BITSAT 1-Year Plan

Complex numbers as a+ib, algebra of complex numbers, modulus and argument, De Moivre's theorem, cube roots of unity, quadratic equations with real and complex roots, discriminant, and nature of roots.

Types of matrices, matrix operations (addition, multiplication, transpose), adjoint and inverse of matrices, determinant evaluation (up to 3×3), properties of determinants, and solving linear equations using matrices.

Fundamental principle of counting, permutation (linear and circular), combination, Pascal's triangle, binomial theorem (general and middle term), binomial expansion for positive integer indices, and arrangement problems.

Arithmetic progression (AP), geometric progression (GP), arithmetic-geometric progression (AGP), harmonic progression (HP), sum of n terms, infinite series convergence, and AM-GM inequality applications.

Positive integral index binomial expansion, general and middle terms, Pascal's triangle, binomial coefficient properties, and applications in finding coefficients and approximations.

Trigonometric ratios, identities (basic and conditional), signs in quadrants, allied angles, sum-to-product and product-to-sum formulas, multiple and submultiple angles, and solving trigonometric equations.

Cartesian coordinate system, distance formula, section formula, area of triangle, slope-intercept form, general equation of line, angle between lines, perpendicular and parallel conditions, and solving linear equations graphically.

Circle (equation, tangents, normals), parabola (standard forms, focal properties), ellipse (eccentricity, latus rectum), hyperbola (asymptotes, rectangular hyperbola), and standard equations with transformations.

Units and dimensions, SI base units, errors in measurement, significant figures, vernier calipers, screw gauge, and dimensional analysis — foundational concepts for all physics problem-solving.

Motion in one and two dimensions — displacement, velocity, acceleration, equations of motion, projectile motion, relative velocity, and circular motion with numerical applications.

Newton's three laws, friction (static and kinetic), circular motion dynamics, tension, spring force, and momentum conservation — core mechanics for engineering entrance exams.

Work done by constant and variable forces, kinetic and potential energy, work-energy theorem, conservation of mechanical energy, power, and collisions (elastic and inelastic).

Torque, moment of inertia, angular momentum, radius of gyration, theorems of moment of inertia, rotational kinematics, and conservation of angular momentum.

Newton's law of gravitation, acceleration due to gravity, variation of g with altitude and depth, Kepler's laws, orbital velocity, escape velocity, and gravitational potential energy.

Elasticity (stress-strain, Hooke's law, Young's modulus), fluid mechanics (Pascal's law, Bernoulli's principle, viscosity, surface tension, capillarity), and Archimedes' principle.

Heat, temperature, calorimetry, heat transfer (conduction, convection, radiation), first and second law of thermodynamics, specific heat capacity, and thermodynamic processes.

Dual nature of matter, de Broglie relation, Heisenberg uncertainty principle, quantum numbers, orbital shapes (s, p, d, f), Aufbau principle, Hund's rule, Pauli's exclusion principle, and electronic configurations.

Ionic and covalent bonding, VSEPR theory, hybridization (sp, sp², sp³, sp³d, sp³d²), valence bond theory, MOT (bond order, HOMO-LUMO), dipole moment, and resonance structures.

Modern periodic table, periodic trends — atomic radius, ionization enthalpy, electron gain enthalpy, electronegativity, valence electrons, metallic/non-metallic character across periods and groups.

Gas laws (Boyle's, Charles's, Avogadro's), ideal gas equation, kinetic theory of gases, van der Waals equation, liquefaction of gases, critical temperature, and solid-state (lattice, crystal systems, Bragg's law).

System and surroundings, first law of thermodynamics (internal energy, work, heat), enthalpy, Hess's law, spontaneity, Gibbs free energy, second law of thermodynamics, and entropy change calculations.

Reversible reactions, equilibrium constant (Kp, Kc), Le Chatelier's principle, factors affecting equilibrium, relationship between Kp and Kc, ionic equilibrium in solutions, pH, buffers, and solubility product.

Rate of reaction, rate law and order, molecularity, zero, first, and second-order reactions, Arrhenius equation, activation energy, catalyst role, and half-life calculations.

Oxidation-reduction concepts, balancing redox equations, electrochemical cells (galvanic, electrolytic), Nernst equation, standard electrode potentials, Faraday's laws of electrolysis, and corrosion prevention.

Tense, subject-verb agreement, articles (a, an, the), prepositions, conjunctions, voice (active/passive), narration (direct/indirect), and error spotting — grammar fundamentals tested in BITSAT English section.

Synonyms, antonyms, one-word substitutions, homophones, idioms, phrases, and phrasal verbs — contextual vocabulary usage and word power tested through sentence completion and reading passages.

Passages on general, scientific, and literary topics with questions on main idea, inference, vocabulary in context, tone, and fact-vs-opinion — speed reading and comprehension skills assessed.

Rearranging jumbled sentences to form a coherent paragraph — tests logical sequencing, connector usage, and understanding of discourse structure in written English.

Identifying the most grammatically correct and stylistically appropriate version of an underlined portion — combines grammar precision with clarity of expression.

Passage with missing words to be filled from given options — tests vocabulary, grammar, and contextual coherence simultaneously in a time-efficient format.

Word pairs with relationships (synonym, antonym, part-whole, function, cause-effect) — reasoning through linguistic relationships and logical word connections.

Identifying the main point or best summary of a passage — tests ability to extract core meaning and distinguish between details and central ideas in written text.

Complex puzzles involving multiple parameters, circular and linear arrangements, grids, and family tree problems — BITSAT logical reasoning tests systematic analytical thinking through multi-constraint puzzle scenarios.

Family tree problems, coded blood relations, generational gaps, relationship terminology, and mixed relations — direct questions where the family structure once decoded yields clear answers.

Cardinal and intercardinal directions, shadow-based direction problems, distance-direction combinations, and coded directional sequences — visual-spatial reasoning for BITSAT LR section.

Letter-number coding, sentence coding, new pattern coding, and mixed alphanumeric series — BITSAT tests pattern recognition speed and attention to detail in encoded sequences.

Number series, alphabet series, alphanumeric series, and figure series — identifying the pattern to complete or find the incorrect term in a given sequence.

Linear (single and double row), circular (facing inside/outside), rectangular, and combined arrangements with multiple positional constraints — high-weight BITSAT LR topic requiring careful diagramming.

Complex multi-constraint puzzles involving ages, professions, colours, and cities — higher-order reasoning combining multiple logic types simultaneously.

Venn diagram method, possibility cases, reverse syllogisms, and logical consistency checking — BITSAT LR tests deductive reasoning through if-then relationship statements.