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⚡ Graduate Aptitude Test in Engineering

GATE DA Exam Portal

Master high-yield GATE Data Science & AI topics with Previous Year Questions, Daily Practice, Question Khazana (Registers & Cheat Sheets), and Virtual Calculator Mock Tests.

Module 01 • Recommended
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GATE DA Previous Year Questions

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Module 02 • Daily Speed
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Daily Quiz

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Module 03 • Simulation
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Module 04 • High Yield
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🎯 Today's GATE DA Practice Target

Q1. In Linear Regression with N training points and D features, what is the time complexity to compute the analytical Ordinary Least Squares (OLS) closed-form solution (XᵀX)⁻¹ Xᵀy? GATE DA • Machine Learning
💡 Solution (Option C): Computing XᵀX takes O(ND²) operations because X is N×D. Inverting the resulting D×D matrix takes O(D³) operations using Gaussian elimination. Hence the total time is O(ND² + D³).
Q2. Let A be a 3×3 real symmetric matrix with eigenvalues 1, 2, and 4. What is the trace of matrix A²? GATE DA • Linear Algebra
💡 Solution (Option C): If λ₁, λ₂, λ₃ are the eigenvalues of A, then λ₁², λ₂², λ₃² are the eigenvalues of A². The trace of a matrix is the sum of its eigenvalues: Trace(A²) = 1² + 2² + 4² = 1 + 4 + 16 = 21.
Q3. If a continuous random variable X follows an Exponential distribution with mean 4, what is P(X > 8 | X > 4)? GATE DA • Probability
💡 Solution (Option A): By the memoryless property of the Exponential distribution: P(X > s + t | X > s) = P(X > t). Here s = 4, t = 4, so P(X > 8 | X > 4) = P(X > 4). Since mean = 1/λ = 4 ⇒ λ = 1/4. P(X > 4) = e^(-λ*4) = e^(-(1/4)*4) = e⁻¹.

📚 GATE 30-Year PYQ Khazana & Topper Registers

Machine Learning & AI Register

Supervised vs Unsupervised algorithms, SVM margin derivations, Decision Tree split criteria (Gini/Entropy), Neural Network backpropagation, and CNN architectures.

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Probability & Mathematical Statistics

Bayes theorem, joint distributions, marginal PDFs, Expectation, Covariance matrices, Central Limit Theorem, Hypothesis testing (t-test, z-test, p-values).

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Linear Algebra & Calculus Handnotes

Vector spaces, rank-nullity theorem, Gram-Schmidt orthogonalization, SVD, PCA transformations, gradient, Hessian matrices, and Taylor series expansions.

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