Mathematics · Class 12 Science

Rajasthan Rbse 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: 8
Total Papers: 8
Real Board Papers: 0
Sample papers: 347
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

53 Q2026complete

53 Q2025complete

51 Q2024complete

50 Q2023complete

50 Q2022complete

—2021Exam cancelled (COVID-19)

30 Q2020complete

30 Q2019complete

30 Q2018complete

2021 — Exam cancelled (COVID-19): RBSE cancelled the Class-12 Senior Secondary Examination in 2021 due to COVID-19 (a Rajasthan State Council of Ministers decision); students were promoted via internal assessment. No exam was administered that year, so there is no genuine previous-year paper to publish.

Rajasthan Board Senior Secondary 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: 80
Questions: 53
Duration: 195 min
Sections: 4

The marks / questions / duration above are the official exam pattern. We currently have 53 of this paper’s questions (100% of the full paper), with 53 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	36	1	36
BSection B	short_answer	10	2	20
CSection C	long_answer	4	3	12
DSection D	essay	3	4	12
Total		53		80

The question paper

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

Board Examination

Mathematics

Rajasthan Board Senior Secondary Examination 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hr 15 minMaximum Marks: 80

General Instructions

This question paper contains 53 questions divided into 4 sections — A, B, C, D.
Section A comprises 36 questions of 1 mark each (objective).
Section B comprises 10 questions of 2 marks each (short_answer).
Section C comprises 4 questions of 3 marks each (long_answer).
Section D comprises 3 questions of 4 marks each (essay).

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

Section A

objective · 1 mark each · 36 of 36 shown

Q1.

f : R \to R

be given by

f(x) = (3 - x^3)^{1/3}

, then

f \circ f(x)

is equal to

(a) $x^{1/3}$
(b) $x^3$
(c) $x$
(d) $(3-x^3)$

[1]

Q2.

The principal value of

\sin^{-1}\left(\frac{1}{\sqrt{2}}\right)

(a) $\pi/4$
(b) $\pi/6$
(c) $\pi/3$
(d) $\pi/2$

[1]

Q3.

A = [a_{ij}]_{m \times n}

is a square matrix, if

(a) $m < n$
(b) $m > n$
(c) $m = n$
(d) None of these

[1]

Q4.

A = \begin{bmatrix}1 & 2 & 3\\ 2 & 3 & 1\end{bmatrix}

and

B = \begin{bmatrix}3 & -1 & 3\\ -1 & 0 & 2\end{bmatrix}

, then the

(2A - B)

will be

(a) $\begin{bmatrix}-1 & 5 & 3\\ 5 & 6 & 0\end{bmatrix}$
(b) $\begin{bmatrix}5 & -1 & 3\\ 5 & 6 & 0\end{bmatrix}$
(c) $\begin{bmatrix}2 & 4 & 6\\ 4 & 6 & 2\end{bmatrix}$
(d) $\begin{bmatrix}-3 & 1 & -3\\ 5 & 6 & 2\end{bmatrix}$

[1]

Q5.

Value of

\begin{vmatrix}x^2-x+1 & x-1\\ x+1 & x+1\end{vmatrix}

will be

(a) $x^2-x+2$
(b) $x^3+x^2-2$
(c) $x^3-x^2+2$
(d) $x^3+x^2+4$

[1]

Q6.

2x + 3y = \sin y

, then

\frac{dy}{dx}

is equal to

(a) $\frac{3}{\sin y - 2}$
(b) $\frac{2}{\cos y - 3}$
(c) $\frac{\cos y + 3}{2}$
(d) $\frac{2}{\cos y}$

[1]

Page 1 of 7

Q7.

If y = cos⁻¹((1-x²)/(1+x²)), 0 < x < 1, then (dy)/(dx) is equal to (a) (1)/(1+x²) (b) (2)/(4+x) (c) (2)/(1+x²) (d) (2)/(x+x²)

[1]

Q8.

