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GATE DA 2026 question paper with answers

Official paper organised by IIT Guwahati: 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: Verbosity is to Brevity as Insolence is to ?General Aptitude1M · MCQAns: B
  2. Q2Sum of digits of a three-digit number whose digit product is 70General Aptitude1M · MCQAns: B
  3. Q3Which figure can be built from four puzzle piecesGeneral Aptitude1M · MCQAns: A
  4. Q4Compare n^(log m) and m^(log n)General Aptitude1M · MCQAns: C
  5. Q5Inference from a counterfactual sentence about a movieGeneral Aptitude1M · MCQAns: D
  6. Q6Prepositions: parted __ the door __ the cabin __ the nightGeneral Aptitude2M · MCQAns: A
  7. Q7Five integers with given mean, median and single modeGeneral Aptitude2M · MCQAns: B
  8. Q8Chess elimination puzzle: who never lostGeneral Aptitude2M · MCQAns: D
  9. Q9Digit puzzle: squares of consecutive two-digit numbersGeneral Aptitude2M · MCQAns: C
  10. Q10Area of a dart-shaped region inside a circleGeneral Aptitude2M · MCQAns: C

Data Science and Artificial Intelligence (Q11–Q65)

  1. Q11Angle between two principal componentsMachine Learning1M · MCQAns: B
  2. Q12Number of LOOCV validation splitsMachine Learning1M · MCQAns: C
  3. Q13Which search algorithm is not uninformedArtificial Intelligence1M · MCQAns: C
  4. Q14Incorrect first-order logic translationArtificial Intelligence1M · MCQAns: C
  5. Q15Expected-time recurrence for randomised-input quicksortProgramming, Data Structures and Algorithms1M · MCQAns: D
  6. Q16Python mutable default argument outputProgramming, Data Structures and Algorithms1M · MCQAns: B
  7. Q17Candidate keys from functional dependenciesDatabase Management and Warehousing1M · MCQAns: A
  8. Q18OLAP operation from Country to StateDatabase Management and Warehousing1M · MCQAns: D
  9. Q19Probability a random subset of {1..2026} has an even productProbability and Statistics1M · MCQAns: C
  10. Q20Probability all parts are positive in n1+n2+n3+n4 = 20Probability and Statistics1M · MCQAns: A
  11. Q21Power of a rotation matrix by 2π/5Linear Algebra1M · MCQAns: B
  12. Q22Area where a ball meets a plane through the originLinear Algebra1M · MCQAns: A
  13. Q23Match ML tasks with algorithmsMachine Learning1M · MSQAns: B
  14. Q24What X entails Y meansArtificial Intelligence1M · MSQAns: A, B, C
  15. Q25Binary tree from preorder and inorder traversalsProgramming, Data Structures and Algorithms1M · MSQAns: A, B
  16. Q26Operations that never violate a foreign keyDatabase Management and Warehousing1M · MSQAns: A, B
  17. Q27Roots and extrema of x³ − 3x² + 2 on (−1, 3]Calculus and Optimization1M · MSQAns: B, D
  18. Q28Comparing the standard normal and t₁ distributionsProbability and Statistics1M · MSQAns: A, C
  19. Q29One SGD step on f(x) = wxMachine Learning1M · NATAns: 8.9 to 9.1
  20. Q30Best MAX strategy in a two-level minimax treeArtificial Intelligence1M · NATAns: 2
  21. Q31Worst-case comparisons in binary search of 1000 elementsProgramming, Data Structures and Algorithms1M · NATAns: 10
  22. Q32Order of a B+ tree non-leaf nodeDatabase Management and Warehousing1M · NATAns: 195
  23. Q33Number of involutions on a 4-element setProbability and Statistics1M · NATAns: 10
  24. Q34Memoryless property of the exponential distributionProbability and Statistics1M · NATAns: 0.34 to 0.36
  25. Q35Double sum of 2^(−i) 3^(−j)Calculus and Optimization1M · NATAns: 1
  26. Q36First merge in agglomerative clustering with Manhattan distanceMachine Learning2M · MCQAns: D
  27. Q37True statement about ridge regressionMachine Learning2M · MCQAns: D
  28. Q38Logical form of 'creative people succeed iff disciplined'Artificial Intelligence2M · MCQAns: B
  29. Q39Number of calls made by a Fibonacci-like recursionProgramming, Data Structures and Algorithms2M · MCQAns: C
  30. Q40Reachability in a graph and its reverseProgramming, Data Structures and Algorithms2M · MCQAns: D
  31. Q41B+ tree root after inserting 3Database Management and Warehousing2M · MCQAns: A
  32. Q42Output of a relational algebra expression with natural joinsDatabase Management and Warehousing2M · MCQAns: D
  33. Q43Number of cuboids from three concept hierarchiesDatabase Management and Warehousing2M · MCQAns: A
  34. Q44Variance of (2X − 1)Y with X Bernoulli and Y normalProbability and Statistics2M · MCQAns: A
  35. Q45Limit of a Poisson CDF at its meanProbability and Statistics2M · MCQAns: A
  36. Q46Rotation angle from the trace of a 3×3 rotation matrixLinear Algebra2M · MCQAns: C
  37. Q47Accuracy, precision and recall for two authorsMachine Learning2M · MSQAns: A, B
  38. Q48Which first-order logic statements are not validArtificial Intelligence2M · MSQAns: B, C, D
  39. Q49Comparisons by bubble sort and insertion sort on a nearly sorted arrayProgramming, Data Structures and Algorithms2M · MSQAns: B, C, D
  40. Q50Python closures sharing an enclosing listProgramming, Data Structures and Algorithms2M · MSQAns: B, D
  41. Q51SQL query for each employee's team sizeDatabase Management and Warehousing2M · MSQAns: A
  42. Q52Properties of the centering matrixLinear Algebra2M · MSQAns: A, D
  43. Q53Chi-square facts for standard normal samplesProbability and Statistics2M · MSQAns: A, B, C
  44. Q54Properties of the CDF of a discrete random variableProbability and Statistics2M · MSQAns: B, C
  45. Q55Regularised loss for one ridge regression exampleMachine Learning2M · NATAns: 6.9 to 7.1
  46. Q56Parameter count of a small MLP without biasesMachine Learning2M · NATAns: 135
  47. Q57Probability of disease given a positive testProbability and Statistics2M · NATAns: 0.76 to 0.78
  48. Q58Total swaps made by repeated recursive bubble passesProgramming, Data Structures and Algorithms2M · NATAns: 8
  49. Q59Tuples returned by a tuple relational calculus queryDatabase Management and Warehousing2M · NATAns: 2 to 3
  50. Q60Rows returned by a correlated count comparisonDatabase Management and Warehousing2M · NATAns: 3
  51. Q61Relations needed for an ER model with a multivalued attributeDatabase Management and Warehousing2M · NATAns: 4
  52. Q62Sample variance from the sum of squared pairwise differencesProbability and Statistics2M · NATAns: 10
  53. Q63Correlation of X and Y when Y depends on X²Probability and Statistics2M · NATAns: 0
  54. Q64Row and column sums of a random 0/1 matrixProbability and Statistics2M · NATAns: 0.08 to 0.12
  55. Q65Maximum of xᵀAx on the unit sphere for the centering matrixLinear Algebra2M · NATAns: 1