संक्षेप में : RBSE Class 12 Maths = 56 marks theory + 24 marks practical/project। Calculus अकेला 20+ marks carry करता है — Integration और Differentiation master करो तो almost half paper confident। इस guide में chapter-wise सारे formulas — Relations & Functions, Matrices, Determinants, Differentiation, Integration, Application of Derivatives, Vectors, 3D Geometry, Linear Programming, Probability — Hindi explanation के साथ दिए गए हैं। ये page bookmark करो, exam से पहले daily revise करो।
RBSE Class 12 Maths — Exam Structure 2027
Component Marks Details Theory Paper 56 Board exam hall Practical/Project 24 Internal assessment कुल 80 —
Chapter-wise Marks Distribution
Unit Chapters Expected Marks Priority संबंध और फलन (Relations & Functions) Ch 1-2 6-8 ★★ बीजगणित (Algebra) Ch 3-4 (Matrices, Determinants) 8-10 ★★★ कलन (Calculus) Ch 5-9 (Differentiation, Integration, etc.) 20-24 ★★★★ Highest सदिश और 3D (Vectors & 3D Geometry) Ch 10-11 8-10 ★★★ रैखिक प्रोग्रामन (Linear Programming) Ch 12 4-5 ★ प्रायिकता (Probability) Ch 13 4-6 ★★
Chapter 1-2: संबंध और फलन (Relations & Functions)
Inverse Trigonometric Functions — Key Formulas
Formula Domain Range sin⁻¹(x) + cos⁻¹(x) = π/2 x ∈ [-1, 1] — tan⁻¹(x) + cot⁻¹(x) = π/2 x ∈ R — sec⁻¹(x) + cosec⁻¹(x) = π/2 |x| ≥ 1 — tan⁻¹(x) + tan⁻¹(y) = tan⁻¹((x+y)/(1-xy)) xy < 1 — 2tan⁻¹(x) = sin⁻¹(2x/(1+x²)) |x| ≤ 1 — 2tan⁻¹(x) = cos⁻¹((1-x²)/(1+x²)) x ≥ 0 — 2tan⁻¹(x) = tan⁻¹(2x/(1-x²)) |x| < 1 —
Principal Value Range
Function Range sin⁻¹(x) [-π/2, π/2] cos⁻¹(x) [0, π] tan⁻¹(x) (-π/2, π/2) cot⁻¹(x) (0, π) sec⁻¹(x) [0, π] - {π/2} cosec⁻¹(x) [-π/2, π/2] - {0}
Chapter 3: आव्यूह (Matrices)
Matrix Operations
Operation Formula Addition [A + B]ᵢⱼ = aᵢⱼ + bᵢⱼ (same order matrices) Scalar multiplication [kA]ᵢⱼ = k × aᵢⱼ Multiplication [AB]ᵢⱼ = Σ aᵢₖ × bₖⱼ Transpose (Aᵀ)ᵢⱼ = aⱼᵢ (AB)ᵀ = BᵀAᵀ Important property (A⁻¹)ᵀ = (Aᵀ)⁻¹ Important property
Types of Matrices
Type Property Symmetric A = Aᵀ Skew-symmetric A = -Aᵀ Orthogonal AAᵀ = I Idempotent A² = A Involutory A² = I
Chapter 4: सारणिक (Determinants)
2×2 Determinant
|a b| = ad - bc
|c d|
3×3 Determinant (Expansion along R₁)
Row 1 expansion: a₁₁(Minor) - a₁₂(Minor) + a₁₃(Minor)
Cramer's Rule (2 variables)
x = D₁/D, y = D₂/D (where D ≠ 0)
Important Properties
Property Statement Row/Column identical Determinant = 0 Row swap Determinant sign changes Scalar multiply row Determinant multiplied by scalar Row addition Determinant unchanged |AB| = |A| × |B| Product rule |A⁻¹| = 1/|A| Inverse rule
Rajasthan Board Maths Padhaao पर Practice करें
AI Tutor — 10 Learning Modes · Quiz, Flashcards, Exam Practice · रोज़ 3 Free Chapters
