GATE CSE 2013 Question Paper with Solutions & Answer Key

General Aptitude and Engineering Mathematics together made up 28 of 100 marks, down 3 from GATE CSE 2012. 0 of 65 questions were NAT, the most since 2012. Quantitative Aptitude was the heaviest single topic with 9 marks across 5 questions. Computer Organization and Architecture moved the most against GATE CSE 2012: up 4 marks.

1. Q1 · MCQ · 1 mark · Discrete MathematicsA binary operation ⊕ on a set of integers is defined as x ⊕ y = x2 + y2. Which one of the following statements is TRUE about ⊕?
2. Q2 · MCQ · 1 mark · Probability and StatisticsSuppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the proba…
3. Q3 · MCQ · 1 mark · Linear AlgebraWhich one of the following does NOT equal 1 & x & x2 1 & y & y2 1 & z & z2 ?
4. Q4 · MCQ · 1 mark · Number Representation and ArithmeticThe smallest integer that can be represented by an 8-bit number in 2's complement form is
5. Q5 · MCQ · 1 mark · Combinational and Sequential CircuitsIn the following truth table, V = 1 if and only if the input is valid. What function does the truth table represent?
6. Q6 · MCQ · 1 mark · Searching, Sorting and HashingWhich one of the following is the tightest upper bound that represents the number of swaps required to sort n numbers using selection sort?
7. Q7 · MCQ · 1 mark · Binary Search TreesWhich one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes?
8. Q8 · MCQ · 1 mark · Regular Expressions and Finite AutomataConsider the languages L1 = and L2 = {a}. Which one of the following represents L1 L2* ∪ L1* ?
9. Q9 · MCQ · 1 mark · ParsingWhat is the maximum number of reduce moves that can be taken by a bottom-up parser for a grammar with no epsilon- and unit-production (i.e., of type A → and A → a) to pa…
10. Q10 · MCQ · 1 mark · CPU and I/O SchedulingA scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero (the lowest priority). The scheduler re-ev…
11. Q11 · MCQ · 1 mark · Relational Model and SQLMatch the problem domains in GROUP I with the solution technologies in GROUP II.
12. Q12 · MCQ · 1 mark · Switching and Performance MetricsThe transport layer protocols used for real time multimedia, file transfer, DNS and email, respectively are
13. Q13 · MCQ · 1 mark · Switching and Performance MetricsUsing public key cryptography, X adds a digital signature to message M, encrypts M, , and sends it to Y, where it is decrypted. Which one of the following sequences of k…
14. Q14 · MCQ · 1 mark · Principles of LayeringAssume that source S and destination D are connected through two intermediate routers labeled R. Determine how many times each packet has to visit the network layer and…
15. Q15 · MCQ · 1 mark · File Organization and IndexingAn index is clustered, if
16. Q16 · MCQ · 1 mark · Concurrency and SynchronizationThree concurrent processes X, Y, and Z execute three different code segments that access and update certain shared variables. Process X executes the P operation (i.e., w…
17. Q17 · MCQ · 1 mark · Turing Machines and UndecidabilityWhich of the following statements is/are FALSE? 1. For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine. 2. Turing recogni…
18. Q18 · MCQ · 1 mark · Asymptotic AnalysisWhich of the following statements are TRUE? 1. The problem of determining whether there exists a cycle in an undirected graph is in P. 2. The problem of determining whet…
19. Q19 · MCQ · 1 mark · Graph AlgorithmsWhat is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices?
20. Q20 · MCQ · 1 mark · Cache Memory and HierarchyIn a k-way set associative cache, the cache is divided into v sets, each of which consists of k lines. The lines of a set are placed in sequence one after another. The l…
21. Q21 · MCQ · 1 mark · Boolean Algebra and MinimizationWhich one of the following expressions does NOT represent exclusive NOR of x and y?
22. Q22 · MCQ · 1 mark · CalculusWhich one of the following functions is continuous at x = 3?
23. Q23 · MCQ · 1 mark · CalculusFunction f is known at the following points: The value of 03 f(x) dx computed using the trapezoidal rule is
