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GATE CSE 2021 Set 1 question paper with answers

Official paper organised by IIT Bombay: 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. Q1Possible class size for a 7 : 3 boys-to-girls ratioGeneral Aptitude1M · MCQAns: C
  2. Q2Which shape is not a convex polygonGeneral Aptitude1M · MCQAns: A
  3. Q3Grammar and ambiguity in two sentencesGeneral Aptitude1M · MCQAns: C
  4. Q4Punched holes after folding a circular sheet twiceGeneral Aptitude1M · MCQAns: A
  5. Q5Analogy: ___ is to surgery as writer is to ___General Aptitude1M · MCQAns: C
  6. Q6Ratio of volumes: rolled cylinder vs cube from the same sheetGeneral Aptitude2M · MCQAns: C
  7. Q7Discount on item Q from cost ratio and profit percentageGeneral Aptitude2M · MCQAns: C
  8. Q8Probability that at least two of five picked chocolates matchGeneral Aptitude2M · MCQAns: C
  9. Q9Syllogism: bacteria, pathogens and microorganismsGeneral Aptitude2M · MCQAns: C, D
  10. Q10Summary of a passage on anti-obesity measuresGeneral Aptitude2M · MCQAns: D

Computer Science and Information Technology (Q11–Q65)

  1. Q11Closure of CFLs under operations with a regular languageTheory of Computation1M · MCQAns: C
  2. Q12Comparisons needed to find both minimum and maximumAlgorithms1M · MCQAns: C
  3. Q13Order 10^n, n^(log n), n^(sqrt n) by growth rateAlgorithms1M · MCQAns: D
  4. Q14Procedure calls and returns vs activation tree traversalsCompiler Design1M · MCQAns: C
  5. Q15SLR(1) grammars, ambiguity and cubic-time CFG parsingCompiler Design1M · MCQAns: C
  6. Q16Hexadecimal form of the base-3 number 210Digital Logic1M · MCQAns: A
  7. Q17Which of two implications involving p and q are tautologiesEngineering Mathematics1M · MCQAns: B
  8. Q18Destination MAC addresses of ARP request and replyComputer Networks1M · MCQAns: C
  9. Q19Fewest comparisons to sort an already sorted arrayAlgorithms1M · MCQAns: C
  10. Q20Time to pick a BST element smaller than the maximumProgramming and Data Structures1M · MCQAns: D
  11. Q21True statements about pagingOperating System1M · MSQAns: A, C
  12. Q22Which DFA/PDA emptiness and universality problems are undecidableTheory of Computation1M · MSQAns: D
  13. Q23Recovering again after a crash during recoveryDatabases1M · MSQAns: A
  14. Q24C library functions that always make a system callOperating System1M · MSQAns: A, C
  15. Q25Directory operations needing a full scan of a linear listOperating System1M · MSQAns: A, C
  16. Q26Edges of a connected planar graph with 8 vertices and 5 facesEngineering Mathematics1M · NATAns: 11
  17. Q27Number of minimum spanning trees of a 3×3 grid graphAlgorithms1M · NATAns: 3
  18. Q28Exponential lifetime exceeding its meanEngineering Mathematics1M · NATAns: 0.35 to 0.39
  19. Q29Assigning 6 ranked jobs to 3 ranked computersEngineering Mathematics1M · NATAns: 65
  20. Q30Limit of (√(2x+22) − 4)/(x+3) as x → −3Engineering Mathematics1M · NATAns: 0.25
  21. Q31Stack pop plus queue dequeue after a sequence of operationsProgramming and Data Structures1M · NATAns: 86
  22. Q32Tag bits for a 32 KB direct-mapped cache with 64-byte blocksComputer Organization and Architecture1M · NATAns: 17
  23. Q33Estimated size of a selection with an OR of two predicatesDatabases1M · NATAns: 819 to 820 (or 205)
  24. Q34Decimal value of an IEEE 754 single-precision patternComputer Organization and Architecture1M · NATAns: -7.75
  25. Q35Minimum average waiting time for bursts of 16, 20 and 10 msOperating System1M · NATAns: 12
  26. Q36What an SDT for int/bool declarations and expressions can type-checkCompiler Design2M · MCQAns: B
  27. Q37Meaning of a self theta-join on employee ageDatabases2M · MCQAns: C
  28. Q38Next three states of a 3-bit T flip-flop counterDigital Logic2M · MCQAns: A
  29. Q39Missing data and check bits in a 12-bit Hamming codewordComputer Networks2M · MCQAns: A
  30. Q40Solve T(n) = T(n/2) + T(2n/5) + 7nAlgorithms2M · MCQAns: C
  31. Q41Fill the blank cells of an LL(1) parsing tableCompiler Design2M · MCQAns: A
  32. Q42Conflict serializability of two two-transaction schedulesDatabases2M · MCQAns: B
  33. Q43Lossless or lossy: two decompositions of R(P,Q,S,T,X,Y,Z,W)Databases2M · MCQAns: A
  34. Q44Cyclicity of a group of order 6 and its proper subgroupsEngineering Mathematics2M · MCQAns: B
  35. Q45Covariance bound and covariance with absolute deviationsEngineering Mathematics2M · MCQAns: D
  36. Q46Diameter of the graph joining vertices within distance twoEngineering Mathematics2M · MCQAns: A
  37. Q47Output of a loop with a short-circuited post-incrementProgramming and Data Structures2M · MCQAns: B
  38. Q48DFA for binary strings ending in 011Theory of Computation2M · MCQAns: D
  39. Q49Decidability of TMs taking more than 2021 steps on all/some inputsTheory of Computation2M · MCQAns: A
  40. Q50Rod cutting: maximum revenue for a rod of length 7Algorithms2M · MSQAns: A, C
  41. Q51Articulation points and the DFS treeAlgorithms2M · MSQAns: B
  42. Q52Expressions equivalent to the complement of a product of sumsDigital Logic2M · MSQAns: B, C, D
  43. Q53Circular relations and equivalence relationsEngineering Mathematics2M · MSQAns: C
  44. Q54TCP client behaviour after the server host crashes and rebootsComputer Networks2M · MSQAns: A, B, C
  45. Q55IP fragmentation of a 1400-byte TCP segment over an 820-byte MTUComputer Networks2M · MSQAns: A, C
  46. Q56Possible outcomes of five threads with double wait on a semaphoreOperating System2M · MSQAns: A, B, D
  47. Q57Insertion order producing a given dynamic hashing stateProgramming and Data Structures2M · MSQAns: C
  48. Q58Value returned by a Horner-style loop on an all-ones arrayProgramming and Data Structures2M · NATAns: 1023
  49. Q59Sliding window size for 50% utilisationComputer Networks2M · NATAns: 50 to 52
  50. Q60Number of nodes in the DAG of a basic blockCompiler Design2M · NATAns: 6
  51. Q61Strings of length 100 accepted by a PDATheory of Computation2M · NATAns: 50
  52. Q62Largest eigenvalue of J − I for a 4×4 all-ones matrixEngineering Mathematics2M · NATAns: 3
  53. Q63Time for 100 instructions on a five-stage pipelineComputer Organization and Architecture2M · NATAns: 17160
  54. Q64Bayes' rule on a noisy two-signal channelEngineering Mathematics2M · NATAns: 0.04
  55. Q65Memory location 3010 after a loop of array updatesComputer Organization and Architecture2M · NATAns: 50