GATE DA
An exam-first track for GATE Data Science & Artificial Intelligence. Ten roadmaps across the full syllabus — Probability & Statistics, Linear Algebra, Calculus, Python & Algorithms, Databases & Warehousing, Machine Learning, AI, and General Aptitude — each taught from first principles to exactly the depth GATE asks, drilled with real previous-year questions, NAT practice, and full mock tests.
- Chapter 01
Orientation
1 lesson - 01 How GATE DA Works Everything you need to know about the paper before you start studying: structure, marking, weightage, and a study plan that starts where the marks…
- Chapter 02
Probability & Statistics
16 lessons - 02 Counting: Permutations & Combinations Three friends and two tickets, and a single quiet question — does the order matter? From that one question the whole of counting opens up: the mult…
- 03 Mean, Median, Mode & z-scores Five quiz marks and a parent's simple question — how did the class do? Three honest answers come out, and they do not always agree. From there we m…
- 04 Sample Space, Events & Axioms You already trust two obvious things about a die's chances — none is negative, and together they make one whole. Write those obvious things down ca…
- 05 Independent vs Mutually Exclusive Two coin tosses ignore each other; a single die cannot be even and odd at once. The two ideas sound alike and the exam swaps them on purpose — so w…
- 06 Conditional & Total Probability You learn it rained last night, and the chance the ground is wet leaps from a guess to near-certain — nothing changed but what you know. That re-ju…
- 07 Bayes' Theorem The direction you can measure — a test's accuracy, P(positive given disease) — is rarely the one you want, P(disease given positive). Bayes is the…
- 08 Random Variables, PMF & CDF Toss three coins and count the heads — you have just turned a messy outcome into a single number. Name that and it is a random variable; list its c…
- 09 Expectation, Variance & SD A die game answers the wish from last lesson: two numbers can stand in for a whole table — the expectation for where the variable sits, the varianc…
- 10 Uniform, Bernoulli & Binomial Three everyday setups in costume: a fair die where every face is equal, a single coin flip, and many flips counted up. These are the repeat-offende…
- 11 Continuous RVs: PDF, CDF & Uniform Ask how long someone waited for the bus and they say 'about eight minutes', never 8.0000 — an exact instant has no chance, because a range holds in…
- 12 Exponential & Poisson Back at the bus stop: how long until the next bus, and how many arrive in an hour? One is a waiting time, the other a count, and a single rate λ go…
- 13 Normal & Standard Normal Squint at anything built from many small influences — heights, errors, exam totals — and the same bell appears. You never integrate it by hand; you…
- 14 Joint, Marginal & Conditional Distributions Real questions rarely involve one variable alone — a height and a weight, a machine and a defect. One little table holds the chance of every pairin…
- 15 Covariance, Correlation & Total Expectation Plot study hours against marks and the dots tilt up; plot TV hours and they tilt down. That tilt is the single number the last lesson wanted — cova…
- 16 Central Limit Theorem & Confidence Intervals The strangest fact in probability, and the answer to where the bell keeps coming from: average enough samples from any population, however lopsided…
- 17 z-test, t-test & chi-squared test The last lesson estimated a mean; now we want a verdict. A hypothesis test is a courtroom for data: presume the boring default, measure how strange…
- Chapter 03
Linear Algebra
16 lessons - 18 Vectors, Matrices & Special Forms A column of numbers is an arrow; a grid of numbers is a row of arrows stacked together. Get fluent adding and multiplying these two objects — row-d…
- 19 Vector Spaces & Subspaces Which parts of a space are self-contained — so that adding or stretching arrows inside them never throws you out? Those are subspaces, decided by t…
- 20 Independence, Span, Basis & Dimension The word that crossed over from probability — independence — now means arrows that each point in a genuinely new direction. From it fall span, basi…
- 21 Systems of Equations & Gaussian Elimination Two prices, two clues, one honest answer. We start from a shopkeeping puzzle, tidy the equations into a staircase, and read the unknowns off the bo…
- 22 Rank, Nullity & Solution Sets Stack a clutch of arrows as a matrix's columns and the count of independent directions has a name — rank. Its partner nullity counts the free direc…
- 23 Determinants & Their Properties The last lesson wanted one number, computed once, that says a square matrix has full rank. The determinant is that number — and it also tells you h…
- 24 Inverse & Invertibility Determinant told you whether a matrix could be undone; here we build the undoing. The 2×2 swap-negate-divide formula, why a zero determinant blocks…
