Mathematics · Class 12 Science

Jammu Kashmir Jkbose 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.

2018–2025
Years of papers: 8
Total Papers: 8
Real Board Papers: 0
Sample papers: 254
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

—2026Paper not yet available

31 Q2025complete

31 Q2024complete

29 Q2023complete

29 Q2022complete

29 Q2021complete

35 Q2020complete

35 Q2019complete

35 Q2018complete

2026 — Paper not yet available: No verified Mathematics question paper for this year has been published by any source we check yet. We publish only a paper we can verify against a real printed original — this one will appear here once it is.

JKBOSE Class 12 Annual Regular Examination 2025 · Set SZ

Real board examination

About this paper

The real Class-12 board examination held in 2025. Every question below is solved the concept-first way. Sample papers are labelled honestly — never shown as a past exam.

Total marks: 80
Questions: 31
Duration: 180 min
Sections: 4

The marks / questions / duration above are the official exam pattern. We currently have 31 of this paper’s questions (100% of the full paper), with 31 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	mixed	10	1	10
BSection B	subjective	10	2	20
CSection C	subjective	8	4	32
DSection D	subjective	3	6	18
Total		31		80

The question paper

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

Board Examination

Mathematics

JKBOSE Class 12 Annual Regular Examination 2025 · Set SZ

Series/Set: SZRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

This question paper contains 31 questions divided into 4 sections — A, B, C, D.
Section A comprises 10 questions of 1 mark each (mixed).
Section B comprises 10 questions of 2 marks each (subjective).
Section C comprises 8 questions of 4 marks each (subjective).
Section D comprises 3 questions of 6 marks each (subjective).

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

Section A

mixed · 1 mark each · 10 of 10 shown

Q1.

\begin{vmatrix} x & 3 \\ 4 & -2 \end{vmatrix} = 0

then

x

is equal to :

(a) 6
(b) -6
(c) 4
(d) -4

[1]

Q2.

For a square matrix A, A(adj A) = ................ .

[1]

Q3.

Derivative of

e^{\log \tan x}

w.r.t.

x

is :

(a) $\cot x$
(b) $\tan x$
(c) $\sec^2 x$
(d) $\csc^2 x$

[1]

Q4.

Second derivative of

\log (\log x)

w.r.t.

x

is :

(a) $\dfrac{1}{x \log x}$
(b) $\dfrac{1}{\log x}$
(c) $\dfrac{1}{x}$
(d) $\dfrac{-(1+\log x)}{(x \log x)^2}$

[1]

Q5.

The function :

f(x) = \dfrac{|x|}{x}

x \neq 0

;

= 0

x = 0

is discontinuous at

x = 0

. (True/False)

[1]

Q6.

Maximum value of

\sin x

is :

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

[1]

Q7.

\int \tan x \, dx

is equal to :

(a) $\log \cos x + C$
(b) $\log \sec x + C$
(c) $\log \sin x + C$
(d) $\log \csc x + C$

[1]

Page 1 of 5

Q8.

Two lines are parallel if their direction ratios are .................... .

[1]

Q9.

Projection of hati on hatj is zero. (True/False)

[1]

Q10.

Define optimal solution.

[1]

Section B

subjective · 2 marks each · 10 of 10 shown

Q1.

Show that the relation R in the set \1, 2, 3\ given by R = \(1, 2), (2, 1)\ is symmetric but neither reflexive nor transitive.

[2]

Q2.

Prove that : 3sin⁻¹ x = sin⁻¹(3x - 4x³), x ∈ [-(1)/(2), (1)/(2)].

[2]

Q3.

The length 'x' of a rectangle is decreasing at the rate of 3 cm/minute and the width 'y' is increasing at the rate of 2 cm/minute. When x = 10 cm and y = 6 cm, find the rate of change of the perimeter.

[2]

Q4.

Find the unit vector in the direction of the vector veca = hati + hatj + 2hatk.

[2]

Q5.

Find |vecx|, if for a unit vector veca, (vecx - veca).(vecx + veca) = 12.

[2]

Page 2 of 5

Q6.

Find : ∫ (sin x)/(1 + cos x) dx.

[2]

Q7.

Evaluate : ∫₂³ (x dx)/(x² + 1).

[2]

Q8.

A coin is tossed three times. If E is the event 'head on third toss' and F is the event 'heads on first two tosses'. Find P(E mid F).

[2]

Q9.

Let E and F be two events with P(E) = (3)/(5), P(F) = (3)/(10) and P(E ∩ F) = (1)/(5). Are E and F independent ?

[2]

Q10.

Find the product : 1 -2 \2 3 1 2 3 \2 3 1 .

[2]

Section C

subjective · 4 marks each · 8 of 8 shown

Q1.

Find the relationship between a and b so that the function f defined by f(x) = ax + 1 if x ≤ 3, = bx + 3 if x > 3 is continuous at x = 3.

[4]

Q2.

Evaluate : ∫₀¹ x(1-x)ⁿ dx.

[4]

Page 3 of 5

Q3.

Differentiate (log x)x + xlog x w.r.t. x.

[4]

Q4.

Find the shortest distance between the lines : vecr = (1-t)hati + (t-2)hatj + (3-2t)hatk and vecr = (s+1)hati + (2s-1)hatj - (2s+1)hatk.

[4]

Q5.

If veca, vecb, vecc are unit vectors such that veca + vecb + vecc = 0, find the value of veca.vecb + vecb.vecc + vecc.veca.

[4]

Q6.

Solve the linear programming problem graphically : Maximize z = 3x + 2y Subject to : x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.

[4]

Q7.

Let A and B be two sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.

[4]

Q8.

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red ?

[4]

Page 4 of 5

Section D

subjective · 6 marks each · 3 of 3 shown

Q1.

For a matrix A = 1 1 1 \1 2 -3 \2 -1 3 show A³ - 6A² + 5A + 11I = 0. **OR** Solve the system of linear equations, using matrix method : 2x + 3y + 3z = 5, x - 2y + z = -4, 3x - y - 2z = 3.

[6]

Q2.

Evaluate : ∫₀π/2 √(sin φ) cos⁵ φ dφ. **OR** Evaluate : ∫ dfracx cos⁻¹ x√(1-x²) dx.

[6]

Q3.

Find the local maxima and local minima, if any, of the function : f(x) = sin x - cos x, 0 < x < 2π. **OR** Find two positive numbers x and y such that x + y = 60 and xy³ is maximum.

[6]

Page 5 of 5