# GATE-CS-2001

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

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

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

Question 4

Consider the following two statements:
• Only S1 is correct
• Only S2 is correct
• Both S1 and S2 are correct
• None of S1 and S2 is correct

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

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!

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

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

Question 9

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