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.
15 min read
Intermediate GATE DA Lesson 118 of 122
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 |