Mathematics · Class 12 Science

Chhattisgarh Cgbse 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.

2018–2026
Years of papers: 9
Total Papers: 9
Real Board Papers: 0
Sample papers: 287
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

35 Q2026complete

29 Q2025complete

29 Q2024complete

29 Q2023complete

29 Q2022complete

29 Q2021complete

29 Q2020complete

39 Q2019complete

39 Q2018complete

CGBSE Intermediate Board 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: 22
Duration: 180 min
Sections: 6

The marks / questions / duration above are the official exam pattern. We currently have 35 of this paper’s questions (159% of the full paper), with 35 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

Section	Type	Questions	Marks each	Total
1(A)Section 1(A)	compulsory	1	1	1
1(B)Section 1(B)	compulsory	1	1	1
Q2-7Section Q2-7	compulsory	6	2	12
Q8-14Section Q8-14	compulsory	7	3	21
Q15-17Section Q15-17	compulsory	3	4	12
Q18-21Section Q18-21	compulsory	4	5	20
Total		22		80

The question paper

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

Board Examination

Mathematics

CGBSE Intermediate Board 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

This question paper contains 22 questions divided into 6 sections — 1(A), 1(B), Q2-7, Q8-14, Q15-17, Q18-21.
Section 1(A) comprises 1 question of 1 mark each (compulsory).
Section 1(B) comprises 1 question of 1 mark each (compulsory).
Section Q2-7 comprises 6 questions of 2 marks each (compulsory).
Section Q8-14 comprises 7 questions of 3 marks each (compulsory).
Section Q15-17 comprises 3 questions of 4 marks each (compulsory).
Section Q18-21 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

Q1.

The distance from x-axis to point (x, y, z) will be:

(a) \sqrt{x^2+y^2}
(b) \sqrt{x^2+z^2}
(c) \sqrt{y^2+z^2}
(d) \sqrt{x^2+y^2+z^2}

[1]

Q2.

The maximum value of the objective function Z = 3x + 4y under the constraints x + y \le 1, x \ge 0, y \ge 0 will be:

(a) 4
(b) 5
(c) 0
(d) 6

[1]

Q3.

The value of \int e^{\log(\cos x)},dx will be:

(a) -\sin x + c
(b) e^{\log(\sin x)} + c
(c) \sin x + c
(d) \sec x + c

[1]

Q4.

The maximum value of the objective function is located:

(a) inside the feasible region
(b) at corner points of the feasible region
(c) outside the feasible region
(d) in second quadrant

[1]

Q5.

If the determinant \begin{vmatrix}2x & 4\ 2 & 1\end{vmatrix} = 0, then the value of x will be:

(a) 2
(b) 4
(c) 6
(d) 8

[1]

Q6.

The differential coefficient of 5^x will be:

(a) 5^x \log_e 5
(b) 5^x \log_5 e
(c) 5^x
(d) \log_e 5^x

[1]

Q7.

A bag contains 3 black and 4 white balls. Probability of drawing one white ball is:

(a) 4/7
(b) 3/7
(c) 1/7
(d) 7/4

[1]

Page 1 of 6

Q8.

The value of tan⁻¹((1)/(x)) will be: (a) tan x (b) cot x (c) cot⁻¹(1)/(x) (d) cot⁻¹ x

[1]

Q9.

If |vec a| = 1, |vec b| = 2 and vec a · vec b = 1, then angle between vec a and vec b is: (a) π/2 (b) π/6 (c) π/3 (d) π/4

[1]

Q10.

Order and degree of differential equation ((d²y)/(dx²))³ = [y + ((dy)/(dx))²] are: (a) 2, 4 (b) 2, 3 (c) 2, 2 (d) 1, 2

[1]

Q11.

Verify that the function y = x² + 2x + c is a solution of differential equation y' - 2x - 2 = 0.

[1]

Q12.

Prove that the function f(x) = 5x - 3 is continuous at x = -3.

[1]

Q13.

Evaluate the determinant Δ = 1 2 4\-1 3 0\4 1 0 .

[1]

Q14.

Evaluate ∫ (2 - 3sin x)/(cos² x)dx.

[1]

Q15.