24. Q24 · MCQ · 1 mark · Probability and StatisticsConsider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered…
25. Q25 · MCQ · 1 mark · Discrete MathematicsWhich of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even.
26. Q26 · MCQ · 2 marks · Discrete MathematicsThe line graph L(G) of a simple graph G is defined as follows: • There is exactly one vertex v(e) in L(G) for each edge e in G. • For any two edges e and e' in G, L(G) h…
27. Q27 · MCQ · 2 marks · Discrete MathematicsWhat is the logical translation of the following statement? “None of my friends are perfect.”
28. Q28 · MCQ · 2 marks · I/O Interface, Interrupts and DMAConsider the following sequence of micro-operations. MBR PC MAR X PC Y Memory MBR Which one of the following is a possible operation performed by this sequence?
29. Q29 · MCQ · 2 marks · File SystemsConsider a hard disk with 16 recording surfaces (0-15) having 16384 cylinders (0-16383) and each cylinder contains 64 sectors (0-63). Data storage capacity in each secto…
30. Q30 · MCQ · 2 marks · Searching, Sorting and HashingThe number of elements that can be sorted in (log n) time using heap sort is
31. Q31 · MCQ · 2 marks · Asymptotic AnalysisConsider the following function: int unknown(int n) { int i, j, k=0; for (i=n/2; i The return value of the function is
32. Q32 · MCQ · 2 marks · Regular and Context-Free LanguagesConsider the following languages. L1 = {0p 1q 0r p,q,r ≥ 0} L2 = {0p 1q 0r p,q,r ≥ 0, p e r} Which one of the following statements is FALSE?
33. Q33 · MCQ · 2 marks · Regular Expressions and Finite AutomataConsider the DFA A given below. Which of the following are FALSE? 1. Complement of L(A) is context-free. 2. L(A) = L((11*0+0)(0 + 1)*0*1*) 3. For the language accepted b…
34. Q34 · MCQ · 2 marks · Concurrency and SynchronizationA shared variable x, initialized to zero, is operated on by four concurrent processes W, X, Y, Z as follows. Each of the processes W and X reads x from memory, increment…
35. Q35 · MCQ · 2 marks · Relational Model and SQLConsider the following relational schema. Students( rollno: integer, sname: string) Courses( courseno: integer, cname: string) Registration( rollno: integer, courseno: i…
36. Q36 · MCQ · 2 marks · Data Link LayerDetermine the maximum length of the cable (in km) for transmitting data at a rate of 500 Mbps in an Ethernet LAN with frames of size 10,000 bits. Assume the signal speed…
37. Q37 · MCQ · 2 marks · IPv4, CIDR and NATIn an IPv4 datagram, the M bit is 0, the value of HLEN is 10, the value of total length is 400 and the fragment offset value is 300. The position of the datagram, the se…
38. Q38 · MCQ · 2 marks · Software EngineeringThe following figure represents access graphs of two modules M1 and M2. The filled circles represent methods and the unfilled circles represent attributes. If method m i…
39. Q39 · MCQ · 2 marks · Concurrency and SynchronizationA certain computation generates two arrays a and b such that a[i] = f(i) for 0 ≤ i a and Y computes the array b . The processes employ two binary semaphores R and S, bot…
40. Q40 · MCQ · 2 marks · ParsingConsider the following two sets of LR(1) items of an LR(1) grammar. ll X → c.X, c/d & X → c.X, X → .cX, c/d & X → .cX, X → .d, c/d & X → .d, \$ Which of the following st…
41. Q41 · MCQ · 2 marks · Turing Machines and UndecidabilityWhich of the following is/are undecidable? 1. G is a CFG. Is L(G) = ? 2. G is a CFG. Is L(G) = *? 3. M is a Turing machine. Is L(M) regular? 4. A is a DFA and N is an NF…
42. Q42 · MCQ · 2 marks · RecursionWhat is the return value of f(p, p) , if the value of p is initialized to 5 before the call? Note that the first parameter is passed by reference, whereas the second par…
43. Q43 · MCQ · 2 marks · Binary Search TreesThe preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42. Which one of the following is the postorder traversal sequence of the same…
44. Q44 · MCQ · 2 marks · Asymptotic AnalysisConsider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter. MultiDequeue (Q) { m = k while (Q is not empty) and…
