PYQs by Topic
Every verified previous-year GATE DA problem, regrouped by subject so you can drill one area at a time — each with its year, a one-line topic, the answer, and a link to the lesson that teaches it.
The year walkthroughs proved the exam’s spine is stable — but they scattered each concept across three separate pages, and the last lesson argued that for revision this is exactly backwards. Days before the exam you do not want to relive a paper; you want to confront a topic and see every way it has ever been asked, all at once. So here is the whole back-catalogue regrouped — not by year, but by subject. Drill one column in a sitting: read the topic, try to recall the answer before your eye reaches it, and wherever it does not come instantly, follow the link and revise that lesson. The gaps you find here are precisely the lessons worth your last week.
Probability & Statistics
| Year | Topic | Answer | Lesson |
|---|---|---|---|
| 2026 | Disease test, posterior P(disease given +) | ≈ 0.77 | Bayes’ Theorem |
| 2025 | Three-box posterior, P(Box 2 given white) | 0.25 | Bayes’ Theorem |
| 2024 | Covariance of two coin-indicators | 0.0625 | Covariance & Correlation |
| 2024 | z-score of a value (μ=96000, σ=21000) | ≈ 0.476 | Mean, Median & z-scores |
| 2024 | Exponential: 5·E(X) = Var(X), find λ | 0.2 | Exponential & Poisson |
| 2025 | Normal approx of a Bernoulli sum, P(60 ≤ Y ≤ 90) | Φ(2) − Φ(−2) ≈ 0.9544 | Central Limit Theorem |
| 2024 | Mutually exclusive events: which always hold (MSQ) | disjoint and dependent | Independent vs Mutually Exclusive |
Linear Algebra
| Year | Topic | Answer | Lesson |
|---|---|---|---|
| 2024 | Eigenvalues of [[2,−1],[3,1]] | complex conjugate pair | Eigenvalues & Eigenvectors |
| 2024 | Sum of singular values of uuᵀ, u=(1..5) | 55 | Singular Value Decomposition |
| 2025 | A³ = A: do A and A² share rank? | yes, always | Eigen-properties & Transforms |
| 2026 | Maximise xᵀAx on the unit sphere (eigenvalues 5, 2) | 5 (largest eigenvalue) | Quadratic Forms |
| 2025 | Norm-preserving A (‖Ax‖ = ‖x‖): what follows (MSQ) | orthogonal, det = ±1 | Orthogonal Matrices |
| 2024 | Projection onto a 2-D subspace of R³: rank, nullity | rank 2, nullity 1 | Projections & Idempotent Matrices |
| mock | det(M² + 12M) when det M = 0 | 0 | Determinants |
Calculus & Optimization
| Year | Topic | Answer | Lesson |
|---|---|---|---|
| 2025 | f⁽¹⁰⁾(0) for f(x) = sinh x | 0 | Taylor & Maclaurin Series |
| 2025 | lim (t→∞) (√(t²+t) − t) | 0.5 | Limit Techniques |
| 2024 | lim (x→0) ln((x²+1)·cos x) / x² | 0.5 | Limit Techniques |
| 2024 | Critical point with f'(x*) = 0 and positive f''(x*) | local minimum | Maxima, Minima & 2nd-Derivative Test |
| 2024 | Solve k so a two-piece function is continuous at x=2 | k = 1.5 | Continuity |
| 2025 | Is ReLU = max(0, x) differentiable at x = 0? | continuous, not differentiable | Differentiability |
| 2025 | Positive f'' everywhere: which statements always hold (MSQ) | convex; min need not exist | Convexity & Optimization |
| 2025 | Global max/min of x³ − 3x on [−2, 2] | max 2, min −2 | Optimization on a Closed Interval |
Programming & DSA
| Year | Topic | Answer | Lesson |
|---|---|---|---|
| 2026 | Mutable default argument: f(1), f(2), f(3, []) | [1], [1,2], [3] | Functions & the Mutable-Default Trap |
| 2025 | Hash h(x)=3x mod 10, linear probing: where do 14, 15 land | slots 4 and 6 | Hash Tables & Linear Probing |
| 2024 | Quicksort (last-pivot) swaps on a sorted array | 0 | Merge Sort & Quicksort |
| 2024 | Valid topological orderings of a DAG (MSQ / count) | check vs edges; 12 total | BFS, DFS & Topological Sort |
| 2025 | List state after A.extend(B) vs append | only extend flattens | Lists, Tuples, Dicts & Gotchas |
| mock | "GATE2026"[::2] step-2 slice | "GT22" | Python: Types & Slicing |
