GATE CSE format:msq PYQs & Answers — Page 6

Questions 51–60 of 160. Imported answers require independent review unless marked reviewed.

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 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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Which of the following statement(s) is/are TRUE while computing First and Follow during top down parsing by a compiler?

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

For a production

will be added to

If there is any input right end marker, it will be added to

, where

is the start symbol.

For a production

will be added to

If there is any input right end marker, it will be added to

, where

is the start symbol.

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Consider the following relational schema along with all the functional dependencies that hold on them.

R1(A, B, C, D, E): {

}

R2(A, B, C, D): {

}

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

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

R1 is in 3NF

R2 is in 3NF

R1 is NOT in 3NF

R2 is NOT in 3NF

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Consider a relational schema

, with functional dependencies

. The relation

is decomposed into two relations,

and

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

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

The relation

is NOT in BCNF.

The relations

and

are in BCNF.

The decomposition constitutes a lossless join.

The relation

is NOT in 3NF.

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Consider a demand paging system with three frames, and the following page reference string: 1 2 3 4 5 4 1 6 4 5 1 3 2. The contents of the frames are as follows initially and after each reference (from left to right):

initial	after
-	1* 2* 3* 4* 5* 4 1 6* 4 5 1* 3* 2*
-	1 1 1 1 1 1 1 6 6 6 6 6 2
-	- 2 2 4 4 4 4 4 4 4 4 1 1
-	- - 3 3 5 5 5 5 5 5 5 3 3

The *-marked references cause page replacements.

Which one or more of the following could be the page replacement policy/policies in use?

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

Least Recently Used page replacement policy

Least Frequently Used page replacement policy

Most Frequently Used page replacement policy

Optimal page replacement policy

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Which of the following predicate logic formula/formula is/are CORRECT representation(s) of the statement: “Everyone has exactly one mother”? The means of the predicates used are:

is the mother of

and

are not equal

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

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consists of all active processes in an operating system.

consists of single instances of distinct types of resources in the system.

The resource allocation graph has the following assignment and claim edges.

Assignment edges:

(the assignment edge

means resource

is assigned to process

, and so on for others)

Claim edges:

(the claim edge

means process

is waiting for resource

, and so on for others)

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

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

Aborting

makes the system deadlock free.

Aborting

makes the system deadlock free.

Aborting

makes the system deadlock free.

Aborting

and

makes the system deadlock free.

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is the set of non-negative integers. Let F be the set of functions from A to itself. For any two functions,

, we define

for every number

in A. Which of the following is/are CORRECT about the mathematical structure

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

is an Abelian group.

is an Abelian monoid.

is a non-Abelian group.

is a non-Abelian monoid.

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Three floating point numbers

, and

are stored in three registers

, and

, respectively in IEEE 754 single precision format as given below in hexadecimal:

, and

Which of the following option(s) is/are CORRECT?

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

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GATE CSE format:msq PYQs

Question 44

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Question 48

Question 49

Question 49