Chemistry of Metals :
General principles of metallurgy – occurrence, concentration of ores, production and purification of metals, mineral wealth of India.
Typical metals (Na, Ca, Al, Fe, Cu and Zn) – occurrence, extraction, purification (where applicable), properties and reactions with air, water, acids and non-metals.
Manufacture of steels and alloy steel (Bessemer, Open-Hearth and L.D. process).
Principles of chemistry involved in electroplating, anodizing and galvanizing.
Sets, Relations and Mappings : Idea of sets, subsets, power set, complement, union, intersection and difference of sets, Venn diagram, De Morgan’s Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian product of sets.
Matrices : Concepts of m x n (m≤3, n≤3) real matrices, operations of addition, scalar multiplication and multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of determinants (statement only). Minor, cofactor and adjoint of a matrix.
Infinite series : Binomial theorem for negative and fractional index. Infinite G.P. series, Exponential and Logarithmic series with range of validity (statement only), simple applications.
Binomial theorem (positive integral index) :Statement of the theorem, general term, middle term, equidistant terms, properties of binomial co-efficients.
Principle of Mathematical Induction : Statement of the principle. Proof by induction for the sum of squares, sum of cubes of first n natural numbers, divisibility properties like 22n–1 is divisible by 3 (n≥1), 7 divides 32n+1+2n+2(n≥1).
