Karnataka PUC Syllabus 2025-26 for All Subjects- Download Karnataka 2nd PUC Syllabus PDF Here

Chapter-wise Solution

Important Topics

Chapter 1 - Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One-to-one and onto functions

Chapter 2 - Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions

Chapter 3 - Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication, and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of the inverse, if it exists; (Here, all matrices will have real entries)

Chapter 4 - Determinants

Determinant of a square matrix (up to 3 x 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 a system of linear equations by examples, solving a system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

Chapter 5 - Continuity and Differentiability

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, ???? sin−1 ? , cos−1 ? and tan−1 ?, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, the derivative of functions expressed in parametric forms. Second-order derivatives

Chapter 6 - Application of Derivatives

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)

Chapter 7 - Integrals

Integration is the inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts. Evaluation of simple integrals of the following types and problems based on them. ∫ dx x 2 ± a 2, ∫ dx √x 2 ± a 2 , ∫ dx √a 2 − x 2, ∫ dx ax2 + bx + c, ∫ dx √ax2+bx+c ∫ px + q ax2 + bx + c dx, ∫ px + q √ax2+bx + c dx, ∫ √a 2 ± x 2 dx, ∫ √x 2 − a 2 dx ∫√??2 + ?? + ? ??, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals

Chapter 8 - Application of Integrals

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

Chapter 9 - Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by the method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equations of the type: dy dx + py = q, where p and q are functions of x or constants. d? d? + px = q, where p and q are functions of y or constants.

Chapter 10 - Vectors

Vectors and scalars, the 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 of a vector by a scalar, and position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

Chapter 11 - Three-Dimensional Geometry

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.

Chapter 12 - Linear Programming

Introduction, related terminology such as constraints, objective function, optimisation, 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).

Chapter 13 - Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of a random variable.

Total

Chapters

Topics

Introductory Microeconomics

A Simple economy

Central problems of an economy

The organisation of economic activities

The centrally planned economy

The market economy

Positive and Normative Economics

Micro and Macro Economics

Plan of the Book.

Preliminary Notations and Assumptions

The Consumer's Budget

Budget set

Price ratio and the slope of the Budget line, and points below the Budget line

Changes in the Budget line

Preferences of the Consumer

Monotonic preferences

Substitution between goods

Diminishing rate of Substitution

Indifference Curve

The shape of the Indifference Curve

Indifference Map

Utility

Optimal Choice of the Consumer

Demand Curve and the Law of Demand

Normal and Inferior Goods

Substitution and Complements

Shifts in the Demand Curve: movements along the Demand Curve and Shifts in the Demand Curve

Market Demand

Elasticity along a Linear Demand Curve

Factors Determining Price Elasticity of Demand for a Good

Production and Costs

TP, AP, and MP

The Law of Diminishing Marginal Product And The Law of Variable Proportions

Returns To Scale

Costs

Long-Run Costs

The Theory of the Firm under Perfect Competition

Perfect Competition

Revenue

Profit Maximisation

Supply Curve of a Firm

The Shut-down Point

The Normal Profit and Break-even Point

Determinants of a Firm's Supply Curve

Technological Progress

Input Prices

Unit Tax

Market Supply Curve

Market Equilibrium

Equilibrium, Excess Demand, Excess Supply

Wage Determination in the Labour Market

Shifts in Demand and Supply

Market Equilibrium: Free Entry and Exit

Non-competitive Markets

Simple Monopoly in The Commodity Market

Market Demand Curve is the Average Revenue Curve

Other Non-Perfectly Competitive Markets

Macroeconomics

Emergence of Macroeconomics

National Income Accounting

Some Basic Concepts of Macroeconomics

Circular Flow of Income And Methods of Calculating National Income

Income Method

Goods and Prices

GDP and Welfare

Money and Banking

Functions of Money

Demand for Money

The Supply of Money

Income Determination

Ex Ante And Ex Post

Movement Along with a Curve Versus Shift of a Curve

The Short Run Fixed Price Analysis of the Product Market

Government Budget and the Economy

Components of the Government Budget

Fiscal Policy

Open-Economy Macroeconomics

The Balance of Payments

The Foreign Exchange Market

The Determination of Income in An Open Economy

Trade Deficits, Saving and Investments