Mathematics · Class 12 Science

Jharkhand Jac 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: 7
Total Papers: 7
Real Board Papers: 0
Sample papers: 302
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

52 Q2026complete

52 Q2025complete

52 Q2024complete

59 Q2023complete

—2022Not available

—2021Not available

29 Q2020complete

29 Q2019complete

29 Q2018complete

JAC 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: —
Questions: —
Duration: —
Sections: —

The marks / questions / duration above are the official exam pattern. We currently have 52 of this paper’s questions, with 52 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

JAC Intermediate Board 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: —Maximum Marks: —

Section A

Q1.

The relation

R

on set

A

is called empty relation if and only if

(a) $R = \phi$
(b) $R = A$
(c) $R = A \times A$
(d) None of these

[1]

Q2.

f: R \to R

such that

f(x) = 6x - 5

then

f^{-1}(x) =

(a) $\dfrac{x+5}{6}$
(b) $\dfrac{x-5}{6}$
(c) $\dfrac{x+6}{5}$
(d) None of these

[1]

Q3.

y = \cos^{-1} x

then

(a) $0 \le y \le \pi$
(b) $-\dfrac{\pi}{2} \le y \le \dfrac{\pi}{2}$
(c) $-\pi \le y \le \pi$
(d) None of these

[1]

Q4.

Principal value of

\tan^{-1}(-1)

(a) $\dfrac{\pi}{4}$
(b) $-\dfrac{\pi}{4}$
(c) $\dfrac{3\pi}{4}$
(d) None of these

[1]

Q5.

\begin{bmatrix} x+y \\ y+z \\ z+x \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix}

then

x+y+z =

(a) 9
(b) 0
(c) 4
(d) 5

[1]

Q6.

A = \begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}

then

A^2 =

(a) $\begin{bmatrix} 4 & 16 \\ 9 & 1 \end{bmatrix}$
(b) $\begin{bmatrix} 2 & 12 \\ 6 & 2 \end{bmatrix}$
(c) $\begin{bmatrix} 16 & 13 \\ 9 & 12 \end{bmatrix}$
(d) None of these

[1]

Q7.

A = \begin{bmatrix} 4 & x+2 \\ 2x-3 & x+1 \end{bmatrix}

is symmetric matrix then

x =

(a) 3
(b) 4
(c) 5
(d) None of these

[1]

Page 1 of 7

Q8.

If x 3 \8 x = 6 2 \18 2 then x = (a) √(24) (b) -√(24) (c) ±√(24) (d) None of these

[1]

Q9.

cos 30^° sin 30^° ; sin 30^° cos 30^° = (a) (1)/(2) (b) dfrac√(3)2 (c) 0 (d) None of these

[1]

Q10.

(d)/(dx)(cos 3x) = (a) sin 3x (b) -3sin 3x (c) cos 3x (d) -3cos 3x

[1]

Q11.

(d)/(dx) tan⁻¹(x²) = (a) (2x)/(1+x⁴) (b) (x)/(1+x²) (c) (x³)/(1+x²) (d) None of these

[1]

Q12.

(d)/(dx) esin x = (a) esin x · cos x (b) esin x (c) cos x (d) None of these

[1]

Q13.

(d)/(dx)(log sec x) = (a) tan x (b) cot x (c) csc x (d) None of these

[1]

Q14.

(d)/(dx)(e^tan⁻¹ x) = (a) dfrace^tan⁻¹ x1+x² (b) e^tan⁻¹ x (c) (1)/(1+x²) (d) None of these

[1]

Q15.

(d)/(dx)(ax) = (a) ax log a (b) log a (c) ax (d) None of these

[1]

Q16.

If x = acosθ, y = asinθ, find (dy)/(dx). (a) -cotθ (b) tanθ (c) atanθ (d) None of these

[1]

Q17.

∫ sin(2x+3)dx = (a) cos(2x+3)+C (b) -(cos(2x+3))/(2)+C (c) tan 2x + C (d) None of these

[1]

Q18.

∫ tan² x dx = (a) cot x - x + C (b) tan x + x + C (c) tan x - x + C (d) None of these

[1]

Page 2 of 7

Q19.

∫ (dx)/(x²+16) = (a) (1)/(4)tan⁻¹((x)/(4))+C (b) tan⁻¹ x + C (c) (1)/(2)tan⁻¹((x)/(2))+C (d) None of these

[1]

Q20.

∫₀π/2 √(1+cos 2x) dx = (a) 0 (b) 1 (c) dfrac1√(2) (d) None of these

[1]

Q21.

∫₁e ((log x)²)/(x) dx = (a) (1)/(3)e³ (b) (1)/(3)(e³-1) (c) (1)/(3) (d) None of these

[1]

Q22.

∫ ex (log sec x + tan x) dx = (a) ex + C (b) ex tan x + C (c) ex(log sec x) + C (d) None of these

[1]

Q23.

The order of the differential equation (d²y)/(dx²) = √(1+((dy)/(dx))²) is (a) 1 (b) 2 (c) 3 (d) None of these

[1]

Q24.