- 25 Eigenvalues & Eigenvectors Most directions a matrix shoves to a new angle; a few it leaves on their own line, only stretched. Those are eigenvectors, the stretch factors are…
- 26 Eigen-properties & Transforms The payoff for finding eigenvalues: you get them free for A², A⁻¹, and A + cI, because the same eigenvector carries through and only λ moves. Plus…
- 27 Orthogonality & Orthogonal Matrices A matrix that turns space rigidly like a sheet of paper — no length stretched, no angle bent. Orthonormal columns make Q transpose Q = I (so the in…
- 28 Projections & Idempotent Matrices A projection casts a shadow — it squashes every vector onto a subspace and leaves vectors already there alone, so the shadow of a shadow is the sam…
- 29 Quadratic Forms & Definiteness Feed a direction into xᵀAx and one number pops out — a warped 'size'. Sweep the direction around and a surface appears: a bowl, a saddle, an upside…
- 30 LU Decomposition Elimination does a pile of work to triangulate a matrix, then we throw it away. LU keeps the receipt: A = L·U splits into a lower- and an upper-tri…
- 31 Partition (Block) Matrices Draw a few lines through a big matrix and treat the rectangles inside as single objects. Blocks largely behave like scalars — you add and multiply…
- 32 Singular Value Decomposition The decomposition that minds nothing — any matrix at all, square or rectangular, factors as A = UΣVᵀ: rotate, stretch by non-negative singular valu…
- 33 Always-True Synthesis Drills Consolidate the linear-algebra web of equivalences for a square matrix and drill the GATE 'which statements are always true' MSQ format, checking e…
- Chapter 04
Calculus & Optimization
13 lessons - 34 Functions of One Variable Domain, range, and the handful of standard function shapes you must recognise on sight — the foundation the whole Calculus block stands on.
- 35 Limits & One-Sided Limits What a limit really means — the value a function heads toward — plus left vs right limits, limits at infinity, and why a limit can exist where the…
- 36 Limit Techniques The toolkit for actually evaluating limits — factoring, conjugate rationalising, standard limits, and Taylor expansion — drilled on real GATE DA NA…
- 37 L'Hopital's Rule A shortcut for limits stuck at 0/0 or ∞/∞: differentiate top and bottom separately and try again. A reliable source of GATE DA limit marks.
- 38 Continuity A function is continuous at a point when its limit there exists and equals the function value — no jump, no hole, no asymptote. A recurring GATE DA…
- 39 Differentiability A function is differentiable where it has a unique tangent slope. Differentiable implies continuous — but NOT the reverse, as ReLU and |x| show at…
- 40 Product, Quotient & Chain Rule The three rules that turn any combination of standard functions into its derivative: product, quotient, and chain. The everyday workhorse of GATE C…
- 41 Taylor & Maclaurin Series Rewrite a smooth function as an infinite polynomial: its Taylor series. The coefficients carry the derivatives, and GATE asks you to read one off.
- 42 Critical Points & Monotonicity Where a curve flattens out: f'(x) = 0 marks the candidates for peaks and valleys, and the sign of f' tells you where the function climbs or falls.
- 43 Maxima, Minima & the 2nd-Derivative Test Once you have a critical point, the second derivative tells you its type: concave up is a valley, concave down is a peak. The single most-tested ca…
- 44 Optimization on a Closed Interval To find the global max and min of a continuous function on a closed interval, compare every critical point against both endpoints — the endpoints a…
- 45 Convexity & Single-Variable Optimization A convex function is bowl-shaped: f''(x) ≥ 0 everywhere. The payoff — any local minimum is automatically global, and a strict bowl has at most one…
- 46 Lipschitz & One-Insight Problems Some GATE calculus problems look brutal but turn on a single idea. The signature one: a squared bound |f(x) − f(y)| ≤ C(x − y)² secretly forces f t…
- Chapter 05
Programming, Data Structures & Algorithms
15 lessons - 47 Python for GATE: Types & Slicing GATE DA programming is in Python, and the signature question is predict the output. Master types, division, and slicing first.
- 48 Lists, Tuples, Dicts, Sets & Gotchas The four built-in collections and the gotchas GATE loves: append vs extend vs +, and aliasing vs copying a list.
- 49 Functions, Scope & the Mutable-Default Trap Define functions, pass default arguments, and understand local vs global scope — plus the mutable-default trap GATE tests directly.
- 50 Recursion & Tracing A function that calls itself on a smaller input until a base case fires. The GATE DA skill is tracing the call tree and counting calls — including…
- 51 Reading Pseudocode & Predicting Output GATE writes some algorithm questions in language-neutral pseudocode. The skill is patient, table-driven tracing — and watching the index base.
