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GATE DA 2024 question paper with answers

Official paper organised by IISc Bangalore: 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. Q1Word analogy by increasing intensity: silly to daftGeneral Aptitude1M · MCQAns: D
  2. Q2Minimum colours for a 15-part figureGeneral Aptitude1M · MCQAns: A
  3. Q34-digit numbers divisible by 3 from {1, 3, 4, 6, 7}General Aptitude1M · MCQAns: B
  4. Q4Sum of an infinite series of powers of 1/2 and 1/3General Aptitude1M · MCQAns: B
  5. Q5Valid votes for two candidates from a pie chartGeneral Aptitude1M · MCQAns: B
  6. Q6Inference from a passage on digesting dairy milkGeneral Aptitude2M · MCQAns: D
  7. Q7Probability of two girls and one boy in three childrenGeneral Aptitude2M · MCQAns: A
  8. Q8Rate of return of mutual fund A from two investors' totalsGeneral Aptitude2M · MCQAns: B
  9. Q9Which paper net folds into the given diceGeneral Aptitude2M · MCQAns: A
  10. Q10Cross-section of two cones joined at the baseGeneral Aptitude2M · MCQAns: A

Data Science and Artificial Intelligence (Q11–Q65)

  1. Q11Mean and variance of Poisson and standard normalProbability and Statistics1M · MCQAns: A
  2. Q12Two or more heads and two or more tails in three tossesProbability and Statistics1M · MCQAns: A
  3. Q13Nature of eigenvalues of a 2×2 matrixLinear Algebra1M · MCQAns: B
  4. Q14Edge type in DFS when explored from nearer vertexProgramming, Data Structures and Algorithms1M · MCQAns: A
  5. Q15Second derivative test: f′=0 and f″>0Calculus and Optimization1M · MCQAns: A
  6. Q16Match FIFO, lookup and LIFO with data structuresProgramming, Data Structures and Algorithms1M · MCQAns: A
  7. Q17Possible support vectors of a hard-margin SVMMachine Learning1M · MCQAns: D
  8. Q18Match PCA, naive Bayes and logistic regression to model typesMachine Learning1M · MCQAns: C
  9. Q19Point necessarily in the same k-means clusterMachine Learning1M · MCQAns: D
  10. Q20Number of parameters of a naive Bayes classifierMachine Learning1M · MCQAns: B
  11. Q21Expected probes to insert into an open-address hash tableProgramming, Data Structures and Algorithms1M · MCQAns: B
  12. Q22Equation satisfied by the Fisher linear discriminantMachine Learning1M · MCQAns: A
  13. Q23Combination of two admissible heuristics that stays admissibleArtificial Intelligence1M · MCQAns: D
  14. Q24False conditional independence in a factorised distributionArtificial Intelligence1M · MCQAns: C
  15. Q25Meaning of alpha and beta in alpha–beta pruningArtificial Intelligence1M · MCQAns: C
  16. Q26Relational algebra check that every team name is a playerDatabase Management and Warehousing1M · MCQAns: C
  17. Q27z-score normalisation of an income valueDatabase Management and Warehousing1M · MCQAns: B
  18. Q28Traversal pairs that rebuild a full binary treeProgramming, Data Structures and Algorithms1M · MSQAns: A, B, C
  19. Q29Which implications of two propositions are tautologiesArtificial Intelligence1M · MSQAns: B, C, D
  20. Q30Swaps by Quicksort with last-element pivot on a sorted arrayProgramming, Data Structures and Algorithms1M · NATAns: 0
  21. Q31Rows returned by a join with filters on two tablesDatabase Management and Warehousing1M · NATAns: 3
  22. Q32Trace operations on a double-ended queueProgramming, Data Structures and Algorithms1M · NATAns: 17
  23. Q33Derivative of the sigmoid where its value is 0.4Calculus and Optimization1M · NATAns: 0.24
  24. Q34Updated sample mean after adding one data pointProbability and Statistics1M · NATAns: 42
  25. Q35Determinant of M² + 12M for a singular matrixLinear Algebra1M · NATAns: 0
  26. Q36Expected throws until two consecutive even numbersProbability and Statistics2M · MCQAns: C
  27. Q37Coefficients making a piecewise function differentiableCalculus and Optimization2M · MCQAns: A
  28. Q38Output of a recursive count over a child dictionaryProgramming, Data Structures and Algorithms2M · MCQAns: D
  29. Q39Trace computeS on an arrayProgramming, Data Structures and Algorithms2M · MCQAns: C
  30. Q40Recurrence for worst-case comparisons in binary searchProgramming, Data Structures and Algorithms2M · MCQAns: A
  31. Q41What a recursive swap function does to a listProgramming, Data Structures and Algorithms2M · MCQAns: C
  32. Q42Dendrogram from single-linkage clusteringMachine Learning2M · MCQAns: A
  33. Q43Equivalent single-layer weights of a ReLU networkMachine Learning2M · MCQAns: A
  34. Q44BFS versus DFS expansions to reach state 6Artificial Intelligence2M · MCQAns: C
  35. Q45Sorting algorithm that sorts [4, 3, 2, 1, 5] in two passesProgramming, Data Structures and Algorithms2M · MCQAns: B
  36. Q46Functional dependencies derivable from a given setDatabase Management and Warehousing2M · MSQAns: A, B, D
  37. Q47Which sets are subspaces of R³Linear Algebra2M · MSQAns: A, C
  38. Q48Possible solution counts of Mx = p and Mx = qLinear Algebra2M · MSQAns: B, D
  39. Q49Properties of a projection matrix onto a subspace of R³Linear Algebra2M · MSQAns: B, C, D
  40. Q50Local extrema of a quartic polynomialCalculus and Optimization2M · MSQAns: A, B
  41. Q51Valid topological orderings of a DAGProgramming, Data Structures and Algorithms2M · MSQAns: B, D
  42. Q52Bounds on height, nodes and leaves of a binary treeProgramming, Data Structures and Algorithms2M · MSQAns: A, B, C
  43. Q53Which two-class datasets are linearly separableMachine Learning2M · MSQAns: A, D
  44. Q54First-order logic for 'all balls are round except rugby balls'Artificial Intelligence2M · MSQAns: A, C
  45. Q55Indexes that speed up a three-table SQL joinDatabase Management and Warehousing2M · MSQAns: A, B
  46. Q56P(X ≥ Y) for two independent uniform variablesProbability and Statistics2M · NATAns: 0.125
  47. Q57Exponential rate when 5E(X) equals Var(X)Probability and Statistics2M · NATAns: 0.2
  48. Q58P(T | S) by Bayes' theoremProbability and Statistics2M · NATAns: 0.25
  49. Q59Conditional expectation from a joint density (marks to all)Probability and Statistics2M · NATAns: Marks to all
  50. Q60Limit of ln((x²+1) cos x) / x² as x → 0Calculus and Optimization2M · NATAns: 0.5
  51. Q61Sum of singular values of uuᵀLinear Algebra2M · NATAns: 55
  52. Q62Information gain of the Pitch attribute in a decision treeMachine Learning2M · NATAns: 0.12 to 0.13
  53. Q63Smallest odd k for which k-NN labels the point squareMachine Learning2M · NATAns: 5
  54. Q64Joint probability from a Bayesian network's tablesArtificial Intelligence2M · NATAns: 0.125
  55. Q65Covariance of 'both heads' and 'at least one head'Probability and Statistics2M · NATAns: 0.062 to 0.063