📚 Official Curriculum & AI Taxonomy Guide

Mathematics

Deterministic two-level syllabus taxonomy (Subjects ➔ Chapters/Units + AI Keywords) with historical PYQ weightage and board examination patterns. Version: V1.

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All Subjects (Complete Syllabus) अनिवार्य सामान्य गणित (सेक्शन A1) संबंध एवं फलन (कोर गणित) बीजगणित: आव्यूह एवं सारणिक (कोर गणित) कलन: अवकलन एवं समाकलन (कोर गणित) सदिश एवं त्रिविमीय ज्यामिति (कोर गणित) रैखिक प्रोग्रामन (कोर गणित) प्रायिकता (कोर गणित) संख्याएं, परिमाणीकरण एवं संख्यात्मक अनुप्रयोग (एप्लाइड) बीजगणित: आव्यूह एवं सारणिक (एप्लाइड) कलन एवं इसके आर्थिक अनुप्रयोग (एप्लाइड) प्रायिकता बंटन (एप्लाइड) काल श्रेणी विश्लेषण (एप्लाइड) आनुमानिक सांख्यिकी एवं परीक्षण (एप्लाइड) वित्तीय गणित (एप्लाइड) रैखिक प्रोग्रामन निर्माण एवं हल (एप्लाइड)

⚙️ Exam Evaluation Pattern & Marking Scheme

Total Questions 100
Total Marks 300
Correct Answer +3
Negative Marking -1/3
Option Format: 5 Options (5th Option Mandatory: 'अनुत्तरित प्रश्न')

🤖 AI Extractor Directives & Mapping Rules

## Instructions for AI Question Extractor & Taxonomy Mapper

When extracting questions and generating Schema v2.0 JSON packages, the AI model MUST strictly adhere to the following deterministic taxonomy protocol:

### 1. Deterministic Ground-Truth ID Assignment
Every extracted question MUST be mapped using the exact database integer IDs from this specification:
- `subject_id`: Integer ID of the Part / Section (e.g., `64` for General Hindi).
- `subject_name`: Canonical title of the Part (e.g., `सामान्य हिन्दी`).
- `subject_slug`: Canonical slug of the Part (e.g., `general-hindi`).
- `chapter_id`: Integer ID from the **Topic ID** column (e.g., `451`).
- `chapter_name`: Canonical title from the **Topic Name** column.
- `chapter_slug`: Slug from the **Topic Slug** column.
- `subtopic_id`: Integer ID from the **Subtopics (Level 3)** column if an atomic subtopic matches, otherwise `null`.
- `subtopic_name`: Subtopic title if mapped, otherwise `null`.
- `subtopic_slug`: Subtopic slug if mapped, otherwise `null`.
- `key_concept`: The specific atomic concept tested by the question (e.g., 'वृद्धि स्वर संधि', 'नागौरी गाय की विशेषताएं', 'अमोनियम सल्फेट में नत्रजन प्रतिशत').

### 2. JSON Mapping Target Schema
```json
{
"subject_id": 64,
"subject_name": "सामान्य हिन्दी",
"subject_slug": "general-hindi",
"chapter_id": 451,
"chapter_name": "संधि एवं संधि-विच्छेद",
"chapter_slug": "sandhi",
"subtopic_id": null,
"subtopic_name": null,
"subtopic_slug": null,
"key_concept": "वृद्धि स्वर संधि",
"question_type": "mcq_single"
}
```

### 3. Core Extraction Rules
- **Strict Section Boundary Isolation**: Respect examination paper sections. Map Hindi questions strictly to Subject ID 64, Rajasthan GK questions to Subject ID 34, Agronomy questions to Subject ID 74, Horticulture to Subject ID 75, and Animal Husbandry to Subject ID 65. Never cross-map questions across disciplines.
- **Strict Canonical Hierarchy**: Map every question extracted from papers for this examination strictly to one of the canonical Units/Chapters listed in the tables below. Do not fabricate or invent new chapter names or IDs.
- **Question Format Auto-Detection**: Identify and classify the question format strictly:
- Standard 4 or 5 options with 1 correct key: `mcq_single`
- Contains Statement I and Statement II or multiple statements: `statement`
- Contains List I and List II or matching columns: `match_list`
- Requires chronological arrangement or step sequence: `chronological_order`
- Contains Assertion (A) and Reason (R): `assertion_reason`
- **Semantic Keyword Anchors**: Use the 'AI Recognition Keywords' listed in the tables as primary semantic triggers. Matching question stems and option terminologies against these keywords provides high-confidence taxonomy assignment.
- **Out of Syllabus Preservation**: If an extracted historical PYQ belongs to a topic marked with `[OUT_OF_SYLLABUS]`, map it to that designated unit and flag `is_out_of_current = 1`. This preserves year-on-year historical practice.
- **Bilingual Terminology**: Ensure both Hindi (Devanagari) and English scientific terms are recognized according to the bilingual titles and keyword lists provided.

