CS and IT Gate 2024 Set-1 Questions with Answer

Ques 27 GATE 2024 SET-1

Consider a network path P-Q-R between nodes P and R via router Q. Node P sends a file of size 10⁶ bytes to R via this path by splitting the file into chunks of 10³ bytes each. Node P sends these chunks one after the other without any wait time between the successive chunk transmissions.
Assume that the size of extra headers added to these chunks is negligible, and that the chunk size is less than the MTU. Each of the links P-Q and Q-R has a bandwidth of 10⁶ bits/sec, and negligible propagation latency. Router Q immediately transmits every packet it receives from P to R, with negligible processing and queueing delays. Router Q can simultaneously receive on link P-Q and transmit on link Q-R. Assume P starts transmitting the chunks at time t = 0.
Which one of the following options gives the time (in seconds, rounded 3 to 3 decimal places) at which R receives all the chunks of the file?

8.000

8.008

8.016

16.000

Ques 28 GATE 2024 SET-1

Consider the following syntax-directed definition (SDD).

Given "MMLK" as the input, which one of the following options is the CORRECT value computed by the SDD (in the attribute S.val)?

(d) is the correct answer.

Ques 29 GATE 2024 SET-1

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

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

Which one of the following options CORRECTLY fills incomplete productions?

(1) S → Rf (2) T → ϵ (3) R → cTR

(1) S → fR (2) T → ϵ R → cTR

(1) S → fR T → cT

(1) S → Rf (2) T → cT (3) R → cR

(a) is the correct answer.

Ques 30 GATE 2024 SET-1

Consider the following pseudo-code.

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

4 and 4

5 and 5

6 and 6

7 and 6

(d) is the correct answer.

Ques 31 GATE 2024 SET-1

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.

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)

Ques 32 GATE 2024 SET-1

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

131, 101, 93

131, 93, 101

131, 11, 93

131, 111, 90

(b) is the correct answer.

Ques 33 GATE 2024 SET-1

Consider the following recurrence relation:

Which one of the following options is CORRECT?

T(n) = Θ(n log log n)

T(n) = Θ(n log n)

T(n) = Θ(n² log n)

T(n) = Θ(n² log log n)

(a) is the correct answer.

Ques 34 GATE 2024 SET-1

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

(a) is the correct answer.

Ques 35 GATE 2024 SET-1

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

(X,Y) → (Z,W) implies X → (Z,W)

(X,Y) → (Z,W) implies (X,Y) → Z

((X,Y) → Z and W → Y) implies (X,W) → Z

(X → Y and Y → Z) implies X → Z

(b,c,d) is the correct answer.

Ques 36 GATE 2024 SET-1

Let G be a directed graph and T a depth first search (DFS) spanning tree in G that is rooted at a vertex v. Suppose T is also a breadth first search (BFS) tree in G, rooted at v. Which of the following statements 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 the tree T

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

The only edges in G are the edges in T

(a,b,c,d) is the correct answer.

Ques 37 GATE 2024 SET-1

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

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

T₁ T₂ T₃

T₁ T₃ T₂

T₃T₂ T₁

T₃T₁ T₂

(a,b,c,d) is the correct answer.

Ques 38 GATE 2024 SET-1

Consider a Boolean function of 3 inputs F(X,Y,Z) = Σ(3,5,6,7). Which of the following expressions is/are CORRECT?

F(X,Y,Z) = Π(0,1,2,4)

F(X,Y,Z) = XY + YZ + XZ

F(X,Y,Z) is independent of input Y

F(X,Y,Z) is independent of input X

(a,b) is the correct answer.

Ques 39 GATE 2024 SET-1

Consider the following C function definition.

Which of the following statements is/are TRUE about the above function?

If the inputs are x = 20 y = 10 then the return value is greater than 2²⁰

If the inputs are x = 20 y = 20, then the return value is greater than 2²⁰

If the inputs are x = 20 y = 10, then the return value is less than 2¹⁰

If the inputs are x = 20 y = 20, then the return value is less than 2²⁰

(a,b) is the correct answer.

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