If A = 1 2 3\2 3 1 and B = 3 -1 3\-1 0 2 , then find the value of 2A - B.

[1]

Section B

Q1.

The radius of a balloon is increasing at the rate of 10 cm/sec. At what rate the surface area of the balloon is increasing when its radius is 15 cm?

[2]

Page 2 of 6

Q2.

If y = sin(log x), then find the value of (dy)/(dx).

[2]

Q3.

Find the unit vector in the direction of the sum of the vectors vec a = 2hat i + 2hat j - 5hat k and vec b = 2hat i + hat j + 3hat k.

[2]

Q4.

If 2 1 3\0 x + y 0\1 2 = 5 6\1 8 , then find the value of x and y.

[2]

Q5.

Prove that sin⁻¹ x + cos⁻¹ x = (π)/(2).

[2]

Q6.

Find the area of parallelogram whose adjacent sides are vec a = 3hat i + hat j + 4hat k and vec b = hat i - hat j + hat k.

[2]

Section C

Q1.

Solve the differential equation (dy)/(dx) + 2y = 4x.

[3]

Q2.

Evaluate ∫ cos⁻¹ xdx.

[3]

Page 3 of 6

Q3.

Find the maximum value of the function Z = 3x + 2y when the constraints are the following: x + 2y ≤ 10 3x + y ≤ 15 and x ≥ 0, y ≥ 0.

[3]

Q4.

Prove that ∫₀π/2 (sin⁴ x)/(sin⁴ x + cos⁴ x)dx = (π)/(4).

[3]

Q5.

Find the Cartesian equation of the line which passes through the point (-2, 4, -5) and parallel to the line given by (x+3)/(3) = (y-4)/(5) = (z+8)/(6).

[3]

Q6.

An unbiased die is thrown twice. Let the event A be 'odd number on the first throw' and B be the event 'odd number on the second throw'. Check the independence of the events A and B.

[3]

Q7.

Evaluate ∫ (cos x - sin x)/(1 + sin 2x)dx.

[3]

Section D

Q1.

Given three identical boxes I, II and III, each containing two coins. In box I, both coins are gold coins, in box II, both are silver coins and in box III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin from it at random. If the coin is of gold, then what is the probability that the other coin in the box is also of gold? **OR** A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a 6. Find the probability that it is actually a 6.

[4]

Page 4 of 6

Q2.

A ladder 5 metres long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 2 metres per second. How fast is its height on the wall decreasing when the foot of the ladder is 4 metres away from the wall? **OR** Find two numbers whose sum is 24 and whose product is as large as possible.

[4]

Q3.

If y = e^mcos⁻¹x, then prove that (1 - x²)(d²y)/(dx²) - x(dy)/(dx) - m² y = 0. **OR** If x = a(cosθ + θsinθ) and y = a(sinθ - θcosθ), then find (dy)/(dx).

[4]

Section E

Q1.

Find the area of circle x² + y² = a² by using the integration method. **OR** Find the area enclosed by the ellipse (x²)/(16) + (y²)/(9) = 1.

[5]

Q2.

Find the shortest distance between the straight lines (x+1)/(7) = (y+1)/(-6) = (z+1)/(1) and (x-3)/(1) = (y-5)/(-2) = (z-7)/(1). **OR** Find the shortest distance between the lines vec r = hat i + 2hat j + 3hat k + t(2hat i + 3hat j + 4hat k) and vec r = 2hat i + 4hat j + 5hat k + s(3hat i + 4hat j + 5hat k).

[5]

Q3.

Solve the following system of equations by the matrix method: 3x - 2y + 3z = 8 2x + y - z = 1 4x - 3y + 2z = 4 **OR** Express the matrix B = 2 -2 4\-1 3 4\1 -2 -3 as the sum of a symmetric and a skew-symmetric matrix.

[5]

Page 5 of 6

Q4.

Let T be the set of all triangles in a plane, with R a relation in T given by R = \(T₁, T₂) : T₁ is congruent to T₂\. Show that R is an equivalence relation. **OR** Prove that the function f : R → R given by f(x) = 2x is one-one and onto, where R is the set of real numbers.

[5]

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