Mathematics · Class 11 Science

Assam Ahsec 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: 357
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

—2026Paper not yet available

—2025Paper not yet available

31 Q2024complete

42 Q2023complete

42 Q2022complete

—2021Exam cancelled (COVID-19)

41 Q2020complete

47 Q2019complete

48 Q2018complete

2026 — Paper not yet available: The AHSEC HS 1st Year exam was presumably held this year, 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 — it will appear here once it is.

2025 — Paper not yet available: The AHSEC HS 1st Year exam was presumably held this year, 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 — it will appear here once it is.

2021 — Exam cancelled (COVID-19): AHSEC cancelled the HS 1st Year (Class-11) examination in 2021 due to COVID-19; an order dated 7 May 2021 promoted all registered students to HS 2nd Year without sitting it. No annual question paper was conducted or printed that year, so none exists to publish.

AHSEC Higher Secondary (HS) 1st Year Examination 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: —
Questions: —
Duration: —
Sections: —

The marks / questions / duration above are the official exam pattern. We currently have 68 of this paper’s questions, with 68 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

The question paper

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

Board Examination

Mathematics

AHSEC Higher Secondary (HS) 1st Year Examination 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: —Maximum Marks: —

Section A

Q1.

Two finite sets have

m

and

n

elements. If the number of subsets of the first set is

112

more than that of the second set. Then the value of

m

and

n

are respectively: (A)

4,\ 7

(B)

7,\ 4

(C)

6,\ 3

(D)

3,\ 6

[1]

Q2.

U

is the universal set and

A \subset U

. Then

\phi' \cap A = ?

(A)

U

(B)

\phi

(C)

A

(D)

A'

[1]

Q3.

A = \{1, 2, \{3, 4\}, 5\}

. Then which one of following is incorrect? (A)

\{3, 4\} \in A

(B)

\{3, 4\} \subset A

(C)

\{\{3, 4\}\} \subset A

(D)

\{1, 2, 5\} \subset A

[1]

Q4.

Let

A = \{x : x \in R,\ x > 4\}

and

B = \{x : x \in R,\ x < 5\}

. Then

A \cap B

is: (A)

(4, 5]

(B)

(4, 5)

(C)

[4, 5]

(D)

[4, 5)

[1]

Q5.

In set builder method, the null set is represented by: (A)

\{\ \ \}

(B)

\phi

(C)

\{x : x \neq x\}

(D)

\{x : x = x\}

[1]

Q6.

A = \{-1, 1\}

, Then the number of elements of

A \times A \times A

is: (A)

6

(B)

8

(C)

12

(D)

20

[1]

Page 1 of 8

Q7.

If f(x) = ax + b, where a and b are integers. f(-1) = -5 and f(3) = 3. Then the value of a and b are respectively: (A) -3,-1 (B) 2,-3 (C) 0,2 (D) 2,3

[1]

Q8.

Domain of √(a² - x²), (a > 0) is: (A) (-a, a) (B) [-a, a] (C) [0, a] (D) (-a, 0]

[1]

Q9.

If R is a relation on a finite set A having n elements. Then the number of relations on A is: (A) 2ⁿ (B) 2n^2 (C) n² (D) nⁿ

[1]

Q10.

Let A = \1, 2, 3\, B = \2, 3, 4\, then which of the following relation is a function from A to B? (A) \(1,2),(1,3),(2,3),(3,3)\ (B) \(1,3),(2,4)\ (C) \(1,3),(2,2),(3,3)\ (D) \(1,2),(2,3),(3,2),(3,4)\

[1]

Q11.

Range of Greatest Integer function is: (A) Z (B) R (C) N (D) Z⁺

[1]

Q12.

The value of sin(-(3π)/(2)) is: (A) 0 (B) 1 (C) -1 (D) ∞

[1]

Q13.

The value of sin(45^° + θ) - cos(45^° - θ) is: (A) 2cosθ (B) 2sinθ (C) 1 (D) 0

[1]

Q14.

In triangle ABC, tan A + tan B + tan C = 0. Then cot A · cot B · cot C = ? (A) 6 (B) 1 (C) ∞ (D) -1

[1]

Q15.

The value of (1 + i)(1 + i²)(1 + i³)(1 + i⁴) is: (A) 2 (B) 0 (C) 1 (D) i

[1]

Q16.

If a + ib = c + id. Then (A) a² + c² = 0 (B) b² + c² = 0 (C) b² + d² = 0 (D) a² + b² = c² + d²

[1]

Q17.

