📐 Class 12 Mathematics
Solved Board Papers (2026–2021)
CBSE · ICSE · State Boards — free PDFs with step‑by‑step solutions, marking scheme & topper answers.
100% solved · chapter‑wise banks included
📋
Pattern mastery
Exactly like real exam – marks distribution, question types, difficulty trend
⏱️
Time management
Solve under 3h, build speed & leave time for revision
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High weightage
Calculus, Algebra, Vectors – repeat questions with value changes
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95+ scorer’s secret
Familiarity + answer‑framing as per marking scheme
CBSE Class 12 Mathematics (solved Papers)
State Boards — Class 12 Maths (solved Papers)
🇮🇳 U.P Board
🇮🇳 Bihar Board
🇮🇳 Rajasthan Board
🇮🇳 M.p Board and many more
✨ pro tip: Focus on high-weightage chapters: Calculus (35–40%), Algebra (20%), Vectors & Probability — most repeated.
🧠 7 reasons to solve
previous year papers
- Exact exam blueprint & question repetition
- Identify 90%+ weightage topics
- Step‑wise marking scheme – fetch partial marks
- Reduce anxiety, build real confidence
- Competency & case‑study question exposure
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- Official topper answer sheets insight
📥 free 2026 solved paper (all boards)
PDF includes step‑by‑step solutions & marking scheme (CBSE pattern)
⚡ All papers are completely solved with detailed steps. Updated for 2026 aspirants.
📐 CBSE XII Mathematics 2025-26
⏱️ 3 Hrs · Max 80+20
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I. Relations & Functions
30 periods · 8 marks
reflexivesymmetrictransitive
equivalence relationone-one (injective)onto (surjective)
bijective functionsinverse trig definition
domain, range, principal value branchgraph of sin⁻¹x
graph of cos⁻¹xgraph of tan⁻¹x
graph of cot⁻¹xgraph of sec⁻¹xgraph of cosec⁻¹x
\(\sin^{-1}x:[-1,1]\to[-\frac\pi2,\frac\pi2]\)
\(\cos^{-1}x:[-1,1]\to[0,\pi]\)
\(\tan^{-1}x:\mathbb{R}\to(-\frac\pi2,\frac\pi2)\)
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II. Algebra (Matrices & Determinants)
50 periods · 10 marks
matrix concept, notation, orderequality of matrices
types: zero, identity, diagonal, scalar, symmetrictranspose
symmetric & skew‑symmetricaddition, scalar multiplication
matrix multiplication (non‑commutativity)existence of non‑zero matrices with product zero (order 2)
invertible matrices & uniqueness of inversedeterminant (2×2, 3×3)
minors, cofactorsarea of triangle (determinant)
adjoint of matrixinverse using adjoint \(A^{-1}=\frac{adj A}{|A|}\)
consistency/inconsistency of linear equations
solving system of 2 or 3 variables (unique solution) using matrix inverse
\((AB)^T = B^T A^T\)
\(|A|\neq0\)
\(A(adj\,A)=|A|I\)
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III. Calculus
80 periods · 35 marks
continuity & differentiabilitychain rule
derivative of sin⁻¹x, cos⁻¹x, tan⁻¹ximplicit functions
exponential & logarithmic functionslogarithmic differentiation
parametric functions derivativesecond order derivatives
rate of change of quantitiesincreasing/decreasing functions
maxima & minima (first derivative test, second derivative test)
integration as inverse differentiationsubstitution method
integration by partial fractionsintegration by parts
\(\int \frac{dx}{x^2+a^2}\)\(\int \frac{dx}{\sqrt{x^2\pm a^2}}\)
\(\int \frac{dx}{\sqrt{a^2-x^2}}\)\(\int \frac{dx}{ax^2+bx+c}\)
\(\int \frac{dx}{\sqrt{ax^2+bx+c}}\)\(\int \frac{px+q}{ax^2+bx+c}dx\)
\(\int \frac{px+q}{\sqrt{ax^2+bx+c}}dx\)\(\int \sqrt{a^2 \pm x^2}\,dx\)
\(\int \sqrt{x^2-a^2}\,dx\)\(\int \sqrt{ax^2+bx+c}\,dx\)
Fundamental Theorem of Calculus (without proof)
basic properties of definite integralsevaluation of definite integrals
area under simple curves (lines, circles, parabolas, ellipses in standard form)
differential equations: definition, order, degree
general & particular solutionsseparation of variables
homogeneous differential equations (first order & first degree)
linear DE: \(\frac{dy}{dx}+Py=Q\) (P,Q functions of x or constant)
linear DE: \(\frac{dx}{dy}+Px=Q\) (P,Q functions of y or constant)
\(\frac{d}{dx}\sin^{-1}x=\frac1{\sqrt{1-x^2}}\)
\(\int \frac{dx}{x^2+a^2}=\frac1a\tan^{-1}\frac xa\)
\(\int e^x\,dx=e^x+C\)
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IV. Vectors & 3D Geometry
30 periods · 14 marks
vectors & scalarsmagnitude & direction
direction cosines & direction ratiosequal, unit, zero, parallel, collinear vectors
position vector, negative of vectorcomponents of vector, addition
multiplication by scalarsection formula (internal/external)
scalar (dot) product, geometrical interpretation, properties
vector (cross) product, geometrical interpretation, properties
direction cosines of line joining two points
cartesian & vector equation of a lineskew lines
shortest distance between two linesangle between two lines
\(\vec{a}\cdot\vec{b}=|a||b|\cos\theta\)
\(|\vec{a}\times\vec{b}|=|a||b|\sin\theta\)
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V. Linear Programming
20 periods · 5 marks
introduction, related terminologyconstraints, objective function
optimizationgraphical method (two variables)
feasible & infeasible regions (bounded & unbounded)
feasible & infeasible solutionsoptimal feasible solutions
up to three non‑trivial constraints
max Z = ax + by
subject to constraints
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VI. Probability
30 periods · 8 marks
conditional probabilitymultiplication theorem on probability
independent eventstotal probability theorem
Bayes' theoremrandom variable & its probability distribution
mean of random variable
\(P(A|B)=\frac{P(A\cap B)}{P(B)}\)
\(P(A_i|B)=\frac{P(A_i)P(B|A_i)}{\sum P(A_j)P(B|A_j)}\)
🧩 Competency Based (MCQ/Case/Integrated) = 50%
📌 Objective (MCQ) = 20%
📝 Constructed response (SA/LA) = 30%
✅ Internal Assessment: 20 marks | Total marks (Theory+IA) = 100 | Total periods: 240
📐 CBSE Class 12 Mathematics (2025-26) – solvedpapers.net.
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