KCET 5h 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.

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.

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.

Cell theory, prokaryotic vs eukaryotic cells, plant vs animal cells, structure and functions of organelles (nucleus, mitochondria, chloroplast, ER, Golgi), cell membrane (fluid mosaic model), and transport mechanisms.

Mendel's laws, inheritance patterns (dominant, recessive, codominance, multiple alleles), DNA structure and replication, RNA transcription and translation, gene expression, genetic code, and human genetics (blood groups, colour blindness, pedigree analysis).