Mathematics · Class 11 Science

Kerala Dhse 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: 9
Total Papers: 9
Real Board Papers: 0
Sample papers: 200
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

20 Q2026complete

20 Q2025complete

20 Q2024complete

20 Q2023complete

22 Q2022complete

30 Q2021complete

20 Q2020complete

24 Q2019complete

24 Q2018complete

Kerala DHSE Plus One Board 2026 · Set ANN

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 20 of this paper’s questions, with 20 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

Kerala DHSE Plus One Board 2026 · Set ANN

Series/Set: ANNRoll No. ________

Time Allowed: —Maximum Marks: —

Section Other

Other / unmarked

Q1.

a) If

A

and

B

are two sets such that

A - B = \{1, 2\}

B - A = \{4, 5\}

and

A \cap B = \{7, 8\}

, then the set

B

is __________.

(1) (A) $\{1, 2, 4, 5\}$ (B) $\{4, 5, 7, 8\}$ (C) $\{1, 2, 7, 8\}$ (D) $\{1, 4, 5, 8\}$
b) $L = \{a, b, c, d\}$ , $M = \{c, d, e, f\}$ and $N = \{a, c\}$ are three sets. Verify that $L - (M \cup N) = (L - M) \cap (L - N)$ . (2)

[3]

Q2.

Show that

\cos 20° + \cos 100° + \cos 140° = 0

[3]

Q3.

a) Solve the inequality,

\dfrac{x}{3} > \dfrac{x}{2} + 1

;

x \in \mathbb{R}

, the real numbers.

(2)
b) Hence, find the greatest integer value, $[x]$ obtained in part (a). (1)

[3]

Q4.

a) If

{}^{n}C_5 + {}^{n}C_6 = {}^{51}C_6

, then the value of

n

is __________.

(1) (A) $49$ (B) $50$ (C) $51$ (D) $45$
b) A committee of 4 persons is to be constructed from a group of 4 women and 5 men. Find the number of ways on which the committee can be formed so that women are in majority. (2)

[3]

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Q5.

Find a point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).

[3]

Q6.

a) Write the coordinate of the focus of the parabola whose vertex is at (0, 0) and passing through the point (8, 4) symmetric with respect to x-axis. (1) b) Write the equation of a circle with centre at the origin and making intercept 4 on y-axis. (2)

[3]

Q7.

a) Write the value of limlimitsx → π(x - (22)/(7)). (1) b) Evaluate limlimitsx → 0 (x² - 2x)/(2 sin x). (2)

[3]

Q8.

a) The distance between the lines 3x + 4y = 7 and 3x + 4y = 2 is k. Find the value of k. (1) b) Find the equation of a line through the points (0, 2) making an angle (2π)/(3) with positive direction of x-axis. (2)

[3]

Q9.

If U = \0, 1, 2, 3, 4, 5, 6\, A = \0, 1, 2, 3, 4\ and B = \x : x is a prime number less than 5\, then a) Write B in roster form. (1) b) Find A' ∩ B'. (1) c) Verify that (A ∪ B)' = A' ∩ B'. (2)

[4]

Q10.

a) Define a relation R on the set mathbbN of natural numbers by R = \(x, y); y = x + 5, x is a natural number less than 4, x, y ∈ mathbbN\ (i) Write R in roster form. (1) (ii) Write the domain and range. (1) b) If g(x) = x² 0 ≤ x ≤ 2 \3x 2 ≤ x ≤ 10 , then show that g is not a function in mathbbR. (2)

[4]

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Q11.

a) If z = -1 + i√(2) is a complex number in the second quadrant, then the quadrant in which (1)/(z) lies is _____. (1) b) If z = (1 + i)/(1 - i) then (i) find |z| (2) (ii) Mark the complex number in the Argand plane. (1)

[4]

Q12.

a) How many ways 3 rings can be wear into 5 fingers? (2) b) How many numbers greater than 1000 can be formed using the digits 0, 1, 2, 3 in which no digits repeated? (2)

[4]

Q13.

Find the equation of the perpendicular bisector of the line segment joining the points A(2, 3) and B(6, -5).

[4]

Q14.

Consider the ellipse (x²)/(36) + (y²)/(16) = 1. Find the following : (i) foci and vertices (1) (ii) length of the major and minor axis (1) (iii) length of the latus rectum (1) (iv) eccentricity (1)

[4]

Q15.

If (1 + px)ⁿ = 1 + 24x + 264x² + …, where p is a constant, then find p and n.

[4]

Q16.

a) If A and B are two events such that P(A) = P(B) = x, P(A ∩ B) = P(A' ∩ B') = (1)/(3), then find the value of x. (2) b) A bag contains 9 balls of which 4 are red and 5 are blue. 4 balls are drawn at random from the bag. Calculate the probability that it will be (2) (i) 3 are red balls (ii) atleast 3 blue balls

[4]

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Q17.

a) If sin A + cos A = 1, then the value of sin 2A = _____. (1) (A) -1 (B) 2 (C) 0 (D) 1 b) Arc of a circle of radius 80 cm subtends an angle 10° at the centre. Find the arc length. (2) c) Show that (sin 24° cos 6° - sin 6° sin 66°)/(sin 21° cos 39° - cos 51° sin 69°) = -1. (3)

[6]

Q18.

a) 3rd and 6th term of a geometric progression are 1 and (1)/(27) respectively. Find the 8th term. (2) b) How many terms of the sequence 1, (1)/(2), (1)/(4), (1)/(8) … are needed to give the sum (1023)/(512)? (4)

[6]

Q19.

a) Find the derivative of the following : (i) sin² x (2) (ii) (2x + 3)/(x - 3) (2) b) Find the derivative of f(x) = x using first principle. (2)

[6]

Q20.

Consider the following frequency distribution : | Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | Frequency | 5 | 8 | 15 | 16 | 6 | Find the following : (i) mean (3) (ii) variance (2) (iii) standard deviation (1)

[6]

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