28 solved GATE DA questions on Machine Learning, drawn from 3 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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State the model, objective, and data split before calculating an update or reporting a score. Training improvement and generalization are different claims. These selected notes connect regression, classification, validation, trees, and unsupervised learning through explicit assumptions and checkable calculations.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
For predictions wx with no intercept, define J(w) = Σ(wxᵢ − yᵢ)²/(2n). Then J′(w) = Σ(wxᵢ − yᵢ)xᵢ/n, and gradient descent subtracts the learning rate times this derivative. A different loss normalization changes the gradient scale, so copy the objective before differentiating.
Check yourself: Are all residuals evaluated at the same current parameter?
A probability estimate becomes a class decision only after choosing a threshold. With a stated positive class, precision is TP/(TP + FP), recall is TP/(TP + FN), and accuracy is (TP + TN)/N. Class imbalance can make accuracy high despite poor positive-class detection.
Check yourself: Are your denominators predicted positives or actual positives?
Fit preprocessing only on training data within each validation split. Select hyperparameters using validation results; reserve untouched test data for final evaluation. Regularization trades training fit against complexity: stronger penalties can reduce variance but increase bias. Training loss alone cannot establish generalization.
Check yourself: Did validation or test information influence the fitted scaler or feature selection?
A classification tree evaluates a split using child impurities weighted by their sample fractions. For class proportions pₖ, Gini impurity is 1 − Σpₖ²; a pure node has zero impurity. Compare the weighted child impurity with the parent under the same criterion. Deep trees can memorize training data, so choose depth or pruning settings using validation, not test results.
Check yourself: Did you weight each child impurity by its sample fraction?
k-means alternates nearest-centroid assignments with mean updates to reduce within-cluster squared distance; initialization affects the result. PCA finds orthogonal directions of greatest variance in centered data. Neither method uses target labels. Feature scaling changes distances and variance, so it changes what these methods emphasize.
Check yourself: Does the chosen scale reflect meaningful feature comparisons?
Original teaching example · not a PYQ
Fit ŷ = wx without intercept or regularization to (1, 1), (2, 3), listed as (x, y). Use J(w) = Σ(wxᵢ − yᵢ)²/(2n) with n = 2. From w = 0, take one full-batch gradient-descent step with learning rate 0.1. Find the new weight and loss.
Updated weight: 0.35. Updated loss: 1.428125 under the stated 1/(2n) convention.
For a binary classifier with TP = 12, FP = 3, FN = 4, and TN = 21, find precision, recall, accuracy, and F1 for the positive class.
Precision = 4/5; recall = 3/4; accuracy = 33/40; F1 = 24/31.
There are 15 predicted positives, 16 actual positives, and 40 observations. Thus precision is 12/15, recall 12/16, and accuracy (12 + 21)/40. The F1 count formula gives 24/(24 + 3 + 4) = 24/31.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental book PDFs and R or Python resources from the authors, covering regression, classification, resampling, regularization, trees, and unsupervised learning.
This page shows 28 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE DA papers. Questions can carry more than one subject tag; counts are not marks weightage.
Task column lists a few tasks related to machine learning. The Algorithm column lists a few algorithms. Each entry “t” from the…MSQ · +1 marks · EasyContinue learning with Success Tracker
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