Mathematics · Class 12 Science

Odisha Chse Class 12 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.

2019–2026
Years of papers: 7
Total Papers: 7
Real Board Papers: 0
Sample papers: 371
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

54 Q2026complete

54 Q2025complete

48 Q2024complete

48 Q2023complete

73 Q2022complete

—2021Exam cancelled (COVID-19)

46 Q2020complete

48 Q2019complete

2021 — Exam cancelled (COVID-19): The Council of Higher Secondary Education, Odisha (CHSE) cancelled the +2 Science Class-12 board exam for this year statewide due to COVID-19; no annual question paper was ever conducted or printed, so none exists to publish.

Odisha CHSE +2 Science 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: 38
Duration: 180 min
Sections: 4

The marks / questions / duration above are the official exam pattern. We currently have 54 of this paper’s questions (142% of the full paper), with 54 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	Objective (MCQ) -- all compulsory, 1 mark each	20	1	20
BSection B	Short answer -- answer any 6 of 11 printed, 2 marks each	6	2	12
CSection C	Short answer -- answer any 6 of 11 printed, 3 marks each	6	3	18
DSection D	Long answer -- answer any 6 of 12 printed, 5 marks each	6	5	30
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

Odisha CHSE +2 Science Board Exam 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

This question paper contains 38 questions divided into 4 sections — A, B, C, D.
Section A comprises 20 questions of 1 mark each (Objective (MCQ) -- all compulsory, 1 mark each).
Section B comprises 6 questions of 2 marks each (Short answer -- answer any 6 of 11 printed, 2 marks each).
Section C comprises 6 questions of 3 marks each (Short answer -- answer any 6 of 11 printed, 3 marks each).
Section D comprises 6 questions of 5 marks each (Long answer -- answer any 6 of 12 printed, 5 marks each).

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

Section A

Objective (MCQ) -- all compulsory, 1 mark each · 1 mark each · 20 of 20 shown

Q1.

R

is the relation

\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}

A=\{1,2,3\}

, then which one of the following is true for

R

(a) Reflexive but not symmetric
(b) Reflexive but not transitive
(c) Symmetric and transitive
(d) Neither symmetric nor transitive

[1]

Q2.

Write the value of

\cos^{-1}\left(\cos \frac{13\pi}{6}\right)

(a) $\frac{13\pi}{6}$
(b) $\frac{7\pi}{6}$
(c) $\frac{5\pi}{6}$
(d) $\frac{\pi}{6}$

[1]

Q3.

If the inverse of the matrix

\begin{bmatrix}2 & -6\\ 1 & -2\end{bmatrix}

\begin{bmatrix}-1 & 3\\ -\frac{1}{2} & \alpha\end{bmatrix}

, then what is the value of

\alpha

(a) 2
(b) 1
(c) -1
(d) 3

[1]

Q4.

What is the type of the matrix

\begin{bmatrix}0 & 0 & 3\\ 0 & 3 & 0\\ 3 & 0 & 0\end{bmatrix}

(a) Scalar
(b) Diagonal
(c) Unit
(d) Square

[1]

Q5.

A

is a square matrix, then which of the following assertions is true?

(a) $\det A = -\det A'$
(b) $\det A = 2\det A'$
(c) $\det A = \det A'$
(d) $\det A = 3\det A'$

[1]

Q6.

What is the equation of the line joining

A(1,3)

and

B(0,0)

(a) $\begin{vmatrix}1 & 3 & 1\\ 0 & 0 & 1\\ x & y & 1\end{vmatrix}=0$
(b) $\begin{vmatrix}1 & -3 & 1\\ 0 & 0 & 1\\ x & y & 1\end{vmatrix}=0$
(c) $\begin{vmatrix}1 & 2 & 1\\ 0 & 0 & 1\\ x & y & 1\end{vmatrix}=0$
(d) $\begin{vmatrix}1 & -2 & 1\\ 0 & 0 & 1\\ x & y & 1\end{vmatrix}=0$

[1]

Page 1 of 8

Q7.

Write the derivative of log(cos ex). (a) -tan ex (b) extan ex (c) -extan ex (d) tan ex

[1]

Q8.

