CS and IT GATE 2023 Questions with Answer

Ques 40 Computer Science

A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0-X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown.

Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7), will realise the Boolean function A̅+A̅C̅+A⋅B̅⋅C?

(1,1,0,0,1,1,1,0)

(1,1,0,0,1,1,0,1)

(1,1,0,1,1,1,0,0)

(0,0,1,1,0,1,1,1)

Ques 41 Computer Science

Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4.
Which one of the following corresponds to the product of these numbers (i.e., P × Q), represented in the IEEE-754 single precision format?

0x404C2EF4

0x405C2EF4

0xC15C2EF4

0xC14C2EF4

Ques 42 Computer Science

Let A be a priority queue for maintaining a set of elements. Suppose A is implemented using a max-heap data structure. The operation EXTRACT-MAX(A) extracts and deletes the maximum element from A. The operation INSERT(A,key) inserts a new element key in A. The properties of a max-heap are preserved at the end of each of these operations.
When A contains n elements, which one of the following statements about the worst case running time of these two operations is TRUE?

Both EXTRACT-MAX(A) and INSERT(A,key) run in O(1)

Both EXTRACT-MAX(A) and INSERT(A,key) run in O(log(n)).

EXTRACT-MAX(A) runs in O(1) whereas INSERT(A,key) runs in O(n).

EXTRACT-MAX(A) runs in O(1) whereas INSERT(A,key) runs in O(log(n)).

Ques 43 Computer Science

Consider the C function foo and the binary tree shown.

When foo is called with a pointer to the root node of the given binary tree, what will it print?

11 10 13 3 8 5

11 13 3 5 8 10

24 50 13 3 8 16

24 13 50 16 8 3

Ques 44 Computer Science

Let U = {1, 2,...,n}, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with |A| = |B| = k and A ∩ B = ∅. We say that a permutation of U separates A from B if one of the following is true.
- All members of A appear in the permutation before any of the members of B.
- All members of B appear in the permutation before any of the members of A.
How many permutations of U separate A from B?

n
2k (n - 2k)!

n
2k (n - 2k)!
(k!)²

2 n
2k (n - 2k)! (k!)²

Ques 45 Computer Science

Let f: A → B be an onto (or surjective) function, where A and B are nonempty sets. Define an equivalence relation ~ on the set A as
a₁ ~ a₂ if f(a₁) = f(a₂),
where a₁, a₂ ∈ A. Let E = {[x]: x ∈ A} be the set of all the equivalence classes under ~. Define a new mapping F: E → B as
F([x]) = f(x), for all the equivalence classes [x] in E.
Which of the following statements is/are TRUE?

F is NOT well-defined.

F is an onto (or surjective) function.

F is a one-to-one (or injective) function.

F is a bijective function.

Ques 46 Computer Science

Suppose you are asked to design a new reliable byte-stream transport protocol like TCP. This protocol, named myTCP, runs over a 100 Mbps network with Round Trip Time of 150 milliseconds and the maximum segment lifetime of 2 minutes.
Which of the following is/are valid lengths of the Sequence Number field in the myTCP header?

30 bits

32 bits

34 bits

36 bits

Ques 47 Computer Science

Let X be a set and 2^X denote the powerset of X. Define a binary operation Δ on 2^X as follows:
AΔB = (A - B) ∪ (B - A). Let H = (2^X, Δ).
Which of the following statements about H is/are correct?

H is a group.

Every element in H has an inverse, but H is NOT a group.

For every A ∈ 2^X, the inverse of A is the complement of A.

For every A ∈ 2^X, the inverse of A is A.

Ques 48 Computer Science

Suppose in a web browser, you click on the www.gate-2023.in URL. The browser cache is empty. The IP address for this URL is not cached in your local host, so a DNS lookup is triggered (by the local DNS server deployed on your local host) over the 3-tier DNS hierarchy in an iterative mode. No resource records are cached anywhere across all DNS servers.
Let RTT denote the round trip time between your local host and DNS servers in the DNS hierarchy. The round trip time between the local host and the web server hosting www.gate-2023.in is also equal to RTT. The HTML file associated with the URL is small enough to have negligible transmission time and negligible rendering time by your web browser, which references 10 equally small objects on the same web server.
Which of the following statements is/are CORRECT about the minimum elapsed time between clicking on the URL and your browser fully rendering it?

7 RTTs, in case of non-persistent HTTP with 5 parallel TCP connections.

5 RTTs, in case of persistent HTTP with pipelining.

9 RTTs, in case of non-persistent HTTP with 5 parallel TCP connections.

6 RTTs, in case of persistent HTTP with pipelining.

Ques 49 Computer Science

Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes HEAD on the first throw, and C be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

A and B are independent.

A and C are independent.

B and C are independent.

Prob(B|C) = Prob(B)

Ques 50 Computer Science

Consider functions Function 1 and Function 2 expressed in pseudocode as follows:

Let f1(n) and f2(n) denote the number of times the statement "x = x + 1" is executed in Function 1 and Function 2, respectively. Which of the following statements is/are TRUE?

f1(n) ∈ Θ(f2(n))

f1(n) ∈ o(f2(n))

f1(n) ∈ ω(f2(n))

f1(n) ∈ O(n)

Ques 51 Computer Science

Let G be a simple, finite, undirected graph with vertex set {v₁,...,v_n}. Let Δ(G) denote the maximum degree of G and let N = {1, 2,...} denote the set of all possible colors. Color the vertices of G using the following greedy strategy: for i = 1,...,n
color(v_i) <- min{j ∈ N: no neighbour of v_i is colored j}
Which of the following statements is/are TRUE?

This procedure results in a proper vertex coloring of G.

The number of colors used is at most Δ(G) + 1.

The number of colors used is at most Δ(G).

The number of colors used is equal to the chromatic number of G.

Ques 52 Computer Science

Let U = {1, 2, 3}. Let 2^U denote the powerset of U. Consider an undirected graph G whose vertex set is 2^U. For any A, B ∈ 2^U, (A, B) is an edge in G if and only if (i) A ≠ B, and (ii) either A ⊂ B or B ⊂ A. For any vertex A in G, the set of all possible orderings in which the vertices of G can be visited in a Breadth First Search (BFS) starting from A is denoted by B(A).
If ∅ denotes the empty set, then the cardinality of B(∅) is _______.

2 is the correct answer.

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CS and IT GATE 2023 Questions with Answer