- 52 Big-O: Best, Average & Worst Case Big-O is the growth rate of work as input grows — drop constants, keep the dominant term. Reading loop nests and simple recurrences underlies every…
- 53 Linear & Binary Search Scan left-to-right in O(n), or halve a sorted range in O(log n) — and count the comparisons the way GATE does.
- 54 Bubble, Insertion & Selection Sort The three quadratic sorts GATE traces pass-by-pass — bubble bubbles, selection picks the min, insertion grows a sorted prefix. Know their passes, s…
- 55 Merge Sort & Quicksort Two divide-and-conquer sorts: mergesort is always Θ(n log n) and stable; quicksort averages Θ(n log n) but degrades to Θ(n²) on the wrong input.
- 56 Stacks, Queues & Deques Three order-defined containers: a stack is LIFO, a queue is FIFO, a deque is both. The exam skill is tracing the contents after a sequence of opera…
- 57 Linked Lists Nodes chained by pointers, not laid out in contiguous memory: O(1) insert and delete at a known node, but O(n) access — the mirror image of an arra…
- 58 Hash Tables & Linear Probing A hash function turns a key into a slot for ~O(1) lookup; when slots collide, linear probing walks to the next free one. The open-addressing idea G…
- 59 Trees, Traversals & Reconstruction How a binary tree is walked four canonical ways — pre, in, post, and level-order — and why inorder plus one other order rebuilds the tree but preor…
- 60 Graph Theory & Representations A graph is just vertices joined by edges. Learn the vocabulary, the handshake fact, and the two ways to store a graph — the bedrock for every BFS/D…
- 61 BFS, DFS, Topological Sort & Shortest Path BFS spreads level by level, DFS plunges deep, topological sort linearises a DAG, and Dijkstra handles weights. The four traversals GATE keeps askin…
- Chapter 06
Database Management & Warehousing
15 lessons - 62 The Relational Model A relation is just a table — rows are tuples, columns are attributes. Get this vocabulary right and the rest of the DBMS block falls into place.
- 63 ER Model & Mapping to Relations Draw the world as boxes, diamonds, and lines — then turn that picture into tables. The two skills GATE tests over and over in database design.
- 64 Keys & Integrity Constraints Keys are how a table guarantees 'this row, not that one' — and how tables link to each other without lying. Super, candidate, primary, foreign: pic…
- 65 Relational Algebra I Filter rows, pick columns, mix tables with set ops — the small toolkit that builds every SQL query underneath. The single most-tested DBMS sub-topi…
- 66 Joins & Division Joins stitch tables together on a shared key; division answers 'who has done every one of these?' — the two heavy-hitters of relational algebra.
- 67 Tuple Relational Calculus Instead of writing the recipe step by step, just describe the dish — TRC is the declarative twin of relational algebra, the same power in different…
- 68 SQL: Computing Results by Hand Read a SQL query and predict its row count — the single skill GATE drills with the SELECT/JOIN/GROUP BY toolkit.
- 69 Functional Dependencies & Closure If two rows share an X-value, must they share a Y-value? That's a functional dependency — the rule that decides keys, normal forms, and half of GAT…
- 70 Finding Candidate Keys from FDs Handed nothing but a tangle of functional dependencies, how do you find every key a table has? One short procedure does it every time — and GATE as…
- 71 Normal Forms: 1NF to BCNF Why does one table design feel clean and another feel messy, even when both store the same facts? Normal forms turn that gut feeling into four name…
- 72 Lossless-Join vs Dependency-Preservation Splitting a table to clean it up should let you tape the pieces back into exactly the original — and still check every rule on the pieces alone. Tw…
- 73 File Organization & Indexing Heap vs sorted files, primary vs secondary indexes, hash vs B+-tree — the handful of choices behind every fast lookup, and the one GATE keeps testing.
- 74 Normalization, Discretization, Sampling, Compression Raw data is rarely ready to analyse — one column dwarfs another, a number wants to be a category, the table is too big to fit. Four small prep move…
- 75 Star vs Snowflake Schemas How a data warehouse arranges facts and dimensions for fast analytics — and why one design deliberately repeats data to save joins while the other…
- 76 Concept Hierarchies & Measures Roll sales up to the year, drill back down to the day — and learn which aggregates you can merge from sub-totals, and which secretly need every raw…
- Chapter 07
Machine Learning
20 lessons - 77 Supervised vs Unsupervised; Train/Test The two great families of machine learning, and the one discipline every experiment obeys: keep the test set sealed until the very end.
