CS and IT GATE 2021 SET-2 Questions with Answer

Ques 14 Data Structures and Algorithms

What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n?

Ques 15 Data Structures and Algorithms

Consider a complete binary tree with 7 nodes. Let A denote the set of first 3 elements obtained by performing Breadth-First Search (BFS) starting from the root. Let B denote the set of first 3 elements obtained by performing Depth-First Search (DFS) starting from the root. The value of |A - B| is _______.

Ques 16 Data Structures and Algorithms

Consider the string abbccddeee. Each letter in the string must be assigned a binary code satisfying the following properties: 1. For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter. 2. For any two letters of the same frequency, the letter which occurs earlier in the dictionary order is assigned a code whose length is at most the length of the code assigned to the other letter. Among the set of all binary code assignments which satisfy the above two properties, what is the minimum length of the encoded string?

Ques 17 Data Structures and Algorithms

Consider the following directed graph:

Ques 18 Data Structures and Algorithms

In a directed acyclic graph with a source vertex s, the quality-score of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex v other than s, the quality-score of v is defined to be the maximum among the quality-scores of all the paths from s to v. The quality-score of s is assumed to be 1.

Ques 19 Databases

Consider the following statements S1 and S2 about the relational data model:
S1: A relation scheme can have at most one foreign key.
S2: A foreign key in a relation scheme R cannot be used to refer to tuples of R.
Which one of the following choices is correct?

Ques 20 Databases

A data file consisting of 1,50,000 student-records is stored on a hard disk with block size of 4096 bytes. The data file is sorted on the primary key RollNo. The size of a record pointer for this disk is 7 bytes. Each student-record has a candidate key attribute called ANum of size 12 bytes. Suppose an index file with records consisting of two fields, ANum value and the record pointer to the corresponding student record, is built and stored on the same disk. Assume that the records of data file and index file are not split across disk blocks. The number of blocks in the index file is _______.

Ques 21 Databases

Suppose the following functional dependencies hold on a relation U with attributes P, Q, R, S, and T:
P → QR
RS → T
Which of the following functional dependencies can be inferred from the above functional dependencies?

Ques 22 Digital Logic

Which one of the following circuits implements the Boolean function given below?
f(x,y,z) = m₀ + m₁ + m₃ + m₄ + m₅ + m₆, where m_i is the i^th minterm.

A

B

C

D

Ques 23 Digital Logic

If x and y are two decimal digits and (0.1101)₂ = (0.8xy5)₁₀, the decimal value of x + y is _______.

Ques 24 Digital Logic

Consider a Boolean function f(w,x,y,z) such that
f(w,0,0,z) = 1
f(1,x,1,z) = x + z
f(w,1,y,z) = wz + y
The number of literals in the minimal sum-of-products expression of f is _______.

Ques 25 English

Gauri said that she can play the keyboard _______ her sister.

Ques 26 English

Pen: Write:: Knife: _______
Which one of the following options maintains a similar logical relation in the above?