• Set theory, set operations, and Venn diagrams.
• De Morgan laws, relation, and the Cartesian product of equivalence.
• Real numbers represented on a line.
• Basic characteristics, modulus, argument, and cube roots of unity of complex numbers.
• Binary number system.
• Conversion of a number between the binary and decimal systems.
• Progressions in geometry, harmony, and arithmetic.
• Real-coefficient quadratic equations
• Graph-based solutions to two-variable linear equations.
• Combination and Permutation.
• The binomial theorem and its uses.
• Applications for logarithms.

• Matrix types and Matrix operations
• Basic characteristics of determinants, a matrix’s determinant.
• Inverse and adjacent to a square matrix.
• Applications include the use of Cramer’s rule and the Matrix method to solve a system of linear equations with two or three unknowns.

• Angles and their degrees and radians measurements.
• Ratios of trigonometry.
• Formulas for the sum and difference of trigonometric identities.
• Sub-multiple and Multiple angles.
• Trigonometric operations in inverse.
• Applications include height and distance as well as triangular properties.

• Cartesian coordinates with a rectangular shape.
• Distance calculation.
• Many variations of a line’s equation and angles between two lines.
• A Point’s separation from a line.
• Circle equation in standard and general form.
• Parabola, ellipse, and hyperbola in their standard forms.
• A conic’s eccentricity and axis.
• Distance between two points at a point in three dimensions.
• Cosines and ratios of directions.
• Equation for two points
• Different equations involve a plane and a line.
• Angles between two planes and two lines.
• Equation for a sphere.

• Real-valued function concept, including domain, range, and function graph.
• Functions that are composite, one-to-one, onto, and inverse.
• Examples of a limit concept and standard limits.
• Examples and algebraic operations on continuous functions for the concept of function continuity.
• Applications for the geometrical and physical interpretations of a derivative of a function at a point.
• Derivatives of a function with respect to another function, derivatives of the sum, product, and quotient of functions, and derivatives of composite functions.
• Derivatives of the second order.
• Functions for increasing and decreasing.
• Application of derivatives to maxima and minima problems.

• Standard integrals using algebraic expressions, and trigonometric, exponential, and hyperbolic functions include integration as the inverse of differentiation, integration by substitution, and integration by parts.
• Applications for evaluating definite integrals include calculating the areas of flat regions bordered by curves.
• Definition of a differential equation’s order and degree, as well as examples of how to construct one.
• Examples include the general and specific solutions to differential equations, as well as the solutions to first-order and first-degree differential equations of various forms.
  application in growth and decay problems.

• Vectors in two and three dimensions, including a vector’s magnitude and direction.
• Unit and null vectors, vector addition, vector scalar multiplication, scalar product, or dot product of two vectors are all examples of vectors. Cross product of two vectors, or vector product.
• Applications include the work carried out by a force and its moment, as well as geometrical problems.

• Data classification, frequency distribution, and cumulative frequency distribution and their examples.
• The graphical representation includes frequency polygons, histograms, and pie charts and their examples.
• Mean, median, and mode constitute central tendency measures.
• Comparison and determination of variance and standard deviation.
• Correlation and regression.

Probability

• Random experiment, events, mutually exclusive and exhaustive events, outcomes and associated sample space, impossible and certain events.
• Intersection and Union of events.
• Elementary, Complementary and composite events.
• Examples and a definition of probability, both classical and statistical.
• Simple problems with basic probability theorems.
• Simple problems include conditional probability and Bayes’ theorem.
• Using a random variable as a sample space function.
• Examples of random experiments that gave rise to the binomial distribution.

• Reading Comprehension & cohesion Questions.
• Cloze Test Questions
• Spotting the Error Questions.
• Fill in the Blanks Questions.
• Synonyms & Antonyms and Vocabulary Questions.
• Idioms and Phrases Questions.
• Sentence Arrangement or Para Jumbled Questions.
• Ordering of words in a Sentence Questions.
• Sentence Improvement or Sentence Correction Questions.
• Grammar and their usage type Questions

• Physical characteristics and states of matter, the Archimedes principle, pressure barometers, and mass, weight, volume, density, and specific gravity.
• Newton’s Laws of Motion, Velocity and Acceleration, Objects’ Motion, Force and Momentum, Parallelogram of Forces, Bodies’ Stability and Equilibrium, Gravitation, Basic Concepts of Work, Power and Energy.
• Effects of Heat, Temperature and Heat Measurement, State Change and Latent Heat, and Heat Transfer Modes.
• Simple musical instruments and their qualities, sound waves. Light propagation, reflection, and refraction along a straight line. Human eye, spherical mirrors, and lenses.
• Earth as a magnet, properties of a magnet, and natural and artificial magnets.
• Electrical power measurement, primary and secondary cells, use of X-rays, conductors and nonconductors, Ohm’s Law, simple electrical circuits, heating, lighting, and magnetic effects of current.
• General Principles for the following tools’ function:
• Simple Pendulums, Simple Pulleys, Siphons, Levers, Balloons, Pumps, Hydrometers, Pressure Cookers, Thermos Flasks, Gramophones, Telephones, Periscopes, Telescopes, Microscopes, Mariner’s Compasses, Lighting Conductors, and Safety Fuses.

• Chemical and physical changes.
• Law of Chemical Combination, Symbols, Formulae, and Simple Chemical Equations, Elements, Mixtures, and Compounds (excluding problems).
• Characteristics of water and air.
• Hydrogen, oxygen, nitrogen, and carbon dioxide preparation and properties, as well as oxidation and reduction.
• Salts, bases, and acids.
• Different types of carbon.
• Natural and artificial fertilizers.
• Materials used in the manufacturing of the substances include soap, glass, ink, paper, cement, paints, safety matches, and gunpowder.
• Basics of atomic structure, atomic equivalents, molecular weights, and valency

• Differences between living things and non-living things.
• Basis of Life: Tissues, Protoplasm, and Cells.
• Plant and animal growth and reproduction.
• Basic knowledge of the human body’s major organs
• The causes and prevention of common epidemics.
• Food: A Human’s source of energy.
• A balanced diet, dietary components.
• The Solar System, comets and meteors, and eclipses.
• Successes of Renowned Scientists.

• A comprehensive examination of Indian history with a focus on culture and civilization.
• Indian Freedom Movement
• Basic instruction on the Indian government and constitution.
• Basic understanding of India’s five-year plans. Cooperatives, Panchayati Raj, and Community Development.
• Basic Teachings of Mahatma Gandhi, Bhoodan, Sarvodaya, National Integration, and Welfare State.
• Renaissance, exploration, and discovery, as well as the American Revolutionary War, are factors influencing the modern world. the Industrial Revolution, the Russian Revolution, and the French Revolution.
• Social effects of science and technology.
• United Nations, Panchsheel, Democracy, Socialism, and Communism concepts. India’s role in the modern world.

• The size and shape of the Earth. Concept of time, latitudes, and longitudes. International Date Line.
• Earth’s movements and their consequences. Genesis of Earth.
• Classification of rocks; mechanical and chemical weathering;earthquakes and volcanoes.
• Climate types, the world’s major natural regions, ocean currents and tides, atmospheric pressure, temperature, planetary winds, cyclones, and anti-cyclones, humidity, condensation, and precipitation.
• India’s regional geography—Climate, Resources for minerals and energy, Natural Vegetation; the location and distribution of industrial and agricultural activity.
• Important seaports and India’s primary land, sea, and air routes.
• India’s primary imports and exports items.

• Knowledge of significant current events that have occurred in India in recent years.
• Current major Global developments.
• Prominent figures of India and around the world, including those involved in sports and culture.