| mock | Worst-case comparisons, binary search on 1024 items | 10 | Linear & Binary Search |
Databases & Warehousing
| Year | Topic | Answer | Lesson |
|---|---|---|---|
| 2024 | RA: “every Team player is both defender and forward” | π(Team) − (D ∩ F) = ∅ | Relational Algebra I |
| 2025 | RA: owners of red cars made by “ABC” (join + select) | the inside-out projection | Joins & Division |
| 2024 | FD closure: which dependencies are derivable | VW → Y and VW → YZ | Functional Dependencies & Closure |
| 2025 | Decomposition splits an FD across fragments | must join to enforce it | Lossless-Join vs Dependency-Preservation |
| 2024 | SQL row count (join + WHERE filters) | 3 rows | SQL: Computing Results by Hand |
| 2024 | Index for range + ORDER BY: B+-tree or hash | B+-tree | File Organization & Indexing |
| mock | Snowflake vs star schema | snowflake normalises dimensions | Star vs Snowflake Schemas |
Machine Learning
| Year | Topic | Answer | Lesson |
|---|---|---|---|
| 2026 | Angle between principal components PC1 and PC10 | 90° | PCA & Dimensionality Reduction |
| 2026 | Parameters of MLP 30 → 4 → 3 → 1, no bias | 135 | Multi-Layer Perceptron |
| 2026 | One SGD step: w = 10 − 0.1·10 | 9.0 | Gradient Descent (One Step) |
| 2026 | Increasing ridge λ: effect on bias and variance | bias up, variance down | Ridge Regression |
| 2026 | First Manhattan-distance merge in agglomerative clustering | P2–P4 (distance 4) | Hierarchical Clustering |
| 2025 | Bayes-optimal classifier error from priors + likelihoods | 0.40 | Naive Bayes |
| 2026 | LOOCV models after removing a 100-of-1000 test set | 900 | Cross-Validation |
| 2026 | Recall from a confusion matrix (TP=8, FN=6) | ≈ 0.571 | Precision, Recall, ROC |
Artificial Intelligence
| Year | Topic | Answer | Lesson |
|---|---|---|---|
| 2026 | Minimax: best strategy from leaves [8,6,−1],[1,5,7],[−4,−3,−12] | strategy 2 (value 1) | Adversarial Search: Minimax |
| 2026 | FOL: “Every king is a person” | ∀x King(x) ⇒ Person(x) | First-Order & Predicate Logic |
| 2026 | Quantifier-implication validity over a non-empty domain | only ∀x P(x) ⇒ ∃x P(x) | First-Order & Predicate Logic |
| 2026 | Statement equivalent to “X entails Y” | X ∧ ¬Y unsatisfiable | Propositional Logic |
| 2024 | Count models of A ∨ ¬B ∨ C over 3 variables | 7 | Propositional Logic |
| 2024 | Alpha-beta pruning: root value (same as minimax) | 3 | Alpha-Beta Pruning |
| 2024 | Bayesian-network posterior by variable elimination | exact (not sampling) | Exact Inference |
| 2024 | Largest admissible heuristic when true cost is 10 | h = 10 | Heuristics & Admissibility |
General Aptitude
| Year | Topic | Answer | Lesson |
|---|---|---|---|
| mock | Successive percentages: 20% discount then 10% tax on ₹1000 | ₹880 | Timed Mock 1 |
| mock | Percentage growth from 120 to 200 | 66.67% | Timed Mock 1 |
| mock | Syllogism: does “some cats are pets” follow? | no, not necessarily | Timed Mock 1 |
A question to carry forward
Run your eye down these columns and you have a diagnosis: the rows whose answers leapt to mind are topics you own, and the rows that made you hesitate are your revision list, named and linked. That is what a topic index is for — it finds the gaps.
But finding a gap on a quiet revision page is the gentle half of the work. The exam hall is unkind in ways no index can rehearse: a countdown ticking, a jolt from a Bayes posterior to a syllogism to an eigenvalue with no warm-up between, and negative marking that punishes the panicked guess you would never have made at leisure. You can know every answer here and still bleed marks to the clock and the chaos. Here is the thread onward: how do you practise the exam itself — the timer, the subject-whiplash, the marking scheme — instead of merely the material, and what does a real timed mock reveal that no amount of calm revision ever will?