1.1 Consider the following statements:

S1 : The sum of two singular n x n matrices may be non-singular

S2 : The sum of two n x n non-singular matrices may be singular

Which of the following statements is correct?

• Both S1 and S2 are true
• S1 is true, S2 is false
• S1 is false, S2 is true
• S1 and S2 are both false

1.2 Consider the following relations:

R1 (a, b) if f(a + b) is even over the set of integers

R2 (a, b) if f(a + b) is odd over the set of integers

R3 (a, b) if f a.b > 0 over the set of non-zero rational numbers

R4 (a, b) iff |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

1.3 Consider two well-formed formulas in prepositional logic

Fl : P Þ Ø P F2 : (P Þ Ø P) v ( Ø P Þ P)

Which of the following statements is correct?

• F1 is satisfiable, F2 is valid
• F1 unsatisfiable, F2 is satisfiable
• F1 is unsatisfiable, F2 is valid
• F1 and F2 are both satisfiable.

• Consider the following two statements:

S1: {O 2n |n ³ l} is a regu1ar language

S2: { O m 1 n O m+n lm ³ l and n ³ l} is a regu1ar language

Which of the following statements is correct?

• Only S1 is correct
• Only S2 is correct
• Both S1 and S2 are correct
• None of S1 andS2 is correct

1.5 Which of the following statements in true?

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

(b) The union of two context free languages is context free

(c) The intersection of two context free languages is context free

(d) The complement of a context free language is context free

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

(a) N 2 (b) 2 N

(c) 2N (d) N!

1.7 More than one word are put in one cache block to

(a) exploit the temporal locality of reference in a program

(b) exploit the spatial locality of reference in a program

(c) reduce the miss penalty

(d) none of the above

1.8 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

• A low memory can be connected to 8085 by using
• INTER
• 
• HOLD
• READY

• Suppose a processor does not have any stack pointer register. Which of the following statements is true?
• It cannot have subroutine call Instruction,
• In can have subroutine call instruction, but no nested subroutine calls

(c) Nested subroutine calls are possible, but interrupts are not

(d) All sequences of subroutine calls and also interrupts are possible

1.11 Given the following Karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?

• xy+y'z (b) wx'y'+xy+xz

(c)w'x+y'z+xy (d) xz+y

1.12 A processor needs software interrupt to

• test the interrupt system of the processor
• implement co-routines

(c) obtain system services which need execution of privileged instructions

(d) return from subroutine

1.13 A CPU has two modes - privileged and non-privileged. In order to change the mode from privileged to non-privileged

• a hardware interrupt is needed
• a software interrupt is needed
• a privileged instruction (which does not generate an interrupt) is needed
• a non-privileged instruction (which does not generate an interrupt) is needed