GATE CSE 2024 | Set 1

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Question 1

Consider the 5-state DFA M accepting the language 𝐿(𝑀) βŠ‚ (0 + 1)* shown below. For any string 𝑀 ∈ (0 + 1)* let 𝑛0(𝑀) be the number of 0 β€² 𝑠 in 𝑀 and 𝑛1(𝑀) be the number of 1′𝑠 in 𝑀.

gate_cs2024set1

Which of the following statements is/are FALSE?

  • States 2 and 4 are distinguishable in M

  • States 3 and 4 are distinguishable in M

  • States 2 and 5 are distinguishable in M

  • Any string w with n0 (𝑀) = n1(w) is in 𝐿(𝑀)

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Question 2

Consider the following read-write schedule S over three transactions T1,T2,T3 where the subscripts in the schedule indicate transaction IDs

S: r1(z), w1(z), r2(x), r3(y), w3(y), r2(y), w2(x), w2(y)

Which of the following transaction schedules is/are conflict equivalent to S?

  • T1T2T3

  • T1T3T2

  • T3T2T1

  • T3T1T2

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Question 3

Let G be the directed graph and T a DFS spanning tree in G such that it is rooted at vertex v. Suppose T is also Breadth First Search (BFS) Tree in such as rooted at v .Which of the following options is/are TRUE for every such graph G and tree T?

  • There are no back-edges in G with respect to the tree T

  • There are no cross-edges in G with respect to T 

  • There are no forward-edges in G with respect to the tree T 

  • The only edges in G are the edges in T.

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Question 4

The symbol β†’ indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?


  • (Xβ†’Y and Yβ†’Z) implies Xβ†’Z

  • (X,Y)β†’(Z,W) implies Xβ†’(Z,W)

  • ((X,Y)β†’Z and Wβ†’Y) implies (X,W)β†’Z

  • (X,Y)β†’(Z,W) implies (X,Y)β†’Z

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Question 5

Consider a binary min-heap containing 105 distinct elements. Let k be the index (in the underlying array) of the maximum element stored in the heap. The number of possible values of k is

  • 52

  • 1

  • 53

  • 27

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Question 6

Consider the following recurrence relation:

T(n)={√n T(√n)+n} for n>=1 
T(n)=1 for n=1

Which one of the following options is CORRECT ?

  • T(n) =ΞΈ(n log log n)

  • T(n) =ΞΈ(n2 log n)

  • T(n) =ΞΈ(n log n)

  • T(n) =ΞΈ(n2 log log n)

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Question 7

An array [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one of the following options represents the first three elements in the heapified array?

  • 82, 90, 101

  • 82, 11, 93 

  • 131, 11, 93

  • 131, 111, 90

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Question 8

Consider the following two threads T1 and T2 that update two shared variables a and b. Assume that initially a = b = 1. Though context switching between threads can happen at any time, each statement of T1 or T2 is executed atomically without interruption.

T1                            T2
a = a + 1;                    b = 2 * b;
b = b + 1;                    a = 2 + a;

Which one of the following options lists all the possible combinations of values of a and b after both T1 and T2 finish execution? 

  • (a = 4, b = 4); (a = 3, b = 3); (a = 4, b = 3)

  • (a = 3, b = 4); (a = 4, b = 3); (a = 3, b = 3)

  • (a = 4, b = 4); (a = 4, b = 3); (a = 3, b = 4)

  • (a = 2, b = 2); (a = 2, b = 3); (a = 3, b = 4)

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Question 9

Consider the following pseudo-code

L1:  t1 = -1
L2:  t2 = 0
L3:  t3 = 0
L4:  t4 = 4 * t3
L5:  t5 = 4 * t2
L6:  t6 = t5 * M
L7:  t7 = t4 + t6
L8:  t8 = a[t7]
L9:  if t8 <= max goto L11
L10: t1 = t8
L11: t3 = t3 + 1
L12: if t3 < M goto L4
L13: t2 = t2 + 1
L14: if t2 < N goto L3
L15: max = t1

Which one of the following options CORRECTLY specifies the number of basic blocks and the number of instructions in the largest basic block, respectively?

  • 6 and 6 

  • 6 and 7 

  • 7 and 6

  • 7 and 7

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Question 10

Consider the following grammar G, with 𝑆 as the start symbol. The grammar G has three incomplete productions denoted by (1), (2), and (3).

 𝑆 β†’ π‘‘π‘Žπ‘‡ | (1) 
𝑇 β†’ π‘Žπ‘† | 𝑏𝑇 | (2) 
𝑅 β†’ (3) | πœ–

The set of terminals is {π‘Ž, 𝑏, 𝑐, 𝑑, 𝑓}. The FIRST and FOLLOW sets of the different non-terminals are as follows. 

FIRST(𝑆) = {𝑐, 𝑑, 𝑓}, FIRST(𝑇) = {π‘Ž, 𝑏, πœ–}, FIRST(𝑅) = {𝑐, πœ–}
FOLLOW(𝑆) = FOLLOW(𝑇) = {𝑐, 𝑓, $}, FOLLOW(𝑅) = {𝑓}

Which one of the following options CORRECTLY fills in the incomplete productions? 

  • A.(1) 𝑆 β†’ 𝑅𝑓 (2) 𝑇 β†’ πœ– (3) 𝑅 β†’ 𝑐𝑇R
  • B.(1) 𝑆 β†’ 𝑓𝑅 (2) 𝑇 β†’ πœ– (3) 𝑅 β†’ 𝑐𝑇R
  • C.(1) 𝑆 β†’ 𝑓𝑅 (2) 𝑇 β†’ 𝑐𝑇 (3) 𝑅 β†’ 𝑐R
  • D.(1) 𝑆 β†’ 𝑅𝑓 (2) 𝑇 β†’ 𝑐𝑇 (3) 𝑅 β†’ 𝑐R
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