The value of arg(x), when x < 0 is: (A) 0 (B) (π)/(2) (C) π (D) None of these

[1]

Page 2 of 8

Q18.

The solution set of the inequalities |x + 2| ≤ 5 is: (A) (-7, 5) (B) [-7, 3] (C) [-5, 5] (D) (-7, 3)

[1]

Q19.

Given that x, y and b are real numbers and x < y, b < 0, then (A) (x)/(b) < (y)/(b) (B) (x)/(b) ≤ (y)/(b) (C) (x)/(b) > (y)/(b) (D) (x)/(b) ≥ (y)/(b)

[1]

Q20.

If ⁿCr + ⁿCr+1 = ⁿ⁺¹Cₓ. Then x = ? (A) r - 1 (B) r (C) r + 1 (D) n

[1]

Q21.

In how many ways can 5 persons occupy 3 seats? (A) 15 (B) 20 (C) 30 (D) 60

[1]

Q22.

The number of arrangement of n different objects taken r at a time where 3 particular objects are always to be included together is: (A) ⁿ⁻³Pr-3 (B) ⁿ⁻³Cr-3 (C) ⁿPr-3 (D) (r-2)!· 3!· ⁿ⁻³Cr-3

[1]

Q23.

The total number of 9 digit numbers which have all different digit is: (A) 10! (B) 9! (C) 9 × 9! (D) 10 × 10!

[1]

Q24.

A group consist of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has no girl? (A) 20 (B) 21 (C) 28 (D) 35

[1]

Q25.

The total number of terms in the expansion of (x + a)¹⁰⁰ + (x - a)¹⁰⁰ after simplification is: (A) 50 (B) 202 (C) 51 (D) 100

[1]

Q26.

The last term in the expansion of (x² - (3)/(x))⁴ is: (A) x⁴ (B) (-81)/(x⁴) (C) (81)/(x⁴) (D) (1)/(x⁴)

[1]

Q27.

If the third term of a GP is 4. Then the product of its first 5 terms is: (A) 4³ (B) 4⁴ (C) 4⁵ (D) 4⁶

[1]

Q28.

The two Geometric mean between the numbers 1 and 64 are: (A) 8,16 (B) 4,16 (C) 8,32 (D) 2,16

[1]

Page 3 of 8

Q29.

The value of 9(1)/(3) · 9(1)/(9) · 9(1)/(27) … ∞ is: (A) 1 (B) 3 (C) 9 (D) 18

[1]

Q30.

The distance between the line of y = mx + c₁ and y = mx + c₂ is: (A) dfracc₁ - c₂√(m² + 1) (B) dfrac|c₁ - c₂|√(1 + m²) (C) dfracc₂ - c₁√(1 + m²) (D) 0

[1]

Q31.

Equation of a line passing through (1, 2) and parallel to the line y = 3x - 1 is: (A) y + 2 = x + 1 (B) y + 2 = 3(x + 1) (C) y - 2 = 3(x - 1) (D) y - 2 = x - 1

[1]

Q32.

Slope of a line which cut off equal intercept on the axes is: (A) -1 (B) 0 (C) 2 (D) 1

[1]

Q33.

The area of the circle centred at (1, 2) and passing through the points (4, 6) is: (A) 5π (B) 10π (C) 25π (D) None of these

[1]

Q34.

The length of the latus rectum of the ellipse 3x² + y² = 12 is: (A) 4 (B) 12 (C) 8 (D) dfrac4√(3)

[1]

Q35.

Equation of a parabola having focus (0, -3) and directrix y = 3 is: (A) y² = -12x (B) x² = -12y (C) x² = 12y (D) y² = 12x

[1]

Q36.

The distance between the foci of the hyperbola (x²)/(16) - (y²)/(9) = 1 is: (A) 5 (B) 10 (C) 8 (D) 6

[1]

Q37.

The distance of point P(3, 4, 5) from YZ plane is: (A) 3 units (B) 4 units (C) 5 units (D) 12 units

[1]

Q38.

The point (-2, -3, -5) lies in the octant: (A) X'OYZ (B) X'OY'Z' (C) X'OY'Z (D) X'OYZ'

[1]

Q39.

Distance between the points P(1, -3, 4) and Q(-4, 1, 2) is: (A) 3√(5) units (B) 4√(5) units (C) 3 units (D) 4 units

[1]

Page 4 of 8

Q40.

