BITSAT 12-Hour Crash

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.

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.

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.

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.

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.