Maths Practice शुरू करें Chapter 5-6: अवकलन (Differentiation)
Basic Differentiation Formulas
Function f(x) Derivative f'(x) xⁿ nxⁿ⁻¹ eˣ eˣ aˣ aˣ ln(a) ln(x) 1/x log_a(x) 1/(x ln a) sin x cos x cos x -sin x tan x sec²x cot x -cosec²x sec x sec x tan x cosec x -cosec x cot x sin⁻¹x 1/√(1-x²) cos⁻¹x -1/√(1-x²) tan⁻¹x 1/(1+x²)
Differentiation Rules
Rule Formula Product Rule (uv)' = u'v + uv' Quotient Rule (u/v)' = (u'v - uv')/v² Chain Rule dy/dx = (dy/du)(du/dx) Parametric dy/dx = (dy/dt)/(dx/dt) Implicit Differentiate both sides, solve for dy/dx Logarithmic Take log → differentiate → solve
Applications of Derivatives
Application Formula/Concept Rate of change dy/dx at point Tangent slope m = dy/dx at (x₁, y₁) Normal slope m = -1/(dy/dx) Tangent equation y - y₁ = m(x - x₁) Increasing function f'(x) > 0 Decreasing function f'(x) < 0 Maxima f'(x)=0, f''(x)<0 Minima f'(x)=0, f''(x)>0
Chapter 7-8: समाकलन (Integration)
Basic Integration Formulas
Function Integral xⁿ xⁿ⁺¹/(n+1) + C (n ≠ -1) 1/x ln|x| + C eˣ eˣ + C aˣ aˣ/ln(a) + C sin x -cos x + C cos x sin x + C sec²x tan x + C cosec²x -cot x + C sec x tan x sec x + C cosec x cot x -cosec x + C
Special Integration Formulas
Type Formula ∫1/(x²+a²) dx (1/a)tan⁻¹(x/a) + C ∫1/(x²-a²) dx (1/2a)ln|(x-a)/(x+a)| + C ∫1/(a²-x²) dx (1/2a)ln|(a+x)/(a-x)| + C ∫1/√(a²-x²) dx sin⁻¹(x/a) + C ∫1/√(x²+a²) dx ln|x + √(x²+a²)| + C ∫1/√(x²-a²) dx ln|x + √(x²-a²)| + C ∫√(a²-x²) dx (x/2)√(a²-x²) + (a²/2)sin⁻¹(x/a) + C
Integration Methods
Method कब Use करें Substitution Composite function — f(g(x)) × g'(x) By Parts ∫u dv = uv - ∫v du (ILATE rule) Partial Fractions Rational function — degree numerator < denominator Trigonometric substitution √(a²-x²), √(x²+a²), √(x²-a²)
ILATE Rule (By Parts — u choose करने का order):
I = Inverse trig → L = Logarithmic → A = Algebraic → T = Trigonometric → E = Exponential
Definite Integrals Properties
Property Formula ∫ₐᵇ f(x)dx = -∫ᵇₐ f(x)dx Limits swap = sign change ∫ₐᵇ f(x)dx = ∫ₐᶜ f(x)dx + ∫ᶜᵇ f(x)dx Split at c ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a-x)dx King's rule ∫₋ₐᵃ f(x)dx = 2∫₀ᵃ f(x)dx if f even Even function ∫₋ₐᵃ f(x)dx = 0 if f odd Odd function
Chapter 9: अवकल समीकरण (Differential Equations)
Type Method Variable Separable dy/dx = f(x)g(y) → ∫dy/g(y) = ∫f(x)dx Homogeneous Put y = vx, then solve Linear dy/dx + Py = Q → IF = e^(∫P dx) Order Highest derivative order Degree Highest power of highest derivative
Chapter 10: सदिश बीजगणित (Vectors)
Vector Operations
