GATE DA syllabus 2027

• Counting: permutations and combinations
• Probability axioms, sample space, events, independent and mutually exclusive events
• Marginal, conditional and joint probability; Bayes' theorem
• Conditional expectation and variance
• Mean, median, mode and standard deviation; correlation and covariance
• Random variables; discrete random variables and probability mass functions
• Uniform, Bernoulli and binomial distributions
• Continuous random variables and probability distribution functions
• Uniform, exponential, Poisson, normal, standard normal, t- and chi-squared distributions
• Cumulative distribution function; conditional PDF
• Central limit theorem
• Confidence intervals; z-test, t-test and chi-squared test

• Vector spaces and subspaces; linear dependence and independence of vectors
• Matrices: projection, orthogonal, idempotent and partition matrices and their properties
• Quadratic forms
• Systems of linear equations and their solutions; Gaussian elimination
• Eigenvalues and eigenvectors
• Determinant, rank and nullity; projections
• LU decomposition and singular value decomposition (SVD)

• Functions of a single variable
• Limit, continuity and differentiability
• Taylor series
• Maxima and minima
• Optimization involving a single variable

• Programming in Python
• Basic data structures: stacks, queues, linked lists, trees and hash tables
• Search algorithms: linear search and binary search
• Basic sorting algorithms: selection sort, bubble sort and insertion sort
• Divide and conquer: merge sort and quicksort
• Introduction to graph theory
• Basic graph algorithms: traversals and shortest path

• ER model
• Relational model: relational algebra, tuple calculus and SQL
• Integrity constraints and normal forms
• File organization and indexing
• Data types; data transformation: normalization, discretization, sampling and compression
• Data warehouse modelling: schemas for multidimensional data models
• Concept hierarchies; measures: categorization and computations

Supervised learning

• Regression and classification problems
• Simple linear regression, multiple linear regression and ridge regression
• Logistic regression
• k-nearest neighbour and naive Bayes classifier
• Linear discriminant analysis
• Support vector machine
• Decision trees
• Bias–variance trade-off
• Cross-validation: leave-one-out (LOO) and k-fold
• Multi-layer perceptron and feed-forward neural networks

Unsupervised learning

• Clustering algorithms: k-means and k-medoid
• Hierarchical clustering: top-down and bottom-up; single-linkage and multiple-linkage
• Dimensionality reduction: principal component analysis (PCA)

• Search: informed, uninformed and adversarial
• Logic: propositional and predicate
• Reasoning under uncertainty: conditional independence representation
• Exact inference through variable elimination
• Approximate inference through sampling

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

Quantitative Aptitude

• Data interpretation: bar graphs, pie charts and other graphs, 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

Spatial Aptitude

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