★ SPACED REVIEW

Review & Mastery Checks

Learning a topic once is acquisition. Remembering it three months later, in a 3-hour exam that mixes every subject, is retention — and that takes a different kind of practice. The checks below interleave questions from across a whole subject, out of lesson order, because mixing topics is what builds durable recall and the ability to switch gears mid-paper. Every question reuses an answer verified against the official 2024–2026 papers.

How to use this page

Don't take these the day you finish a subject — that just re-tests what's still in working memory. Space them out. Each time you successfully recall a topic after partly forgetting it, the memory gets stronger and lasts longer. A simple, research-backed schedule:

• Right after a subject: do its per-lesson quizzes (you already have these).
• About a week later: take that subject's mastery check below — cold, no notes.
• A month on: retake it and write down every question you miss. Those misses are your real syllabus — go re-read just those lesson sections.
• Mock season (week ~10+): cycle all four, then move to full timed mocks.

Mastery checks for the four heaviest subjects are below. (Calculus, Databases, AI, and General Aptitude have full per-lesson quizzes in their roadmaps; mixed checks for them are on the way.)

Probability & Statistics

Interleaves Bayes, independence, distributions, covariance, CLT, and descriptive stats.

Probability — interleaved mastery check

0/8

Q1A disease affects 30% of a population. A test is 80% sensitive (P(+|disease)=0.80) with a 10% false-positive rate. A person tests positive. P(disease | positive)? (2 decimals)numerical answer — type a number

Q2Events A and B have non-zero probability and are mutually exclusive. Which are ALWAYS true? (select all)select all that apply

Q3X ~ Binomial(n=5, p=0.5). What is P(X = 3)? (4 decimals)numerical answer — type a number

Q4Toss two fair coins. X = 1 if both heads (else 0), Y = 1 if at least one head (else 0). Cov(X, Y)? (4 decimals)numerical answer — type a number

Q5X is Exponential with rate λ. Given that 5·E(X) = Var(X), find λ.numerical answer — type a number

Q6Y is the sum of 300 i.i.d. Bernoulli(0.25) trials. Using the CLT with Φ(2) ≈ 0.9772, estimate P(60 ≤ Y ≤ 90). (2 decimals)numerical answer — type a number

Q7A salary of 106000 comes from a population with mean 96000 and standard deviation 21000. Its z-score is? (3 decimals)numerical answer — type a number

Q8Machine 1 makes 60% of items at a 2% defect rate; Machine 2 makes 40% at 5%. Overall P(defective)? (3 decimals)numerical answer — type a number

Machine Learning

Mixes naive Bayes, neural nets, clustering, PCA, ridge, metrics, SVM, and regression.

Machine Learning — interleaved mastery check

0/8

Q1Priors P(y1)=1/3, P(y2)=2/3; likelihoods P(x|y1)=3/4, P(x|y2)=1/4. A naive-Bayes classifier predicts the higher posterior. What is the probability it misclassifies x? (2 decimals)numerical answer — type a number

Q2A fully-connected MLP has layers 30 → 4 → 3 → 1 with NO bias terms. How many learnable parameters?numerical answer — type a number

Q3In one k-means iteration, the points nearest centroid C are (6,6) and (9,9). The updated centroid is (a, a). Find a.numerical answer — type a number

Q4PCA reduces 100 dimensions to 10. What is the angle (in degrees) between principal components PC1 and PC10?numerical answer — type a number

Q5As the ridge regularization coefficient λ increases, what happens to bias and variance?

Q6A confusion matrix has TP=8, FP=2, FN=6, TN=14. What is the recall? (3 decimals)numerical answer — type a number

Q7A hard-margin SVM has weight vector with ‖w‖ = 2. What is its margin width (2/‖w‖)?numerical answer — type a number

Q8Least-squares fit of y = wx to the points (−1, 1), (2, −5), (3, 5). Optimal w? (3 decimals)numerical answer — type a number

Linear Algebra

Mixes eigenvalues, SVD, determinants, projections, quadratic forms, orthogonality, and rank.

Linear Algebra — interleaved mastery check

0/8

Q1The matrix M = [[2, −1], [3, 1]] has eigenvalues that are:

Q2u = (1, 2, 3, 4, 5)ᵀ and M = uuᵀ (a 5×5 rank-1 matrix). What is the sum of the singular values of M?numerical answer — type a number

Q3M is a 3×3 matrix whose rows are linearly dependent (so det(M) = 0). What is det(M² + 12M)?numerical answer — type a number

Q4M is an orthogonal projection onto a 2-dimensional subspace of ℝ³. What is the nullity of M?numerical answer — type a number

Q5A symmetric matrix A has eigenvalues 5 and 2. What is the maximum of xᵀAx over all unit vectors ‖x‖ = 1?numerical answer — type a number

Q6A real matrix A satisfies ‖Ax‖ = ‖x‖ for every vector x. Which are ALWAYS true? (select all)select all that apply

Q7A is 3×3 with rank 2. By rank–nullity, what is the dimension of its null space (nullity)?numerical answer — type a number

Q8If a real matrix satisfies A³ = A, which statement is always true?

Programming, Data Structures & Algorithms

Mixes Python gotchas, binary search, sorting, quicksort, hashing, and tree traversal.

Programming & DSA — interleaved mastery check

0/8

Q1In Python, what does `"GATE2026"[::2]` evaluate to?

Q2`def f(val, lst=[]): lst.append(val); return lst`. After calling f(1) then f(2), what does f(2) return?

Q3A = [1, 2, 3], B = [4, 5, 6]. Which single statement makes A equal to [1, 2, 3, 4, 5, 6]?

Q4Worst-case comparisons in binary search obey F(n) = F(⌊n/2⌋) + 1. For a sorted array of 1024 elements, the worst-case number of comparisons is:numerical answer — type a number

Q5Which of bubble, insertion, selection sort puts [4, 3, 2, 1, 5] into sorted order in exactly TWO passes?

Q6In-place quicksort with the LAST element as pivot runs on the already-sorted array [60, 70, 80, 90, 100]. Minimum number of swaps?numerical answer — type a number

Q7Hash table of size 10, h(x) = 3x mod 10, linear probing. After inserting 1, 4, 5, 6 (at slots 3, 2, 5, 8), key 14 is inserted into which slot?numerical answer — type a number

Q8Which traversal pairs let you uniquely reconstruct a general binary tree? (select all)select all that apply

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