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GATE DA 2025 question paper with answers

Official paper organised by IIT Roorkee: 65 questions, 100 marks. Every answer is from the official final answer key. Open any question to try it, see the answer and the concept behind it.

Practise this paper free →Official question paper (PDF)Official answer key (PDF)

General Aptitude (Q1–Q10)

  1. Q1Analogy: Courage : Bravery :: Yearning : ?General Aptitude1M · MCQAns: A
  2. Q2Tense: We ___ tennis when it started to rainGeneral Aptitude1M · MCQAns: B
  3. Q3Count pixels with intensity U ≤ 4 in a 4 × 4 imageGeneral Aptitude1M · MCQAns: C
  4. Q4Overlapping shapes: find P, Q and RGeneral Aptitude1M · MCQAns: A
  5. Q5Rectangle: effect of increasing the width by 10%General Aptitude1M · MCQAns: C
  6. Q6Match statements with phrasal-verb responsesGeneral Aptitude2M · MCQAns: B
  7. Q7Brothers with the same weight function: compare agesGeneral Aptitude2M · MCQAns: B
  8. Q8Dodecagon triangles rearranged into squares of side rGeneral Aptitude2M · MCQAns: A
  9. Q9Exponents: 3^(x²) = 27 × 9^xGeneral Aptitude2M · MCQAns: C
  10. Q10Average earnings per shift from a bar chartGeneral Aptitude2M · MCQAns: A

Data Science and Artificial Intelligence (Q11–Q65)

