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GATE CSE 2021 Set 2 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. Q1Sentence completion: play the keyboard ____ her sisterGeneral Aptitude1M · MCQAns: A
  2. Q2Transparent square sheet folded along a dotted lineGeneral Aptitude1M · MCQAns: B
  3. Q3Angle between the longest diagonal and an edge of a cubeGeneral Aptitude1M · MCQAns: B
  4. Q4Solve a difference of two squares equal to x + 2General Aptitude1M · MCQAns: B
  5. Q5Analogy: Pen is to Write as Knife is to ?General Aptitude1M · MCQAns: C
  6. Q6Inference: effect of music on exercise and on learningGeneral Aptitude2M · MCQAns: C
  7. Q7Missing jigsaw piece that completes a rectangleGeneral Aptitude2M · MCQAns: A
  8. Q8Class strengths from ratios before and after adding 18General Aptitude2M · MCQAns: C
  9. Q9Ratio of selling prices from units, cost and tax dataGeneral Aptitude2M · MCQAns: A
  10. Q10Height ordering of six students from four observationsGeneral Aptitude2M · MCQAns: C

Computer Science and Information Technology (Q11–Q65)

  1. Q11Minimum weight edge in every MST; distinct weights give unique MSTAlgorithms1M · MCQAns: C
  2. Q12Finding the maximum element in a binary min-heapProgramming and Data Structures1M · MCQAns: C
  3. Q13Compiler phase that reports an error for 'Integer x;'Compiler Design1M · MCQAns: C
  4. Q14Smallest normalized positive IEEE 754 single-precision numberComputer Organization and Architecture1M · MCQAns: C
  5. Q154×1 MUX implementing f = Σm(0, 1, 3, 4, 5, 6)Digital Logic1M · MCQAns: A
  6. Q16Foreign keys: how many per relation, and self-referenceDatabases1M · MCQAns: D
  7. Q17TCP SYN-ACK segment in the three-way handshakeComputer Networks1M · MCQAns: C
  8. Q18Arithmetic operations in recursive binary searchAlgorithms1M · MCQAns: B
  9. Q19Language that always has a minimal DFA with the same k statesTheory of Computation1M · MCQAns: C
  10. Q20Output of *(arr[1] + 9) for a 4×5 int arrayProgramming and Data Structures1M · MCQAns: C
  11. Q21Bijection between n×n matrices over {a,b,c} and functionsEngineering Mathematics1M · MSQAns: B, C
  12. Q22Closure: regular L1 and context-free L2 combinationsTheory of Computation1M · MSQAns: B, C, D
  13. Q23Which is NOT an intermediate representationCompiler Design1M · MSQAns: D
  14. Q24True statements about CPU schedulingOperating System1M · MSQAns: A, C, D
  15. Q25Is ((P∧Q)→R)→((P∧Q)→(Q→R)) a tautology?Engineering Mathematics1M · MSQAns: B, D
  16. Q26BFS vs DFS: first three nodes of a 7-node complete binary treeAlgorithms1M · NATAns: 1
  17. Q27Number of length-8 strings accepted by a given DFATheory of Computation1M · NATAns: 256
  18. Q28Binary fraction 0.1101 equals decimal 0.8xy5Digital Logic1M · NATAns: 3
  19. Q29Associativity of a 2 KB cache with a 22-bit tagComputer Organization and Architecture1M · NATAns: 2
  20. Q30DMA cycle stealing: device data rate from 0.5% of cyclesComputer Organization and Architecture1M · NATAns: 80000
  21. Q31Number of blocks in a dense index on a candidate keyDatabases1M · NATAns: 698
  22. Q32Standard deviation of heads in 1000 biased coin tossesEngineering Mathematics1M · NATAns: 15 to 16
  23. Q33Value returned by a subtraction-based recursive functionProgramming and Data Structures1M · NATAns: 15
  24. Q34Rank of a 4×5 matrix with a one-dimensional null spaceEngineering Mathematics1M · NATAns: 4
  25. Q35Upper bound on f(3) via the mean value theoremEngineering Mathematics1M · NATAns: 19
  26. Q36Minimum encoded length of abbccddeee with a prefix codeAlgorithms2M · MCQAns: B
  27. Q37Write-through L1 read misses and write-allocate policyComputer Organization and Architecture2M · MCQAns: A
  28. Q38Two-state Mealy machine that clears the first 1 of each runDigital Logic2M · MCQAns: B
  29. Q39Best order to attempt two questions for maximum expected marksEngineering Mathematics2M · MCQAns: D
  30. Q40Additions and dereferences after common subexpression eliminationCompiler Design2M · MCQAns: D
  31. Q41Meaning of a GROUP BY query with an uncorrelated subqueryDatabases2M · MCQAns: B
  32. Q42Conflict serializability and recoverability of a scheduleDatabases2M · MCQAns: B
  33. Q43Pólya urn: probability of red on the fourth drawEngineering Mathematics2M · MCQAns: A
  34. Q44CRC check bits for message 11000 with generator x³+x+1Computer Networks2M · MCQAns: C
  35. Q45Bug in a linked-list program: uninitialized next pointerProgramming and Data Structures2M · MCQAns: D
  36. Q46Undecidable subsets of infinite regular languages; finite languagesTheory of Computation2M · MCQAns: C
  37. Q47Maximum number of mutually orthogonal non-zero vectors in R^10Engineering Mathematics2M · MCQAns: B
  38. Q48Liveness: relation between OUT(S1) and IN(S2)Compiler Design2M · MCQAns: A
  39. Q49Master theorem cases for T(n) = aT(n/b) + f(n)Algorithms2M · MCQAns: C
  40. Q50FDs implied by P → QR and RS → TDatabases2M · MSQAns: A, C, D
  41. Q51Which reversal-based languages are context-freeTheory of Computation2M · MSQAns: B, C, D
  42. Q52Values printed by two processes each running two locked threadsOperating System2M · MSQAns: A, D
  43. Q53Resource scheme that kills and restarts the ownerOperating System2M · MSQAns: A, B, C
  44. Q542-byte value 255 larger on little endian than on big endianComputer Organization and Architecture2M · MSQAns: A, D
  45. Q55Distance vector update at R from neighbours X, Y, ZComputer Networks2M · MSQAns: B, C
  46. Q56Properties of a directed 4×4 grid graph from vertex SAlgorithms2M · MSQAns: A, B
  47. Q57Regular expressions for binary numbers divisible by threeTheory of Computation2M · MSQAns: A, B, C
  48. Q58Minimum page-table memory for 2 GB with a three-level tableOperating System2M · NATAns: 4108
  49. Q59Output of a doubly recursive function foo(15, 15, 10)Programming and Data Structures2M · NATAns: 60
  50. Q60Number of pairs (A, B) of subsets with A ⊆ B ⊆ S, |S| = 10Engineering Mathematics2M · NATAns: 59049
  51. Q61Items in GOTO(GOTO(I0, <), <) for an LR(0) grammarCompiler Design2M · NATAns: 8
  52. Q62Literals in the minimal SOP of a partially specified f(w,x,y,z)Digital Logic2M · NATAns: 6
  53. Q63Speedup from operand forwarding for alternating ADD/MULComputer Organization and Architecture2M · NATAns: 1.87 to 1.88
  54. Q64Pure ALOHA throughput at 1000 frames/s on a 1 Mbps channelComputer Networks2M · NATAns: 130 to 140
  55. Q65Sum of maximum-product path scores in a weighted DAGAlgorithms2M · NATAns: 929