Curriculum Units & AI Recognition Dictionary

अनिवार्य सामान्य गणित (सेक्शन A1) (Compulsory Common Mathematics)

6 Chapters / Units
🟢 ACTIVE 📊 0 Qs
Keywords: (i) Matrices and types of Matrices; (ii) Equality of Matrices transpose of a Matrix Symmetric and Skew Symmetric Matrix; (iii) Algebra of Matrices; (iv) Determinants; (v) Inverse of a Matrix; (vi) Solving of simultaneous equations using Matrix Method
🟢 ACTIVE 📊 0 Qs
Keywords: (i) Higher order derivatives up to second order; (ii) Increasing and Decreasing Functions; (iii) Maxima and Minima
🟢 ACTIVE 📊 0 Qs
Keywords: (i) Indefinite integrals of simple functions; (ii) Evaluation of indefinite integrals; (iii) Definite Integrals; (iv) Application of Integration as area under the curve (simple curve)
#4

अवकल समीकरण

(Differential Equations)
🟢 ACTIVE 📊 0 Qs
Keywords: (i) Order and degree of differential equations; (ii) Solving of differential equations with variable separable
#5

प्रायिकता बंटन

(Probability Distributions)
🟢 ACTIVE 📊 0 Qs
Keywords: Simple Probability
🟢 ACTIVE 📊 0 Qs
Keywords: (i) Graphical method of solution for problems in two variables; (ii) Feasible and infeasible regions; (iii) Optimal feasible solution

संबंध एवं फलन (कोर गणित) (Relations and Functions (Core))

2 Chapters / Units
#1

संबंध एवं फलन

(Relations and Functions)
🟢 ACTIVE 📊 0 Qs
Keywords: Types of relations: Reflexive symmetric transitive and equivalence relations; One to one and onto functions
🟢 ACTIVE 📊 0 Qs
Keywords: Definition range domain principal value branches; Graphs of inverse trigonometric functions

बीजगणित: आव्यूह एवं सारणिक (कोर गणित) (Algebra (Core))

2 Chapters / Units
#1

आव्यूह

(Matrices)
🟢 ACTIVE 📊 0 Qs
Keywords: Concept notation order equality types of matrices zero matrix transpose of a matrix symmetric and skew symmetric matrices; Operations on matrices: Addition multiplication and multiplication with a scalar; Simple properties; Non-commutativity of multiplication and existence of non-zero matrices whose product is the zero matrix (order 2); Invertible matrices and uniqueness of inverse
#2

सारणिक

(Determinants)
🟢 ACTIVE 📊 0 Qs
Keywords: Determinant of a square matrix (up to 3\times 3 matrices) minors cofactors and applications of determinants in finding the area of a triangle; Adjoint and inverse of a square matrix; Consistency inconsistency and number of solutions of system of linear equations by examples solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

कलन: अवकलन एवं समाकलन (कोर गणित) (Calculus (Core))

5 Chapters / Units
🟢 ACTIVE 📊 0 Qs
Keywords: Continuity and differentiability chain rule derivatives of inverse trigonometric functions (\sin^{-1}x \cos^{-1}x \tan^{-1}x) derivative of implicit functions; Concepts of exponential and logarithmic functions; Derivatives of logarithmic and exponential functions; Logarithmic differentiation derivative of functions expressed in parametric forms; Second-order derivatives
🟢 ACTIVE 📊 0 Qs
Keywords: Rate of change of quantities increasing/decreasing functions maxima and minima (first derivative test motivated geometrically and second derivative test given as provable tool); Simple problems illustrating basic principles and real-life situations
#3

समाकलन

(Integrals)
🟢 ACTIVE 📊 0 Qs
Keywords: Integration as inverse process of differentiation; Integration of a variety of functions by substitution by partial fractions and by parts; Evaluation of standard integrals; Fundamental Theorem of Calculus (without proof); Basic properties of definite integrals and evaluation of definite integrals
🟢 ACTIVE 📊 0 Qs
Keywords: Applications in finding the area under simple curves especially lines circles/parabolas/ellipses (in standard form only)
#5

अवकल समीकरण

(Differential Equations)
🟢 ACTIVE 📊 0 Qs
Keywords: Definition order and degree general and particular solutions of a differential equation; Solution by method of separation of variables; Solutions of homogeneous differential equations of first order and first degree; Solutions of linear differential equations of the type \frac{dy}{dx} + Py = Q and \frac{dx}{dy} + Px = Q

सदिश एवं त्रिविमीय ज्यामिति (कोर गणित) (Vectors and Three-Dimensional Geometry (Core))

