Class 12 · Mathematics (041)

Types of relations, functions, invertibility, and composition.

Domain, range, and principal values of $\sin^{-1}, \cos^{-1}, \tan^{-1}$, and identities.

Matrix operations, transpose, symmetric/skew-symmetric, elementary operations, and inverse.

Determinant of a square matrix, properties, minors and cofactors, adjoint, and application to solving systems.

Continuity at a point and on an interval, differentiability, chain rule, and derivatives of implicit/parametric/logarithmic functions.

Rate of change, tangents and normals, increasing/decreasing functions, maxima and minima.

Indefinite and definite integrals, standard forms, substitution, by parts, partial fractions.

Area under simple curves, area between two curves.

Order and degree, general/particular solutions, variables separable, homogeneous, and linear DEs.

Vector algebra: addition, scalar and cross products, projections.

Direction cosines, lines, planes, angle between two lines/planes, shortest distance.

Formulation of LPPs, graphical method for two variables, feasible region, optimal value.

Conditional probability, multiplication rule, Bayes' theorem, random variables and their distributions.