- 78 Simple Linear Regression Out of every straight line you could draw through a cloud of points, least squares names the single best one — and hands you a formula for it. A re…
- 79 Multiple Linear Regression One model, many features. The normal equation w = (XᵀX)⁻¹Xᵀy solves it in closed form — a formula GATE wants you to apply to tiny matrices, not to…
- 80 Gradient Descent (One Step) The workhorse of model training, reduced to a single line: w ← w − η·(∂L/∂w). GATE asks you to perform exactly one update by hand.
- 81 Ridge Regression & Regularization Ordinary least squares can overfit. Ridge adds an L2 penalty that shrinks the weights, trading a little bias for a lot less variance.
- 82 The Bias-Variance Trade-off Total error splits into bias, variance, and irreducible noise. Reduce one and you usually raise the other — the conceptual backbone of the ML section.
- 83 Cross-Validation: k-fold, LOO, Stratified One train/test split is a coin flip. Cross-validation rotates the validation set so every sample is tested once — averaging out the luck.
- 84 Confusion Matrix, Precision, Recall, ROC Accuracy hides failure on imbalanced data. The confusion matrix splits errors into the two kinds that matter — and precision, recall, F1, and AUC r…
- 85 Logistic Regression Despite the name it is a classifier: a linear score wᵀx + b squashed by the sigmoid into a probability, trained with log-loss.
- 86 k-Nearest Neighbours A lazy learner with no training step: classify a point by the majority vote of its k closest neighbours, where k trades bias against variance.
- 87 Naive Bayes A classifier that applies Bayes' rule under one bold shortcut: features are conditionally independent given the class. Few parameters, fast, and a…
- 88 Linear Discriminant Analysis A supervised projection that pulls classes apart: LDA maximises between-class separation relative to within-class scatter. Its GATE hook is the con…
- 89 Support Vector Machines Find the separating line with the widest margin. The margin is 2/‖w‖, only the support vectors define it, and kernels bend it into curves — all GAT…
- 90 Decision Trees: Entropy, Gini & Info Gain A decision tree splits data to drive down impurity. Entropy and Gini measure that impurity; information gain picks the split — a recurring GATE DA…
- 91 Perceptron & the Update Rule The original neural unit: predict sign(wᵀx + b), then nudge the weights toward every misclassified point until the classes are separated.
- 92 Multi-Layer Perceptron & Activations An MLP stacks fully-connected layers with nonlinear activations. Counting its trainable parameters is a recurring GATE DA NAT — once with bias, onc…
- 93 Backpropagation (One Step) Backprop is the chain rule walked backward over a computation graph. GATE asks for one partial derivative through a small net — here is the exact r…
- 94 k-means & k-medoid Clustering Clustering by alternation: assign every point to its nearest centroid, then move each centroid to the mean of its points. Repeat. A recurring GATE…
- 95 Hierarchical Clustering & Linkage Build clusters by merging: start with every point alone and repeatedly join the two closest. The linkage rule decides what closest means — single i…
- 96 PCA & Dimensionality Reduction Rotate to the axes of maximum variance: PCA reads off the eigenvectors of the covariance matrix as new orthogonal components, keeping the top few t…
- Chapter 08
Artificial Intelligence
11 lessons - 97 Problem-Solving as Search Turn an AI puzzle into a search problem — states, actions, transitions, goal test, path cost — and watch the search tree unfold from the start state.
- 98 BFS, DFS, UCS & IDDFS Four uninformed search strategies — what they explore, when they're complete, what they cost in time and space, and why IDDFS re-expanding the root…
- 99 Heuristics & Admissibility A heuristic h(n) estimates the cost from a node to the goal. Admissible means it never overestimates; consistent means it obeys the triangle inequa…
- 100 A* Search Add what a step actually cost to what the heuristic guesses is left, then always expand the smallest sum. That's A*.
- 101 Adversarial Search: Minimax Two perfect players, one game tree. MAX chases the largest value, MIN chases the smallest — back the values up and read the root.
- 102 Alpha-Beta Pruning Same minimax answer, fewer nodes touched. Track the best each side has guaranteed so far, and cut whole subtrees the parent will never pick.
- 103 Propositional Logic Truth tables, models, satisfiability, equivalence, and entailment — the algebra of true/false that GATE DA quietly tests every year.
- 104 First-Order & Predicate Logic Translate English into ∀ and ∃ without falling into the most common GATE trap — the ∀ uses ⇒, ∃ uses ∧ rule.
