Part A – English

The English question paper assesses candidates' understanding and practical use of the language. The syllabus includes:

• Grammar and Usage: Proper sentence structure, punctuation, and grammatical rules.
• Vocabulary: Understanding word meanings and usage in context.
• Comprehension: Reading passages followed by questions to test understanding and inference.
• Cohesion in Extended Texts: Analyzing and connecting ideas in longer written works.

Part B – General Knowledge

The General Knowledge paper covers a wide range of subjects. It is essential to have a thorough understanding of the topics listed below, as well as related concepts not explicitly mentioned.

Section A: Physics

• Properties and States of Matter: Mass, weight, volume, density, pressure.
• Motion: Velocity, acceleration, Newton's laws, force, and momentum.
• Heat and Temperature: Measurement, change of state, latent heat, modes of heat transfer.
• Light: Reflection, refraction, human eye, lenses.
• Electricity: Conductors, Ohm's law, electrical circuits, X-rays.
• Principles of Mechanics: Simple machines and their applications (e.g., levers, pulleys).

Section B: Chemistry

• Basic Concepts: Physical vs. chemical changes, elements, compounds, and simple chemical equations.
• Properties of Gases: Hydrogen, oxygen, nitrogen, carbon dioxide.
• Acids and Bases: Their properties and common uses.
• Elementary Atomic Structure: Atomic weights, valency, and chemical combinations.

Section C: General Science

• Life Sciences: Differences between living and non-living things, cell structure, and human anatomy.
• Epidemics: Causes, prevention, and common diseases.
• Nutrition: Energy sources, balanced diet, and food constituents.

Section D: History and Freedom Movement

• Indian History: Cultural and civilizational development, independence movements.
• Indian Constitution: Basic structure and principles.
• Global Events: Renaissance, revolutions, and their impacts.

Section E: Geography

• Earth’s Structure: Shape, size, movements, and effects.
• Natural Resources: Classification of rocks, weather patterns, climate zones, and geographical regions of India.
• Economic Geography: Agricultural and industrial distribution, trade routes.

Section F: Current Events

• Recent Developments: Key events in India and the world, including cultural and sports figures.

Algebra

• Sets: Concept of a set, operations on sets, Venn diagrams, De Morgan's laws, Cartesian products, relations, equivalence relations.
• Real Numbers: Representation on a number line.
• Complex Numbers: Basic properties, modulus, argument, cube roots of unity.
• Number Systems: Binary system, conversion between decimal and binary.
• Progressions: Arithmetic, geometric, and harmonic progressions.
• Quadratic Equations: Solving quadratic equations with real coefficients.
• Inequalities: Solution of linear inequalities in two variables using graphs.
• Combinatorics: Permutation and combination, binomial theorem and its applications.

Matrices and Determinants

• Matrices: Types and operations.
• Determinants: Calculation and properties.
• Adjoint and Inverse: Finding the adjoint and inverse of a square matrix.
• Applications: Solving systems of linear equations using Cramer’s rule and matrices.

Trigonometry

• Angles: Measurement in degrees and radians.
• Trigonometric Ratios: Basic ratios and identities, sum and difference formulas.
• Inverse Trigonometric Functions: Applications in height and distance.

Analytical Geometry

• Coordinate Systems: Rectangular Cartesian coordinates.
• Distance and Lines: Distance formula, equations of lines in various forms, angles between lines.
• Circles and Conics: Standard and general forms of circles, parabolas, ellipses, and hyperbolas.
• 3D Geometry: Points in space, distance between points, direction cosines, equations of planes and lines.

Differential Calculus

• Functions: Concepts of domain, range, and graphs, composite functions.
• Limits and Continuity: Notion of limit, standard limits, examples.
• Derivatives: Definition, interpretation, applications, rules for derivatives (sum, product, quotient, composite functions), second-order derivatives.
• Increasing/Decreasing Functions: Analysis of function behavior.

Integral Calculus and Differential Equations

• Integration: Inverse of differentiation, methods (substitution, by parts), evaluation of definite integrals.
• Differential Equations: Definition, formation, general and particular solutions, first-order and first-degree equations.
• Applications: Problems of growth and decay.

Vector Algebra

• Vectors: Concepts in two and three dimensions, magnitude and direction.
• Operations: Addition, scalar multiplication, dot product, and cross product.
• Applications: Work done by a force and moments in geometry.

Statistics and Probability

• Statistics: Classification and frequency distribution, cumulative frequency.
• Graphical Representation: Histograms, pie charts, frequency polygons.
• Measures of Central Tendency: Mean, median, mode.
• Dispersion: Variance and standard deviation.