The rate of change of the area of a circle with respect to its radius r at r = 5 cm is (a) 12π (b) 8π (c) 5π (d) 10π

[1]

Q9.

∫ (dx)/(sin² x cos² x) equals (a) tan x + sin x + c (b) tan x - cot x + c (c) tan x cot x + c (d) 2tan x - cot 2x + c

[1]

Q10.

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is (a) 2 (b) 4/9 (c) 9/4 (d) 9/2

[1]

Q11.

The order of the differential equation 2x² (d²y)/(dx²) - 3(dy)/(dx) + y = 0 is (a) 2 (b) 1 (c) 0 (d) Not defined

[1]

Q12.

Which of the following is a vector quantity? (a) Time (b) Volume (c) Force (d) Speed

[1]

Q13.

The sum of the vectors veca = hati - 2hatj + hatk, vecb = -2hati + 4hatj + 5hatk and vecc = hati - 6hatj - 7hatk is (a) -4hatj-hatk (b) 4hati-hatk (c) 4hatj+5hatk (d) hati+4hatj-hatk

[1]

Q14.

The unit vector in the direction of the vector veca = hati+hatj+2hatk is (a) frachati+hatj+2hatk√(5) (b) frachati+hatj+hatk√(6) (c) frac2hati+hatj+hatk√(6) (d) frachati+hatj+2hatk√(6)

[1]

Q15.

If the straight lines (x+1)/(1)=(y+2)/(λ)=(z-1)/(-1) and (x-1)/(-λ)=(y+1)/(2)=(z+1)/(1) are perpendicular to each other, then the value of λ is (a) 0 (b) 1 (c) 2 (d) 3

[1]

Q16.

Two cards are drawn at random without replacement from a pack of 52 playing cards, then the probability that both the cards are black in color, is (a) 1/2 (b) 1/12 (c) 25/102 (d) 1/4

[1]

Page 2 of 7

Q17.

If A and B are independent events and P(A) = 0.3 and P(B) = 0.4, then the value of P(A ∪ B) will be (a) 0.58 (b) 0.70 (c) 0.12 (d) 0.10

[1]

Q18.

If a pair of dice is thrown, then the probability of getting an even prime number on each die will be (a) 1/3 (b) 1/12 (c) 1/36 (d) 0

[1]

Q19.

sin⁻¹x is a function whose domain is _____.

[1]

Q20.

The value of determinant Δ = 1 2 4\-1 3 0\4 1 0 is _____.

[1]

Q21.

The edge of a variable cube is increasing at the rate of 3 cm/s. The volume of the cube is increasing at the rate of _____ while the edge is 10 cm long.

[1]

Q22.

∫(2x - 3cos x + ex)dx = _____.

[1]

Q23.

The general solution of the differential equation (dy)/(dx) = (1+y²)/(1+x²) is _____.

[1]

Q24.

The vector joining the points P(2, 3, 0) and Q(-1, -2, -4) directed from P to Q is _____.

[1]

Q25.

If A = 1 -2 3\-4 2 5 and B = 2 3\4 5\2 1 , then find AB.

[1]

Q26.

Find the value of determinant Δ = 0 sinα -cosα\-sinα 0 sinβ; cosα -sinβ 0 .

[1]

Q27.

If y = (ex)/(sin x), then find (dy)/(dx).

[1]

Page 3 of 7

Q28.

If y = ex + ex^2 + … + ex^5, then find (dy)/(dx).

[1]

Q29.

The radius of an air bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm?

[1]

Q30.

The total revenue in rupees received from the sale of x units of a product is given by R(x) = 13x² + 26x + 15. Find the marginal revenue when x = 7.

[1]

Q31.

Evaluate ∫ fracdx√(2x - x²).

[1]

Q32.

Find the area of the circle x² + y² = a².

[1]

Q33.

Verify that the function y = acos x + bsin x, where a, b ∈ R is a solution of the differential equation (d²y)/(dx²) + y = 0.

