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GATE DA study materials
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GATE DA: Data Science and Artificial Intelligence

GATE DA · Work through your exam, one topic at a time.

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Data Science and Artificial Intelligence

GATE DA (Data Science and Artificial Intelligence) tests mathematical foundations and their use in data-centric systems: probability and statistics, linear algebra, calculus and optimization, programming and algorithms, databases, machine learning, and AI. Questions often combine a definition with a short calculation, so know both the formula and when it applies.

Core rules and concepts

  • Probability: total probability and Bayes' rule; distinguish P(A|B) from P(B|A), and independence P(A∩B)=P(A)P(B) from mutual exclusivity.
  • Statistics: maximum likelihood, estimators, confidence intervals, and hypothesis tests; know when a test is one- or two-sided.
  • Linear algebra: matrix multiplication, rank, eigenvalues, and positive semidefiniteness; covariance matrices are symmetric PSD.
  • Calculus and optimization: gradients, chain rule, convexity, and regularization. L2 adds λ||w||² and keeps least squares unique when XᵀX is singular.
  • ML: empirical risk, train/validation/test separation, bias–variance, and confusion-matrix metrics.
  • Databases: relational algebra, SQL joins, NULL three-valued logic, normalization, and OLAP versus OLTP.
  • Algorithms and AI: asymptotic complexity, recurrences, hashing, trees, graph traversal, and search with admissible A* heuristics.

Worked example

A disease has prevalence 1%. A test has sensitivity 99% and specificity 95%. Find P(disease | positive). Let D be disease and + be positive. P(+|D)=0.99, P(+|¬D)=0.05, P(D)=0.01. Bayes: P(D|+)=[0.01×0.99]/[0.01×0.99+0.99×0.05]=0.0099/(0.0099+0.0495)=0.0099/0.0594≈0.167. So a positive result implies about 16.7% posterior probability, not 99%. The low prior dominates.

Traps that cost marks

Do not invert conditional probabilities without Bayes. In SQL, NULL = NULL is unknown, and COUNT(column) skips NULLs. In Python, mutable default arguments persist across calls. In ML, fit preprocessing on training data only; scaling before the split leaks information. In complexity, distinguish average from worst case and include hidden log factors. Also check whether a metric is micro- or macro-averaged, and whether accuracy is misleading under class imbalance. For matrices, verify dimensions before applying a formula; for recurrences, state the base case.