Let f(x)=∫ ex (x-1)(x-2)dx. Then write the interval in which f(x) decreases. (a) (-∞,-2) (b) (-2,-1) (c) (1,2) (d) (2,+∞)

[1]

Q9.

Write the value of ∫ ex(sin x-cos x)dx. (a) -excos x+c (b) exsin x+c (c) -exsec x+c (d) exoperatornamecosec x+c

[1]

Q10.

Write the value of ∫-aa\f(x)-f(-x)\dx. (a) 0 (b) 2f(a) (c) 2f(-a) (d) 2f(0)

[1]

Q11.

Write the area of the curve y=sin x between x=0 and x=π in sq units. (a) 3 (b) 4 (c) 2 (d) 5

[1]

Q12.

What is the degree of the differential equation (d⁴y)/(dx⁴)-sin((d³y)/(dx³))=0? (a) 4 (b) 3 (c) 0 (d) Undefined

[1]

Q13.

If 2veca+3vecb-5vecc=vec0, then write the ratio in which vecc divides overlineAB, where the position vectors of A and B are respectively veca and vecb. (a) 3 : 2 internally (b) 3 : 2 externally (c) 2 : 3 internally (d) 2 : 3 externally

[1]

Q14.

Write the projection of the vector hati-hatj on the vector hati+hatj. (a) 0 (b) 1 (c) -1 (d) 2

[1]

Q15.

If a line makes angles of 30° and 45° with X-axis and Y-axis respectively, then what is the angle made by it with Z-axis? (a) 45° (b) 60° (c) 120° (d) Cannot be determined

[1]

Q16.

Write the angle between the lines through the points (4,7,8), (2,3,4) and (-1,-2,1), (1,2,5). (a) (π)/(2) (b) (π)/(4) (c) 0 (d) (π)/(6)

[1]

Page 2 of 8

Q17.

What is the objective function of an LPP? (a) A constant (b) A function to be optimized (c) A relation between the variables (d) Non-negative restriction

[1]

Q18.

What is the maximum value of Z=3x+4y subject to the constraints x+y≤ 4, x≥ 0 and y≥ 0? (a) 12 (b) 14 (c) 16 (d) 19

[1]

Q19.

If P(B)=0.5 and P(A∩ B)=0.32, then write the value of P(Amid B). (a) (15)/(23) (b) (16)/(25) (c) (16)/(27) (d) (16)/(23)

[1]

Q20.

In a box containing 100 bulbs, 10 are defective. Write the probability that out of a sample of 5 bulbs, none is defective. (a) 10⁻¹ (b) ((1)/(2))⁵ (c) ((9)/(10))⁵ (d) (9)/(10)

[1]

Section B

Short answer -- answer any 6 of 11 printed, 2 marks each · 2 marks each · 11 of 6 shown

Q1.

Write the relation R=\(x,y):(2x-y)=0\ on A=\1,2,3,…,13\ in tabular form. Determine its type.

[2]

Q2.

Show that the function f:mathbbR→mathbbR defined by f(x)=(x)/(x²+1)∀ x∈mathbbR is not onto.

[2]

Q3.

Test whether the relation R=\(m,n):m+n is not divisible by 3\ on mathbbZ is reflexive or transitive.

[2]

Q4.

Write the principal value branch of cos⁻¹ function and state the range of sec⁻¹ function.

[2]

Q5.

Find the value of tan⁻¹√(3)-sec⁻¹(-2).

[2]

Page 3 of 8

Q6.

Find the set of points where the function f(x)=|2x-1| is differentiable.

[2]

Q7.

Show that the four points (1,2,3), (-1,1,0), (2,1,3) and (1,1,2) are coplanar.

[2]

Q8.

Solve the following LPP graphically: Maximize Z=5x₁+6x₂ subject to 2x₁+3x₂≤ 6, x₁-x₂≥ 0, x₁,x₂≥ 0.

[2]

Q9.

Solve the following linear programming problem graphically: Minimize Z=3x+2y subject to x+y≥ 8, 3x+5y≤ 15, x≥ 0,y≥ 0.

[2]

Q10.

Solve the following LPP graphically: Minimize Z=4x+y subject to x+2y≥ 4, x≥ 0,y≥ 0.

[2]

Q11.