  1. Q11Law of total expectation: E[E[X|Y]]Probability and Statistics1M · MCQAns: C
  2. Q12Cost of Gaussian elimination on an upper triangular matrixLinear Algebra1M · MCQAns: B
  3. Q13Row sums equal 1: solutions of Bx = 0 for B = A³ − 2A² + ALinear Algebra1M · MCQAns: C
  4. Q1410th derivative of (eˣ − e⁻ˣ)/2 at 0Calculus and Optimization1M · MCQAns: A
  5. Q15Propositional logic: which statements are equivalent?Artificial Intelligence1M · MCQAns: A
  6. Q16Non-dependency-preserving decomposition: which operator runs more?Database Management and Warehousing1M · MCQAns: C
  7. Q17Relational algebra on Car, Make and OwnDatabase Management and Warehousing1M · MCQAns: C
  8. Q18Hashing with linear probing: h(x) = 3x mod 10Programming, Data Structures and Algorithms1M · MCQAns: D
  9. Q19Uniform CDF on [t, 4] with median 3: find tProbability and Statistics1M · MCQAns: A
  10. Q20X = aZ + b with Z standard normal: find a and bProbability and Statistics1M · MCQAns: A
  11. Q21Exponential distribution: P(X ≥ 2) = 0.25, find λProbability and Statistics1M · MCQAns: A
  12. Q22Perceptron update on a misclassified positive sampleMachine Learning1M · MCQAns: A
  13. Q23Python lists: which call gives A = [1, 2, 3, 4, 5, 6]?Programming, Data Structures and Algorithms1M · MCQAns: A
  14. Q24Which combinations of f and g are always differentiable at c?Calculus and Optimization1M · MSQAns: A, B, C
  15. Q25Orthonormal bases and linear independence in ℝⁿLinear Algebra1M · MSQAns: B, D
  16. Q26Bayesian networks: exact vs approximate inferenceArtificial Intelligence1M · MSQAns: C, D
  17. Q27When does binary search run in O(log n)?Programming, Data Structures and Algorithms1M · MSQAns: C
  18. Q28Properties of A = Iₙ + xxᵀ with xᵀx = 1Linear Algebra1M · MSQAns: A, B
  19. Q29Insertion sort with exactly two swaps: possible values of xProgramming, Data Structures and Algorithms1M · MSQAns: A, C
  20. Q30Single vs complete linkage dissimilarityMachine Learning1M · MSQAns: B, D
  21. Q31Bayes' theorem: white ball came from Box-2Probability and Statistics1M · NATAns: 0.25
  22. Q32Limit of √(t² + t) − t as t → ∞Calculus and Optimization1M · NATAns: 0.5
  23. Q33SQL: loans larger than every SR Nagar loanDatabase Management and Warehousing1M · NATAns: 3
  24. Q34Least squares through the origin: fit y = wxMachine Learning1M · NATAns: 0.285 to 0.287
  25. Q35Naive Bayes: probability of misclassifying xMachine Learning1M · NATAns: 0.39 to 0.41
  26. Q36Variance of Y = Z² for a standardised normal ZProbability and Statistics2M · MCQAns: B
  27. Q37If A³ = A, what is always true?Linear Algebra2M · MCQAns: D
  28. Q38Gram matrix of linearly independent vectorsLinear Algebra2M · MCQAns: A
  29. Q39Using a CDF to find P(X² ≤ 0.25)Probability and Statistics2M · MCQAns: C
  30. Q40CLT approximation for a sum of 300 Bernoulli(0.25)Probability and Statistics2M · MCQAns: A
  31. Q41Floor of an exponential random variable is geometricProbability and Statistics2M · MCQAns: A
  32. Q42Backpropagation through a small ReLU networkMachine Learning2M · MCQAns: A
  33. Q43Alpha-beta pruning: ranges of x and yArtificial Intelligence2M · MCQAns: C
  34. Q44A* search: order of node expansionArtificial Intelligence2M · MCQAns: C
  35. Q45100 dice: probability that at least one shows 1Probability and Statistics2M · MCQAns: C
  36. Q46OLAP: rows returned by GROUP BY CUBE(D1, D2)Database Management and Warehousing2M · MCQAns: D
  37. Q47Python sets in a while loop: which set ends up with "this"?Programming, Data Structures and Algorithms2M · MCQAns: B
  38. Q48Properties of the ReLU activation functionMachine Learning2M · MSQAns: A, C
  39. Q49Maxima and minima of a cubic on [−8, 0]Calculus and Optimization2M · MSQAns: C, D
  40. Q50Sum of five orthonormal outer products in ℝ¹⁰Linear Algebra2M · MSQAns: A, B
  41. Q51Consequences of f″(x) > 0 everywhereCalculus and Optimization2M · MSQAns: B, C, D
  42. Q52Matrices that preserve the Euclidean normLinear Algebra2M · MSQAns: A, D
  43. Q53Hard-margin SVM on four points in ℝ²Machine Learning2M · MSQAns: B, C
  44. Q54Sample proportion of heads: mean and varianceProbability and Statistics2M · MSQAns: A, C
  45. Q55Nearest-mean classifier: is the decision function linear?Machine Learning2M · MSQAns: B, C
  46. Q56Keys and NULLs in Person and Customer tablesDatabase Management and Warehousing2M · MSQAns: B, C
  47. Q57Candidate keys and BCNF for R(ABCDEFG)Database Management and Warehousing2M · MSQAns: B, D
  48. Q58Shortest paths: which edges cannot be in G?Programming, Data Structures and Algorithms2M · MSQAns: A, C, D
  49. Q59|f(x) − f(y)| ≤ (x − y)²: find f(1) − f(0)Calculus and Optimization2M · NATAns: 0
  50. Q60PCA: variance along the top principal directionMachine Learning2M · NATAns: 100
  51. Q61Expected black balls in 100 draws with replacementProbability and Statistics2M · NATAns: 66.6 to 66.7
  52. Q62Relational division: customers with loans at every branchDatabase Management and Warehousing2M · NATAns: 1
  53. Q63Python recursion: value of f(15, 10)Programming, Data Structures and Algorithms2M · NATAns: 160
  54. Q64Stack pseudocode: value of sumProgramming, Data Structures and Algorithms2M · NATAns: 24
  55. Q65DFS with decreasing adjacency lists: vertices after 50Programming, Data Structures and Algorithms2M · NATAns: 75