1. Geometry: Two-Dimentional; straight lines, circles and conic sections, Three-Dimensional; straight lines and spheres.
2. Algebra: Sets theory, Relations, Mappings and its applications, Permutations and Combinations, Bionomial Theorem, Complex numbers and their properties: Demoivre’s theorem and its applications.
3. Calculus: Limits, Continuity and Differentiability, Rolle’s and Mean value theorems, Differentiation, Partial Differentiation, Maxima and Minima of functions of one and two variable. Successive differentiation. Integration by using substitution, partial fraction and by parts, Definite integral and its properties, Applications of definite integral to evaluate length and are of simple plane curves.
4. Vector Analysis: Scalar and vector products including their applications.
5. Statistics, Probability and Linear Programming : Measures of Central tendency, Dispersion, Skewness and Kurtosis. Correlation and Regression. Basic concepts of probability, Conditional probability, Baye’s theorem, Discrete and continuous distributions (Binomial, Poisson, and normal distributions), Fundamentals of linear programming problems, Graphical solution, Simplex method and its variants.
6. Matrices: Types of matrices, rank of a matrix, solution of system of linear equations, Cayley Hamilton theorem, Inverse of a matrix, Determinant and its properties.
7. Ordinary Differential Equations: Differential equations of first order and their solutions, Linear differential equations of first and higher order with constant coefficients.
8. Numerical Analysis: Solution of non-linear equations using iterative methods, Interpolation (Newton’s, Lagrange’s and Forward formulae), Numerical Integration (Trapezoid and Simpson Rule).
o Computer Basics: Organization of a computer, Central Processing Unit (CPU), Structure of instructions in CPU, input/output devices, computer memory, memory organization, back-up devices.
o Data Representation: Representation of characters, integers, and fractions, binary and hexadecimal representations, Binary Arithmetic: Addition, subtraction, division, multiplication, floating point representation of numbers, normalized floating point representation, Boolean algebra: truth tables, Venn diagrams.
o Computer Architecture: Block structure of computers, communications between processor and I/O devices, interrupts.
o Computer Language and Operating Systems: Flow charts and algorithms, Concepts of low level and high level languages, Computer programming in C (data types, loop and control statements, functions), Fundamentals of operating systems: multiprogramming, multitasking and time sharing systems.
General Knowledge/Analytical Ability
The question in this section will cover logical reasoning, quantitative reasoning, visual-spatial reasoning and also this section shall carry questions to test the general awareness about business, finance, industry, transportation, scientific inventions, information technology, governance, healthcare and cultural dimensions etc.
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