If veca = 2hati - 7hatj - 3hatk then hata = (a) dfrac2hati-7hatj-3hatk√(62) (b) 2hati-7hatj-3hatk (c) dfrac1√(62) (d) None of these

[1]

Q25.

For what value of x, vectors xhati-3hatj-5hatk and -hati+hatj+2hatk are perpendicular to each other? (a) 4 (b) 7 (c) -13 (d) None of these

[1]

Q26.

Find the projection of vector veca = 2hati+3hatj+2hatk on the vector vecb = hati+2hatj+hatk. (a) (3)/(2) (b) dfrac10√(6) (c) dfrac√(6)10 (d) None of these

[1]

Q27.

Find the value of (2hati+3hatj) × (hati+2hatj) (a) hati (b) hatj (c) hatk (d) None of these

[1]

Q28.

If a line makes angles α, β, γ with coordinate axes then sin²α + sin²β + sin²γ = (a) 2 (b) 1 (c) -2 (d) 0

[1]

Page 3 of 7

Q29.

If P(A) = 0.8, P(B) = 0.5 and P((B)/(A)) = 0.4 then P(A ∩ B) = (a) 0.8 (b) 0.5 (c) 0.32 (d) 0.4

[1]

Q30.

A line passing through (2, -1, 3) has direction ratio (d.r.) (3, -1, 2), then its equation is (a) (x+2)/(3) = (y-1)/(-1) = (z-3)/(2) (b) (x+2)/(3) = (y+1)/(-1) = (z-3)/(2) (c) (x-2)/(3) = (y+1)/(-1) = (z-3)/(2) (d) None of these

[1]

Section B

Q1.

Let A = \1, 2, 3\, B = \a, b, c, d\ and f = \(1, a), (2, b), (3, c)\ is a function from A to B, show that f is one-one function.

[2]

Q2.

Write in simplest form: tan⁻¹(√((1+cos x)/(1-cos x))), 0 < x < π.

[2]

Q3.

Find x and y, if 2 x 5 \7 y-3 + 3 -4 \1 2 = 7 6 \15 14 .

[2]

Q4.

Find the area of the triangle whose vertices are (3, 8), (-4, 2) and (5, 1).

[2]

Q5.

An edge of a variable cube is increasing at a rate of 3 cm/sec. How fast the volume of the cube is increasing when edge is 10 cm long?

[2]

Q6.

Evaluate: ∫ (cos 2x)/(cos² x · sin² x) dx.

[2]

Page 4 of 7

Q7.

If y = 4sin 3x then show that (d²y)/(dx²) + 9y = 0.

[2]

Q8.

Two dice are rolled. Find the probability that the sum of the numbers coming up on them is 9 if it is known that 5 always comes on the first die.

[2]

Q9.

Test the continuity of the function f(x) at x = 0 where f(x) = (sin 3x)/(x), when x ≠ 0 \3, when x = 0

[3]

Q10.

If y = xsin x + (x²+1)/(x²-1), find (dy)/(dx).

[3]

Q11.

Evaluate: ∫ (2x+1)/((x+2)(x-3)) dx.

[3]

Q12.

Find the interval in which the function f(x) = x³ - 6x² + 9x + 20 is strictly increasing or strictly decreasing.

[3]

Q13.

Evaluate: ∫₀π/2 (sin x - cos x)/(1 + sin x · cos x) dx.

[3]

Page 5 of 7

Q14.

Find the area enclosed by the ellipse (x²)/(a²) + (y²)/(b²) = 1.

[3]

Q15.

If veca = 3hati+2hatj+hatk, vecb = 4hati-hatj+3hatk then find (i) veca+vecb (ii) 3veca-2vecb (iii) veca·vecb.

[3]

Q16.

Find the angle between the following pair of lines: (x-2)/(3) = (y+5)/(2) = (z-1)/(6) and (x-7)/(2) = (y)/(1) = (z+6)/(2).

[3]

Q17.

Solve the system of linear equations using matrix method: 2x+3y+3z=5, x-2y+z=-4, 3x-y-2z=3.

[5]

Q18.

Find two positive numbers whose sum is 16 and whose product is maximum.

[5]

Q19.

Solve the differential equation: (x²+1)(dy)/(dx) + 2xy = √(x²+4).

[5]

Page 6 of 7

Q20.

Find the shortest distance between the pair of the following lines: vecr = (hati+2hatj+hatk) + λ(hati-hatj+hatk) and vecr = (2hati-hatj-hatk) + μ(2hati+hatj+2hatk).

[5]

Q21.

Solve the following LPP graphically: Minimize Z = -3x + 4y subject to constraints x+2y ≤ 8, 3x+2y ≤ 12, x ≥ 0, y ≥ 0.

[5]

Q22.

A man is known to speak truth 3 out of 4 times. He rolls a die and reports that the number coming on the die it is a six (6). Find the probability that the number is actually six (6).

[5]

Page 7 of 7