Discrete Mathematics

Propositional and first-order logic. Sets, relations, functions, partial orders, and lattices. Monoids, Groups. Graphs: connectivity, matching, coloring. Combinatorics: counting, recurrence relations, generating functions.

Linear Algebra

Matrices, determinants, a system of linear equations, eigenvalues and eigenvectors, LU decomposition.

Calculus

Limits, continuity, and differentiability. Maxima and minima. Mean value theorem., Integration.

Probability and Statistics

Random variables. Uniform, normal, exponential, Poisson, and binomial distributions. Mean, median, mode, and standard deviation. Conditional probability and Bayes theorem.

QUANTITATIVE APTITUDE

Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing the data), 2- and 3-dimensional plots, maps, and tables Numerical computation and estimation: ratios, percentages, powers, exponents, and logarithms, permutations, and combinations, and series Mensuration and geometry Elementary statistics and probability.

ANALYTICAL APTITUDE

Logic: deduction and induction, Analogy, Numerical relations, and reasoning

VERBAL APTITUDE

Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech Basic vocabulary: words, idioms, and phrases in context Reading and comprehension Narrative sequencing

SPATIAL APTITUDE

Transformation of shapes: translation, rotation, scaling, mirroring, assembling, and grouping Paper folding, cutting, and patterns in 2 and 3 dimensions

Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point).

Machine instructions and addressing modes. ALU, data path, and control unit. Instruction pipelining, pipeline hazards. Memory hierarchy: cache, main memory, and secondary storage; I/O interface (interrupt and DMA mode).

Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search trees,
binary heaps, graphs.

Searching, sorting, hashing. Asymptotic worst-case time and space complexity. Algorithm design techniques: greedy, dynamic programming, and divide‐and‐conquer. Graph traversals, minimum spanning trees, shortest paths.

Regular expressions and finite automata. Context-free grammar and push-down automata. Regular and context-free languages, pumping lemma. Turing machines and undecidability.

Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate code generation. Local optimization, Data flow analyses: constant propagation, liveness analysis, common subexpression elimination.

System calls, processes, threads, inter‐process communication, concurrency, and synchronization. Deadlock. CPU and I/O scheduling. Memory management and virtual memory. File systems.

ER‐model. Relational model: relational algebra, tuple calculus, SQL. Integrity constraints, normal forms. File organization, indexing (e.g., B and B+ trees). Transactions and concurrency control.

Concept of layering

OSI and TCP/IP Protocol Stacks; Basics of the packet, circuit, and virtual circuit switching; Data link layer: framing, error detection, Medium Access Control, Ethernet bridging;

Routing protocols

shortest path, flooding, distance vector, and link state routing; Fragmentation and IP addressing, IPv4, CIDR notation, Basics of IP support protocols (ARP, DHCP, ICMP), Network Address Translation (NAT); Transport layer: flow control and congestion control, UDP, TCP, sockets; Application layer protocols: DNS, SMTP, HTTP, FTP, Email.