2 Chapters / Units
🟢 ACTIVE 📊 0 Qs
Keywords: Vectors and scalars magnitude and direction of a vector; Direction cosines and direction ratios of a vector; Types of vectors (equal unit zero parallel and collinear vectors) position vector of a point negative of a vector components of a vector addition of vectors multiplication by a scalar position vector of a point dividing a line segment in a given ratio; Scalar (dot) product and vector (cross) product of vectors
🟢 ACTIVE 📊 0 Qs
Keywords: Direction cosines and direction ratios of a line joining two points; Cartesian equation and vector equation of a line skew lines shortest distance between two lines; Angle between two lines

रैखिक प्रोग्रामन (कोर गणित) (Linear Programming (Core))

1 Chapters / Units
🟢 ACTIVE 📊 0 Qs
Keywords: Introduction related terminology such as constraints objective function optimization graphical method of solution for problems in two variables feasible and infeasible regions (bounded or unbounded) feasible and infeasible solutions optimal feasible solutions (up to three non-trivial constraints)

प्रायिकता (कोर गणित) (Probability (Core))

1 Chapters / Units
🟢 ACTIVE 📊 0 Qs
Keywords: Conditional probability Multiplication theorem on probability independent events total probability Bayes' theorem

संख्याएं, परिमाणीकरण एवं संख्यात्मक अनुप्रयोग (एप्लाइड) (Numbers, Quantification and Numerical Applications (Applied))

2 Chapters / Units
🟢 ACTIVE 📊 0 Qs
Keywords: A. Modulo Arithmetic (modulus of an integer arithmetic operations); B. Congruence Modulo (definition and problems); C. Allegation and Mixture (rule of allegation mean price of mixture)
🟢 ACTIVE 📊 0 Qs
Keywords: D. Numerical Problems; E. Boats and Streams (upstream and downstream equations); F. Pipes and Cisterns; G. Races and Games; H. Numerical Inequalities

बीजगणित: आव्यूह एवं सारणिक (एप्लाइड) (Algebra (Applied))

1 Chapters / Units
🟢 ACTIVE 📊 0 Qs
Keywords: A. Matrices and types of matrices; B. Equality of matrices Transpose Symmetric and Skew symmetric matrix; C. Algebra of Matrices; D. Determinant of Matrices (properties singular/non-singular $

कलन एवं इसके आर्थिक अनुप्रयोग (एप्लाइड) (Calculus (Applied))

2 Chapters / Units
Keywords: A. Higher Order Derivatives (up to second order parametric and implicit functions); B. Application of Derivatives (rate of change); C. Marginal Cost and Marginal Revenue using derivatives; D. Increasing/Decreasing Functions; E. Maxima and Minima (critical points local and absolute extrema applied problems)
🟢 ACTIVE 📊 0 Qs
Keywords: F. Integration (indefinite integrals as anti-derivative); G. Indefinite integrals by substitution partial fraction and by parts; H. Definite Integral as area under the curve & Fundamental theorem; I. Application of Integration (Consumer Surplus and Producer Surplus); J. Differential Equations (order and degree); K. Formulating and solving simple differential equations

प्रायिकता बंटन (एप्लाइड) (Probability Distributions (Applied))

1 Chapters / Units
Keywords: A. Probability Distribution of discrete random variable; B. Mathematical Expectation; C. Variance and S.D. of a random variable; D. Binomial Distribution (Bernoulli trials Mean Variance S.D.); E. Poisson Distribution (conditions Mean Variance); F. Normal Distribution (standard normal variate area relationship)

काल श्रेणी विश्लेषण (एप्लाइड) (Time Based Data (Applied))

1 Chapters / Units
🟢 ACTIVE 📊 0 Qs
Keywords: A. Time Series as chronological data; B. Components of Time Series; C. Time Series analysis for univariate data; D. Secular trend; E. Methods of Measuring trend

आनुमानिक सांख्यिकी एवं परीक्षण (एप्लाइड) (Inferential Statistics (Applied))

1 Chapters / Units
Keywords: A. Population and Sample (simple and systematic random sampling); B. Parameter and Statistics Statistical Significance Central Limit Theorem; C. t-Test (one sample t-test for a small group sample Null and Alternate hypothesis degree of freedom)

वित्तीय गणित (एप्लाइड) (Financial Mathematics (Applied))

1 Chapters / Units
Keywords: A. Perpetuity and Sinking Funds; B. Calculation of EMI; C. Calculation of Returns Nominal Rate of Return; D. Compound Annual Growth Rate (CAGR); E. Linear method of Depreciation; F. Valuation of Bonds (present value approach)

रैखिक प्रोग्रामन निर्माण एवं हल (एप्लाइड) (Linear Programming (Applied))

1 Chapters / Units
Keywords: A. Introduction and related terminology; B. Mathematical formulation of LPP; C. Different types of LPP; D. Graphical Method of Solution for problems in two Variables; E. Feasible and Infeasible Regions; F. Feasible and infeasible solutions optimal feasible solution
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