, \dfrac{1}{2}$
(b) $\dfrac{1}{6}, -\dfrac{1}{6}, -\dfrac{1}{2}$
(c) $-\dfrac{1}{6}, \dfrac{1}{6}, \dfrac{1}{3}$
(d) $\dfrac{1}{3}, \dfrac{1}{2}, \dfrac{1}{6}$

[1]

Q6.

The Geometric mean of 2 and 8 is:

(a) $-4$
(b) $5$
(c) $-5$
(d) $4$

[1]

Page 1 of 6

Q7.

The slope of any line parallel to X-axis is: (a) 0 (b) 1 (c) -1 (d) Not defined.

[1]

Q8.

Length of Latus rectum of an ellipse (x²)/(a²) + (y²)/(b²) = 1 is (a) (2a²)/(b) (b) 2a (c) 2b (d) (2b²)/(a)

[1]

Q9.

The value of limx → 0 (tan x)/(x) is (a) 0 (b) 1 (c) -1 (d) 2

[1]

Q10.

The derivative of tan x w.r.t. 'x' is: (a) sec x (b) sec³ x (c) sec² x (d) -sec x

[1]

Q11.

Assertion (A): The function sin x is negative in the third and fourth quadrant. Reason (R): The function sin x is decreasing in the interval 0 ≤ x ≤ (π)/(2). (a) Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are correct, but Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is correct, but Reason (R) is incorrect. (d) Assertion (A) is incorrect, but Reason (R) is correct.

[1]

Q12.

Assertion (A): The derivative of a constant function is zero. Reason (R): A constant function does not change, hence its rate of change is zero. (a) Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are correct, but Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is correct, but Reason (R) is incorrect. (d) Assertion (A) is incorrect, but Reason (R) is correct.

[1]

Q13.

Assertion (A): The probability of getting a prime number when a die is thrown once is (2)/(3). Reason (R): On the faces of a die, prime numbers are 2, 3, 5. (a) Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are correct, but Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is correct, but Reason (R) is incorrect. (d) Assertion (A) is incorrect, but Reason (R) is correct.

[1]

Section B

compulsory · 3 marks each · 12 of 12 shown

Q1.

If U = \1, 2, 3, 4, 5, 6, 7, 8, 9\, A = \1, 2, 3, 4\, B = \2, 4, 6, 8\, C = \3, 4, 5, 6\ find: (i) A' (ii) (A ∪ C)' (iii) (B - C)'.

[3]

Page 2 of 6

Q2.

A = \1, 2, 3, 5\ and B = \4, 6, 9\. Define a relation from A to B by R = \(x, y) : the difference between x and y is odd, x ∈ A, y ∈ B\. Write R in roaster form.

[3]

Q3.

A Wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

[3]

Q4.

Find the multiplicative inverse of 2 - 3i. **OR** If ((1+i)/(1-i))m = 1, then find the least positive integral value of m.

[3]

Q5.

Solve the inequality for Real 'x': (1)/(2)((3x)/(5) + 4) ≥ (1)/(3)(x - 6). **OR** Solve the system of inequalities 3x - 7 < 5 + x, 11 - 5x ≤ 1 and represent the solution on the number line graphically.

[3]

Q6.

How many words with or without meaning can be formed using all the letters of the word 'EQUATION' using each letter exactly once?

[3]

Q7.

Determine n if ²ⁿC₃ : ⁿC₃ = 12 : 1.

[3]

Q8.

Find the 12th term of a G.P., whose 8th term is 192 and the common ratio is 2.

[3]

Page 3 of 6

Q9.

Find the equation of set of the points P such that its distances from the points A(3, 4, -5) and B(-2, 1, 4) are equal. **OR** Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are Collinear.

[3]

Q10.

Evaluate limx → 0 (sin 4x)/(sin 2x).

[3]

Q11.

One card is drawn from a well shuffled deck of 52 cards, if each outcome is equally likely, calculate the probability that card will be: (i) a diamond (ii) not an ace (iii) not a black card.

[3]

Q12.

A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine: (a) P(not A) (b) P(not B) (c) P(A or B). **OR** In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these student is selected at random, find the probability that: (a) The student opted for NCC or NSS. (b) The student has opted neither NCC nor NSS. (c) The student has opted NSS but not NCC.

[3]

Section C

compulsory · 4 marks each · 2 of 2 shown

Q1.

Using Binomial theorem evaluate (99)⁵. **OR** Find (a + b)⁴ - (a - b)⁴. Hence evaluate (√(3) + √(2))⁴ - (√(3) - √(2))⁴.

[4]

Page 4 of 6

Q2.

The vertices of triangle PQR are P(2, 1), Q(-2, 3) and R(4, 5). Find the equation of the median through the vertex R. **OR** If p is the length of perpendicular from the origin to the line whose intercepts on the axis are a and b, then show that (1)/(p²) = (1)/(a²) + (1)/(b²).

[4]

Section D

compulsory · 5 marks each · 4 of 4 shown

Q1.

Prove that: cos 6x = 32cos⁶ x - 48cos⁴ x + 18cos² x - 1.

[5]

Q2.

Given a G.P. with a = 729 and 7th term is 64, determine S₇ (i.e. sum of First Seven terms). **OR** If 4th, 10th and 16th terms of a G.P. are x, y and z respectively. Prove that x, y and z are in G.P.

[5]

Q3.

Find the equation of the parabola having Focus (6, 0) and directrix x = -6. **OR** Find the Coordinates of foci, the vertices, the length of major axis, minor axis, the eccentricity and length of Latus rectum of the ellipse: 4x² + 9y² = 36.

[5]

Page 5 of 6

Q4.

Calculate the Mean, Variance and Standard deviation for the following distribution: Classes 0–10, Frequency 5; Classes 10–20, Frequency 8; Classes 20–30, Frequency 15; Classes 30–40, Frequency 16; Classes 40–50, Frequency 6.

[5]

Page 6 of 6