GATE-CS-2001

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Question 1

Consider the following statements: 

S1: The sum of two singular n × n matrices may be non-singular
S2: The sum of two n × n non-singular matrices may be singular.

Which of the following statements is correct?

  • S1 and S2 are both true

  • S1 is true, S2 is false

  • S1 is false, S2 is true

  • S1 and S2 are both false

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Question 2

Consider the following relations:

R1(a,b) if (a+b) is even over the set of integers
R2(a,b) if (a+b) is odd over the set of integers
R3(a,b) if a.b > 0 over the set of non-zero rational numbers
R4(a,b) if |a - b| <= 2 over the set of natural numbers

Which of the following statements is correct?

  • R1 and R2 are equivalence relations, R3 and R4 are not

  • R1 and R3 are equivalence relations, R2 and R4 are not

  • R1 and R4 are equivalence relations, R2 and R3 are not

  • R1, R2, R3 and R4 are all equivalence relations

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Question 3

Consider two well-formed formulas in prepositional logic. 

F1 : P ⇒ ¬P
F2 : ( P⇒¬P)∨(¬P⇒P)

Which of the following statements is correct? 
 

  • F1 unsatisfiable, F2 is satisfiable

  • F1 and F2 are both satisfiable

  • F1 is unsatisfiable, F2 is valid 

  • F1 is satisfiable, F2 is valid

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Question 4

Consider the following two statements:
GATECS2000Q4

  • Only S1 is correct

  • Only S2 is correct

  • Both S1 and S2 are correct

  • None of S1 and S2 is correct

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Question 5

Which of the following statements is true?

  • If a language is context free it can always be accepted by a deterministic push-down automaton

  • The union of two context free languages is context free

  • The intersection of two context free languages is context free

  • The complement of a context free language is context free

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Question 6

Given an arbitary non-deterministic finite automaton (NFA) with N states, the maximum number of states in an equivalent minimized DFA is at least

  • N2

  • 2N

  • 2N

  • N!

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Question 7

More than one word are put in one cache block to

  • exploit the temporal locality of reference in a program

  • exploit the spatial locality of reference in a program

  • reduce the miss penalty

  • none of the above

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Question 8

Which of the following statements is false?

  • Virtual memory implements the translation of a program‘s address space into physical memory address space

  • Virtual memory allows each program to exceed the size of the primary memory

  • Virtual memory increases the degree of multiprogramming

  • Virtual memory reduces the context switching overhead

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Question 9

A slow memory can be connected to 8085 by using

  • INTER

  • [Tex]\bar{\text{RESET IN}} [/Tex]

  • HOLD

  • READY

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Question 10

Suppose a processor does not have any stack pointer register. Which of the following statements is true?

  • It cannot have subroutine call instruction

  • It can have subroutine call instruction, but no nested subroutine calls

  • Nested subroutine calls are possible, but interrupts are not

  • All sequences of subroutine calls and also interrupts are possible

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