GATE CSE 2027 Preparation

Trace insertion, deletion, and reversal operations on singly and doubly linked lists.

Implement and analyze stack and queue operations using arrays and linked representations.

Convert between infix, postfix, and prefix expressions and evaluate stack-based expressions.

Derive traversal orders and structural properties of binary trees.

Trace search, insertion, and deletion operations in binary search trees.

Trace binary-heap operations and use heaps to implement priority queues.

Resolve hash-table collisions using chaining and open addressing and calculate probe sequences.

Represent graphs and trace breadth-first and depth-first traversals.

Compare algorithm growth rates using asymptotic upper, lower, and tight bounds.

Solve divide-and-conquer running-time recurrences using substitution, recursion trees, and the Master theorem.

Trace comparison-based sorting algorithms and compare their time, space, and stability properties.

Apply binary search and divide-and-conquer reasoning to array-based problems.

Construct greedy solutions and test whether the greedy-choice property holds.

Formulate dynamic-programming states, transitions, base cases, and evaluation order.

Compute minimum spanning trees using Kruskal’s and Prim’s algorithms.

Compute single-source shortest paths and select an appropriate shortest-path algorithm for a given graph.

Translate statements into propositional or first-order logic and determine validity using formal reasoning.

Apply set identities and classify functions as injective, surjective, or bijective.

Compute relation closures and determine whether a relation is an equivalence relation.

Construct Hasse diagrams and determine bounds and lattice properties of partially ordered sets.

Classify algebraic structures by testing closure, identity, inverses, and associativity.

Solve counting problems using permutations, combinations, pigeonhole reasoning, and inclusion–exclusion.

Solve linear recurrence relations and extract coefficients from simple generating functions.

Solve graph-theory problems involving connectivity, trees, planarity, coloring, and matching.

Solve systems of linear equations using matrix rank and row reduction.

Compute eigenvalues and eigenvectors and use them to analyze a matrix.

Evaluate limits and determine continuity and differentiability of functions.

Find local and constrained extrema of single-variable and multivariable functions.

Evaluate definite and improper integrals using standard techniques.

Compute conditional probabilities using independence, total probability, and Bayes’ theorem.

Calculate probabilities for binomial, Poisson, normal, and exponential random variables.

Compute expectation, variance, covariance, and common descriptive statistics.

Perform signed and unsigned binary arithmetic and detect overflow under common number representations.

Decode machine instructions and compute effective addresses for standard addressing modes.

Trace data movement through an ALU, register set, and processor datapath during instruction execution.

Compare hardwired and microprogrammed control and derive control actions for simple instructions.

Calculate pipeline execution time, speedup, and stalls caused by structural, data, and control hazards.

Relate locality and memory-technology characteristics to the design of a memory hierarchy.

Compute cache contents, hits, misses, and address fields for common mapping and write policies.

Trace programmed I/O, interrupt-driven I/O, and DMA transfers and compare their processor overhead.

Convert among regular expressions, nondeterministic finite automata, and deterministic finite automata.

Minimize a deterministic finite automaton and test whether two states or automata are equivalent.

Use closure properties and the pumping lemma to test claims about regular languages.

Generate and parse strings with context-free grammars and detect ambiguity in derivations.

Construct pushdown automata for standard context-free languages and relate them to grammars.

Use closure properties and pumping arguments to test claims about context-free languages.

Trace and design Turing machines for basic language-recognition tasks.

Classify decision problems as decidable, recognizable, or undecidable using reductions and standard results.

Construct token specifications and trace lexical analysis using finite automata.

Compute FIRST and FOLLOW sets and construct an LL(1) predictive parsing table.

Identify handles and trace shift-reduce parsing for a context-free grammar.

Construct LR item sets and an SLR parsing table for a small grammar.

Apply syntax-directed definitions to type checking and expression translation.

Determine runtime storage organization and trace parameter-passing mechanisms.

Generate three-address code and basic blocks for expressions and control flow.

Apply local and data-flow-based compiler optimizations to intermediate code.

Convert an entity–relationship design into a relational schema with appropriate constraints.

Evaluate relational-algebra expressions involving selection, projection, joins, and division.

Write and trace SQL queries using joins, nested queries, aggregation, and NULL semantics.

Compute attribute closures and identify candidate keys from functional dependencies.

Decompose schemas into 3NF or BCNF and test lossless join and dependency preservation.

Calculate record placement and lookup costs for file organizations and B/B+ tree indexes.

Test transaction schedules for conflict serializability and recoverability.

Trace locking, timestamp-ordering, and logging-based recovery protocols.

Trace encapsulation through the network layers and calculate delay, throughput, and bandwidth–delay product.

Detect transmission errors using parity, checksums, and cyclic redundancy checks.

Trace medium-access protocols, Ethernet frame delivery, and learning-switch behavior.

Perform IPv4 subnetting and longest-prefix matching for forwarding-table lookups.

Compute routing outcomes using distance-vector and link-state algorithms.

Trace packet delivery using fragmentation, ARP, ICMP, DHCP, and network address translation.

Analyze reliable transport using sequence numbers, windows, retransmissions, and TCP congestion control.

Trace common application protocols including DNS, HTTP, email, and socket-based client–server communication.

Correct sentence-level errors involving grammar, usage, and word relationships.

Infer claims, assumptions, tone, and conclusions from short reading passages.

Solve verbal analogy, logical-ordering, and statement-based reasoning questions.

Solve percentage, ratio, average, profit-and-loss, and mixture problems.

Solve time-and-work and time–speed–distance problems.

Solve elementary algebra, counting, and probability aptitude questions.

Interpret tables, charts, and multi-step quantitative data sets accurately.

Solve analytical and spatial reasoning problems using diagrams and constraint elimination.

Diagnose Operating Systems gaps by solving timed PYQs on processes, scheduling, synchronization, and deadlocks.

Diagnose Operating Systems gaps by solving timed PYQs on memory management, file systems, and I/O.

Diagnose Digital Logic gaps by solving timed PYQs on Boolean simplification and combinational circuits.

Diagnose Digital Logic gaps by solving timed PYQs on number systems and sequential circuits.

Classify mistakes as conceptual, computational, interpretation, recall, or time-management errors and assign a corrective action.

Apply question selection, marking, and time-allocation rules in a timed mixed-subject test.

Complete a full-length mock using a two-pass attempt strategy under GATE exam constraints.

Analyze mock performance by subject, error type, and time spent to choose the next revision priorities.