- 105 Bayesian Networks & Joint Factorization Draw who causes what as a DAG, attach a small probability table to each node, and the whole joint distribution falls out as a product. The compact…
- 106 Exact Inference: Variable Elimination Want the exact posterior on a Bayes net? Multiply the CPTs together and sum out the variables you don't care about, one at a time. That's variable…
- 107 Approximate Inference: Sampling When exact inference is too slow, draw a few thousand samples from the Bayes net and estimate the answer. Rejection, likelihood-weighting, and Gibb…
- Chapter 09
General Aptitude
7 lessons - 108 General Aptitude: The 15 Marks GA is 15 marks of cheap, reliable points on every GATE paper — same questions, same buckets, friendly to a few hours of prep. Don't skip it.
- 109 Verbal Ability Articles, prepositions, sentence correction, vocabulary in context, analogies — the four shapes every GA verbal question takes.
- 110 Reading Comprehension & Narrative A short passage, two or three questions, your answer must be supported by the text — not by what you already know.
- 111 Quantitative Aptitude Percentages, ratios, powers, simple algebra, basic geometry, time-speed-distance — the small toolkit that covers almost every GA quant question.
- 112 Data Interpretation Read the chart, then do the arithmetic. Most DI questions are just percentages, ratios, or differences hiding behind a bar or pie.
- 113 Analytical & Logical Reasoning Seating puzzles, blood relations, and syllogisms — the skill is drawing a diagram, not holding everything in your head.
- 114 Spatial Aptitude Rotate, reflect, fold, assemble. Track one distinguishing feature through the transformation — the rest falls into place.
- Chapter 10
The Exam Lab — PYQs & Mock Tests
8 lessons - 115 GATE DA 2024 — Solved Walkthrough A curated set of fully-worked GATE DA 2024 problems across every subject — see exactly how each concept turns into an exam question and its verifie…
- 116 GATE DA 2025 — Solved Walkthrough A curated set of fully-worked GATE DA 2025 problems across every subject — see exactly how each concept turns into an exam question and its verifie…
- 117 GATE DA 2026 — Solved Walkthrough A guided walk through representative solved problems from GATE DA 2026 — one per subject, each worked to its verified answer and linked to the less…
- 118 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…
- 119 Timed Mock 1 (mixed) A timed, mixed mock under exam conditions — every subject, GATE negative marking, and a per-subject score breakdown at the end. The closest thing t…
- 120 Timed Mock 2 (mixed) A second timed, mixed mock under exam conditions — a fresh set of questions across every subject, GATE negative marking, and a per-subject score br…
- 121 Subject Mini-Mocks Short, timed, single-subject drills for the four heaviest GATE DA subjects — a 12-minute sprint each, with GATE negative marking and a score at the…
- 122 Formula & Trap Revision Sheets One compact, scannable formula-and-trap sheet per subject — the night-before-the-exam reference where the Traps lines flag exactly where marks leak.
- End of section 0 / 122 complete
Make it stick — pass every quiz.
Each lesson has a short quiz at the bottom. Passing the quiz is what marks the lesson complete.
Section complete 122 / 122 lessonsNice work — you finished GATE DA.
Now lock it in — drill the Review & Mastery Checks and the full mock tests until you're exam-ready.
GATE DA — frequently asked questions
Straight answers to the questions people ask most about gate da.
What is the GATE DA exam?
GATE DA (Data Science and Artificial Intelligence) is an Indian graduate-entrance exam, introduced in 2024, covering probability and statistics, linear algebra, calculus, programming and data structures, databases, machine learning, and AI. It tests conceptual understanding and problem-solving rather than rote memorisation.
What subjects does GATE DA cover?
The syllabus spans probability and statistics, linear algebra, calculus and optimization, programming and data structures, algorithms, database management, data warehousing, machine learning, and AI (search, logic, reasoning), plus the common General Aptitude section. Probability, linear algebra, and ML carry significant weight.
How should I prepare for GATE DA?
Build concepts first, then drill previous-year-style problems under timed conditions, and review with spaced retrieval so material sticks. Prioritise high-weight topics like probability, linear algebra, and ML, and practice General Aptitude, which is high-return for the time invested.
How is GATE DA different from a typical ML course?
GATE DA is exam-oriented — it rewards precise definitions, derivations, and fast, accurate problem-solving against the official syllabus, where an ML course is project-oriented. The concepts overlap heavily, but the exam demands speed and rigor on paper rather than building systems.
How accurate should my study answers be?
Always verify solutions against official answer keys and primary sources, since small differences in convention or rounding can change a multiple-choice answer. Reputable preparation material checks every previous-year answer against the official key for exactly this reason.