[1]

Q34.

Find the angle between two vectors veca and vecb with magnitudes √(3) and 2 respectively and veca.vecb = √(6).

[1]

Q35.

Find the direction cosines of the line passing through the two points (-2, 4, -5) and (1, 2, 3).

[1]

Q36.

A family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

[1]

Section B

short_answer · 2 marks each · 10 of 10 shown

Q1.

Prove that the relation R defined by R = \(a, b) : a ≤ b\ on the set R of real numbers is reflexive and transitive but not symmetric.

[2]

Page 4 of 7

Q2.

Show that sin⁻¹(2x√(1-x²)) = 2sin⁻¹x, -frac1√(2) ≤ x ≤ frac1√(2).

[2]

Q3.

If x 2; 3 + y -1; 1 = 10; 5 , find the values of x and y.

[2]

Q4.

Find the area of the triangle whose vertices are (1, 0), (6, 0) and (4, 3).

[2]

Q5.

Find (dy)/(dx), if x = cosθ - cos 2θ, y = sinθ - sin 2θ.

[2]

Q6.

If y = sin⁻¹x, show that (1-x²)(d²y)/(dx²) - x(dy)/(dx) = 0.

[2]

Q7.

Find local maximum and local minimum values of the function f given by f(x) = 3x⁴ + 4x³ - 12x² + 12.

[2]

Q8.

Find ∫ (x²)/(1-x⁶)dx.

[2]

Q9.

Find the area of the region bounded by the circle x² + y² = 4 and the lines x = 0, x = 2 in the first quadrant.

[2]

Q10.

Find the area of a parallelogram whose adjacent sides are given by the vectors veca = 3hati + hatj + 4hatk and vecb = hati - hatj + hatk.

[2]

Page 5 of 7

Section C

long_answer · 3 marks each · 4 of 4 shown

Q1.

Find ∫ fracx²√(x⁶+a⁶)dx. **OR** Using partial fraction find ∫ (1)/(x²-9)dx.

[3]

Q2.

Find the general solution of the differential equation (dx)/(dy) - (x)/(y) = 2y. **OR** Find the particular solution of the differential equation (dy)/(dx) + ycot x = 2x + x²cot x(x ≠ 0) given that y = 0 when x = (π)/(2).

[3]

Q3.

Show that the three lines with direction cosines (12)/(13), (-3)/(13), (-4)/(13); (4)/(13), (12)/(13), (3)/(13); (3)/(13), (-4)/(13), (12)/(13) are mutually perpendicular. **OR** Find the equation of the line in vector and in Cartesian form that passes through the point with position vector 2hati - hatj + 4hatk and is in the direction hati + 2hatj - hatk.

[3]

Q4.

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event, the sum of numbers on the dice is 4. **OR** A die is thrown once. If E is the event 'the number appearing is a multiple of 3' and F be the event 'the number appearing is even', then find whether E and F are independent.

[3]

Section D

essay · 4 marks each · 3 of 3 shown

Q1.

Find the value of ∫₂³ (dx)/(x²-1). **OR** Find ∫ √(3-2x-x²)dx.

[4]

Page 6 of 7

Q2.

Find the angle between the pair of lines (x)/(2) = (y)/(2) = (z)/(1) and (x-5)/(4) = (y-2)/(1) = (z-3)/(8). **OR** Find the values of P so that the lines (1-x)/(3) = (7y-14)/(2P) = (z-3)/(2) and (7-7x)/(3P) = (y-5)/(1) = (6-z)/(5) are at right angles.

[4]

Q3.

Determine graphically the maximum value of the objective function z = 4x + y subject to the following constraints: x + y ≤ 50, 3x + y ≤ 90, x ≥ 0, y ≥ 0. **OR** Determine graphically the minimum value of the objective function z = 200x + 500y subject to the following constraints: x + 2y ≥ 10, 3x + 4y ≤ 24, x ≥ 0, y ≥ 0.

[4]

Page 7 of 7