Find the corner points of the feasible region of the following LPP: Maximize Z=11x+7y subject to 2x+y≤ 6, x≤ 2, x≥ 0,y≥ 0.

[2]

Section C

Short answer -- answer any 6 of 11 printed, 3 marks each · 3 marks each · 11 of 6 shown

Q1.

Show that AB=AC, where A= 1 2 0\1 1 0\-1 4 0 , B= 1 2 3\1 1 -1\1 1 1 , C= 1 2 3\1 1 -1\2 2 2 .

[3]

Page 4 of 8

Q2.

Let A= 1 -1 1\2 1 -3\1 1 1 and 10B= 4 2 -2\-5 0 α\1 -2 3 . If B happens to be inverse of A, then find the value of α.

[3]

Q3.

Show that a+d a+d+k a+d+cc c+b cd d+k d+c =abc.

[3]

Q4.

If Δ= 1 x x²\1 y y²\1 z z² and Δ₁= 1 1 1yz zx xyx y z , then show that Δ+Δ₁=0.

[3]

Q5.

If y=(tan⁻¹x)², then show that (x²+1)²y₂+2x(x²+1)y₁-2=0.

[3]

Q6.

Find the area enclosed by two parabolas y²=4ax and x²=4ay.

[3]

Q7.

Evaluate: ∫₀π(xtan x)/(sec x+tan x)dx.

[3]

Q8.

If veca=2hati+hatj-hatk, vecb=-hati+2hatj-4hatk and vecc=hati+hatj+hatk, then find the vector (veca×vecb)·(veca×vecc).

[3]

Page 5 of 8

Q9.

If 2hati-hatj+hatk, hati-3hatj-5hatk, 3hati-4hatj-4hatk are the position vectors of the points A, B, C respectively, then prove that ABC is a right-angled triangle.

[3]

Q10.

Find the coordinates of the point where the perpendicular from the origin meets the line joining the points (-9,4,5) and (11,0,-1).

[3]

Q11.

Find the vector and Cartesian equations of the line that passes through (3,-2,-5) and (3,-2,6).

[3]

Section D

Long answer -- answer any 6 of 12 printed, 5 marks each · 5 marks each · 12 of 6 shown

Q1.

Test whether the relation R=\(m,n):3 divides m-n\ on \1,2,3,…,10\ is reflexive, symmetric or transitive. What is the conclusion?

[5]

Q2.

Examine the function f:(-1,1)→mathbbR, f(x)=(x)/(1-x²) for injectivity and surjectivity. Also find the value of tan⁻¹[2sin(2cos⁻¹(√3)/(2))].

[5]

Page 6 of 8

Q3.

Find the inverse of the following matrix using elementary row operations: 1 2 3\2 1 4\1 0 2 .

[5]

Q4.

Show that b+c a+b ac+a b+c ba+b c+a c =a³+b³+c³-3abc.

[5]

Q5.

Find the altitude of a right circular cylinder of maximum volume inscribed in a sphere of radius r.

[5]

Q6.

Solve: (4x+6y+5)dx-(2x+3y+4)dy=0.

[5]

Q7.

If vecA=2hati+hatk, vecB=hati+hatj+hatk and vecC=4hati-3hatj+7hatk, then find the vector vecR which satisfies vecR×vecB=vecC×vecB and vecR·vecA=0.

[5]

Page 7 of 8

Q8.

Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/(1) and (x+3)/(-3)=(y+7)/(2)=(z-6)/(4). Also find the equation of the line of the shortest distance.

[5]

Q9.

Solve the following LPP by graphical method: Maximize Z=4x₁+3x₂ subject to x₁+x₂≤ 50, x₁+2x₂≤ 80, 2x₁+x₂≥ 20, x₁,x₂≥ 0.

[5]

Q10.

Solve the following LPP by graphical method: Minimize Z=16x+20y subject to x+2y≥ 10, x+y≥ 6, 3x+y≥ 8, x,y≥ 0.

[5]

Q11.

Two groups are competing for the position of the board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Then find the probability that the new product introduced was by the second group.

[5]

Q12.

From a box containing 32 bulbs out of which 8 are defective, 4 bulbs are drawn at random successively one after another with replacement. Find the probability distribution of number of defective bulbs. Find the mean.

[5]

Page 8 of 8