45. Q45 · MCQ · 2 marks · Instruction PipeliningConsider an instruction pipeline with five stages without any branch prediction: Fetch Instruction (FI), Decode Instruction (DI), Fetch Operand (FO), Execute Instruction…
46. Q46 · MCQ · 2 marks · Cache Memory and HierarchyA RAM chip has a capacity of 1024 words of 8 bits each (1K × 8). The number of 2 × 4 decoders with enable line needed to construct a 16K × 16 RAM from 1K × 8 RAM is
47. Q47 · MCQ · 2 marks · Propositional and First-Order LogicWhich one of the following is NOT logically equivalent to eg ∃ x (∀ y ( ) ∀ z ( ))?
48. Q48 · MCQ · 2 marks · Local OptimisationCommon Data for Questions 48 and 49: The following code segment is executed on a processor which allows only register operands in its instructions. Each instruction can…
49. Q49 · MCQ · 2 marks · Code GenerationCommon Data for Questions 48 and 49: The following code segment is executed on a processor which allows only register operands in its instructions. Each instruction can…
50. Q50 · MCQ · 2 marks · Programming in CCommon Data for Questions 50 and 51: The procedure given below is required to find and replace certain characters inside an input character string supplied in array A .…
51. Q51 · MCQ · 2 marks · Programming in CCommon Data for Questions 50 and 51: The procedure given below is required to find and replace certain characters inside an input character string supplied in array A .…
52. Q52 · MCQ · 2 marks · Memory Management and Virtual MemoryStatement for Linked Answer Questions 52 and 53: A computer uses 46-bit virtual address, 32-bit physical address, and a three-level paged page table organization. The pa…
53. Q53 · MCQ · 2 marks · Cache Memory and HierarchyStatement for Linked Answer Questions 52 and 53: A computer uses 46-bit virtual address, 32-bit physical address, and a three-level paged page table organization. The pa…
54. Q54 · MCQ · 2 marks · Integrity Constraints and Normal FormsStatement for Linked Answer Questions 54 and 55: Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values. F={CH→ G, A→ BC, B→ CFH, E→ A, F→ EG}…
55. Q55 · MCQ · 2 marks · Integrity Constraints and Normal FormsStatement for Linked Answer Questions 54 and 55: Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values. F={CH→ G, A→ BC, B→ CFH, E→ A, F→ EG}…
56. Q56 · MCQ · 1 mark · Verbal AptitudeWhich one of the following options is the closest in meaning to the word given below? Nadir
57. Q57 · MCQ · 1 mark · Verbal AptitudeComplete the sentence: Universalism is to particularism as diffuseness is to …
58. Q58 · MCQ · 1 mark · Quantitative AptitudeWhat will be the maximum sum of 44, 42, 40, ?
59. Q59 · MCQ · 1 mark · Verbal AptitudeWere you a bird, you … in the sky.
60. Q60 · MCQ · 1 mark · Verbal AptitudeChoose the grammatically INCORRECT sentence:
61. Q61 · MCQ · 2 marks · Quantitative AptitudeFind the sum of the expression 1√(1)+√(2) + 1√(2)+√(3) + 1√(3)+√(4) + + 1√(80)+√(81)
62. Q62 · MCQ · 2 marks · Quantitative AptitudeOut of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?
63. Q63 · MCQ · 2 marks · Verbal AptitudeAfter several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to…
64. Q64 · MCQ · 2 marks · Quantitative AptitudeA tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in k…
65. Q65 · MCQ · 2 marks · Quantitative AptitudeThe current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the cu…

How many questions were in GATE CSE 2013?

GATE CSE 2013 had 65 questions for 100 marks: 65 MCQ, 0 MSQ and 0 NAT.

Which subject carried the most marks in GATE CSE 2013?

General Aptitude carried the most marks (15 of 100). The top three were General Aptitude (15), Engineering Mathematics (13), Operating Systems (10).

Where can I find the GATE CSE 2013 answer key?

The answer key table on this page lists the answer to every question of GATE CSE 2013. Open any question for its full verified solution.

Is the GATE CSE 2013 paper useful for GATE 2027 preparation?

Yes. Solving past GATE CSE papers shows how marks are spread across subjects and which topics repeat. Compare it with other GATE CSE question papers and the topic-wise GATE CSE PYQs.

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