Operation Formula Magnitude |a⃗| = √(a₁² + a₂² + a₃²) Unit vector â = a⃗/|a⃗| Dot product a⃗·b⃗ = a₁b₁ + a₂b₂ + a₃b₃ = |a⃗||b⃗|cosθ Cross product |a⃗×b⃗| = |a⃗||b⃗|sinθ Angle between vectors cosθ = (a⃗·b⃗)/(|a⃗||b⃗|) Perpendicular condition a⃗·b⃗ = 0 Parallel condition a⃗×b⃗ = 0⃗ Area of triangle (1/2)|a⃗×b⃗| Area of parallelogram |a⃗×b⃗|
Chapter 11: त्रिविमीय ज्यामिति (3D Geometry)
Line Equations
Form Equation Two-point form (x-x₁)/(x₂-x₁) = (y-y₁)/(y₂-y₁) = (z-z₁)/(z₂-z₁) Direction ratios form (x-x₁)/a = (y-y₁)/b = (z-z₁)/c Vector form r⃗ = a⃗ + λb⃗
Plane Equations
Form Equation General form ax + by + cz + d = 0 Normal form r⃗·n⃗ = d Intercept form x/a + y/b + z/c = 1
Distance Formulas
Formula Use Distance point to plane d = |ax₁+by₁+cz₁+d|/√(a²+b²+c²) Angle between planes cosθ = |(a₁a₂+b₁b₂+c₁c₂)|/(√(a₁²+b₁²+c₁²)×√(a₂²+b₂²+c₂²)) Angle between lines cosθ = |(a₁a₂+b₁b₂+c₁c₂)|/(√(a₁²+b₁²+c₁²)×√(a₂²+b₂²+c₂²))
Chapter 13: प्रायिकता (Probability)
Key Formulas
Formula Description P(A∪B) = P(A) + P(B) - P(A∩B) Addition theorem P(A|B) = P(A∩B)/P(B) Conditional probability P(A∩B) = P(A) × P(B|A) Multiplication theorem Bayes' Theorem P(Aᵢ|B) = P(B|Aᵢ)P(Aᵢ) / ΣP(B|Aⱼ)P(Aⱼ) Mean (Binomial) μ = np Variance (Binomial) σ² = npq P(X=r) Binomial ⁿCᵣ pʳ qⁿ⁻ʳ
Quick Revision Strategy
Formula Revision Order (Priority-based)
Priority Topics Marks Revision Time 1st Integration formulas 10-12 Daily 10 min 2nd Differentiation formulas 8-10 Daily 8 min 3rd Vectors + 3D formulas 8-10 Daily 8 min 4th Matrices/Determinants 6-8 Daily 5 min 5th Probability 4-6 Daily 5 min 6th Inverse Trig + LP 4-6 Daily 4 min Total — 40-52/56 40 min/day
Frequently Asked Questions
Class 12 Maths में सबसे ज़्यादा marks किस topic से आते हैं?
Calculus (Differentiation + Integration + Applications + Differential Equations) से 20-24 marks आते हैं — paper का 40%+। Integration formulas और Differentiation rules master करो तो almost half paper confident। ILATE rule, substitution methods, और partial fractions — ये 3 techniques cover करो।
Formula sheet exam hall में ले जा सकते हैं?
नहीं! Board exam में कोई notes/formula sheet allowed नहीं। इसलिए formulas को memory में रखना ज़रूरी है। Daily 40 minutes formula revision करो — exam तक permanent memory बन जाएगी। ये page bookmark करो और daily revise करो।
RBSE और CBSE Maths syllabus same है?
RBSE Class 12 Maths syllabus NCERT based है — CBSE जैसा ही। Chapters same हैं, formulas same हैं। Difference सिर्फ marks distribution और paper pattern में है — RBSE 56 marks theory + 24 practical, CBSE 80 marks theory + 20 internal। NCERT textbook दोनों boards के लिए primary source है।
Padhaao AI tutor से Class 12 Maths chapter-wise practice करो — Integration, Differentiation, Vectors सब step-by-step explain होता है। Free = 3 chapters/day।
अभी free में शुरू करें →
