GATE CSE topic:information-technology PYQs & Answers — Page 22

Questions 211–220 of 975. Imported answers require independent review unless marked reviewed.

Let

be a

matrix as given.

What are the eigenvalues of the matrix

Your answerChoose one option.

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An array

of length

with distinct elements is said to be bitonic if there is an index

such that

is sorted in the non-decreasing order and

is sorted in the non-increasing order.

Which ONE of the following represents the best possible asymptotic bound for the worst-case number of comparisons by an algorithm that searches for an element in a bitonic array

Your answerChoose one option.

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Consider the following four variable Boolean function in sum-of-product form

where the value of the function is computed by considering

as a 4-bit binary number, where

denotes the most significant bit and

denotes the least significant bit. Note that there are no don’t care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for

Your answerChoose one option.

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Let

be the set of all functions from

. Define the binary relation

as follows:

if and only if

, where

Which of the following statement(s) is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is a symmetric relation

is a partial order

is a lattice

is an equivalence relation

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Let

be an undirected and unweighted graph with 100 vertices. Let

denote the number of edges in a shortest path between vertices

and

. Let the maximum value of

such that

, be 30. Let

be a breadth-first-search tree of

. Which ONE of the given options is CORRECT for every such graph

Your answerChoose one option.

The height of

is exactly 15.

The height of

is exactly 30.

The height of

is at least 15.

The height of

is at least 30.

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Given the following Karnaugh Map for a Boolean function

Rows

and columns

, both in Gray code order

. Map values, row by row:

;

Which one or more of the following Boolean expression(s) represent(s)

Diagram for Computer Science and Information Technology question 43

Your answerSelect all correct options. You can choose more than one.

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Consider the following two languages over the alphabet

Which ONE of the following statements is CORRECT?

Your answerChoose one option.

Both

and

are regular languages.

is a regular language but

is not a regular language.

is not a regular language but

is a regular language.

Neither

nor

is a regular language.

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Consider a system of linear equations

where

and

. Suppose

has an LU decomposition,

, where

Which of the following statement(s) is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The system

can be solved by first solving

and then

is invertible, then both

and

are invertible.

is singular, then at least one of the diagonal elements of

is zero.

is symmetric, then both

and

are symmetric.

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Consider the following two languages over the alphabet

, where

and

are natural numbers.

Which ONE of the following statements is CORRECT?

Your answerChoose one option.

Both

and

are context-free languages.

is a context-free language but

is not a context-free language.

is not a context-free language but

is a context-free language.

Neither

nor

are context-free languages.

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Consider a stack data structure into which we can PUSH and POP records. Assume that each record pushed in the stack has a positive integer key and that all keys are distinct.

We wish to augment the stack data structure with an

time MIN operation that returns a pointer to the record with smallest key present in the stack

without deleting the corresponding record, and

without increasing the complexities of the standard stack operations.

Which one or more of the following approach(es) can achieve it?

Your answerSelect all correct options. You can choose more than one.

Keep with every record in the stack, a pointer to the record with the smallest key below it.

Keep a pointer to the record with the smallest key in the stack.

Keep an auxiliary array in which the key values of the records in the stack are maintained in sorted order.

Keep a Min-Heap in which the key values of the records in the stack are maintained.

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GATE CSE topic:information-technology PYQs

Question 41

Question 41

Question 42

Question 42

Question 43

Question 43

Question 44

Question 44

Question 45

Question 45