If the co-ordinate of the vertices A, B, C of triangle ABC are (3, -5, 7), (-1, 7, -6) and (4, 1, 2) respectively. Then co-ordinates of centroid is: (A) (1, 1, 2) (B) (2, 1, 1) (C) (1, 1, 1) (D) (2, 2, 2)

[1]

Q41.

limx → a (xⁿ - aⁿ)/(x - a) is equal to: (A) naⁿ (B) naⁿ⁻¹ (C) na (D) 1

[1]

Q42.

The value of limx → 0 (sin ax)/(bx) is: (A) (a)/(b) (B) (b)/(a) (C) 0 (D) 1

[1]

Q43.

Value of limx → 3⁺ (x)/([x]): (A) 0 (B) 3 (C) -3 (D) 1

[1]

Q44.

If f(x) = 1 - x + x² - x³ + … - x⁹⁹ + x¹⁰⁰, then f'(1) is equal to: (A) 150 (B) -50 (C) -150 (D) 50

[1]

Q45.

If y = √(x) + dfrac1√(x), then (dy)/(dx) at x = 1 is: (A) 1 (B) (1)/(2) (C) dfrac1√(2) (D) 0

[1]

Q46.

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is: (A) 2 (B) 2.57 (C) 3 (D) 3.75

[1]

Q47.

If x₁, x₂, x₃, …, xₙ be n observations and barx be their arithmetic mean. Then formula for the standard deviation is given by (A) Σ (xᵢ - barx)² (B) dfracΣ (xᵢ - barx)²2 (C) √dfracΣ (xᵢ - barx)²n (D) √(Σ xᵢ²)/(n) + barx²

[1]

Q48.

In a non leap year, the probability of having 53 Tuesday is: (A) (1)/(7) (B) (2)/(7) (C) (3)/(7) (D) None of these

[1]

Q49.

Two events A and B are said to be exhaustive for sample space S, if (A) A ∩ B = φ (B) A ∩ B = S (C) A ∪ B = S (D) A ∪ B = φ

[1]

Page 5 of 8

Q50.

If M and N are two events. The probability that at least one of them occurs is: (A) P(M) + P(N) - P(M ∩ N) (B) P(M) + P(N) - 2P(M ∩ N) (C) P(M) + P(N) + P(M ∩ N) (D) P(M) + P(N) + 2P(M ∩ N)

[1]

Section B

Q1.

Draw Venn-diagram: (A ∩ B) ∪ (A ∩ C)

[2]

Q2.

For any sets A and B, Show that A = (A ∩ B) ∪ (A - B)

[2]

Q3.

If R = \(x, y) : x and y are Integers and x² + y² = 64\ is a relation. Then write R in roster form.

[2]

Q4.

Solve the inequality: -8 ≤ 5x - 3 < 7

[2]

Q5.

Evaluate by using binomial theorem: (98)⁴

[2]

Q6.

Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9

[2]

Q7.

Find the equation of the circle with radius 4 whose centre lies on the x-axis and passes through the point (2, 3)

[2]

Page 6 of 8

Q8.

Find the derivative of (log x)/(x) with respect to x

[2]

Q9.

Find limx → 0 f(x) if f(x) = 2x + 3, x ≤ 0 \3(x + 1), x > 0

[2]

Q10.

In a lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.

[2]

Section C

Q1.

Draw the graph of the trigonometric function f(x) = cos x and write its Range.

[3]

Q2.

Find the square root of -5 + 12i

[3]

Q3.

Prove that ⁿ⁻¹Pr + r · ⁿ⁻¹Pr-1 = ⁿPr

[3]

Q4.

If the pth, qth and rth terms of a GP are a, b and c respectively. Prove that aq-r · br-p · cp-q = 1

[3]

Page 7 of 8

Q5.

Find the derivative with respect to x (any one): (i) (x⁵ - cos x)/(sin x) (ii) x · sinⁿ x

[3]

Section D

Q1.

Two lines passing through the point (2, 3) intersect each other at an angle of 60^°. If the slope of one line is 2. Find the equation of other line.

[5]

Q2.

If (sin(x + y))/(sin(x - y)) = (a + b)/(a - b), then show that (tan x)/(tan y) = (a)/(b)

[5]

Q3.

Find the mean deviation about median for the following frequency distribution. | Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | Frequency | 5 | 8 | 15 | 16 | 6 |

[5]

Page 8 of 8