# Engineering-Mathematics |Gate-2013| Previous Year Questions| Set-8

Engineering-Mathematics |Gate-2013|

1. A binary operation ⊕ on a set of integers is defined as x ⊕ y = x+ y2. Which one of the following statements is TRUE about ⊕?[GATE – 2013]

a. Commutative but not associative
b. Both commutative and associative
c. Associative but not commutative
d. Neither commutative nor associative

2. Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval? [GATE – 2013]

a. 8/(2e3)
b. 9/(2e3)
c. 17/(2e3)
d. 26/(2e3)

3. Which one of the following does NOT equal to : [GATE – 2013]

a.

b.

c.

d.

4. What is the logical translation of the following statement? [GATE – 2013]

`  "None of my friends are perfect."`

a. ∃x(F(x)∧¬P(x))
b. ∃x(¬F(x)∧P(x))
c. ∃x(¬F(x)∧¬P(x))
d. ¬∃x(F(x)∧P(x))

5. The following code segment is excuted on a process which allows only register operands in its instructuoins. Each instructions can have atmost two sources operands and one destination opernad. Assume that all variables are dead after this code segement

c = a+b;
d= c*a;
e= c+a;
x= c*c;
if(x>a)
{
y= a*a;
}
else
{
d= d*d;
e= e*e;
}

Suppose the instructions set architecture of the processor has only two register. Theonly allowed compiler optimization is code motion, which moves statements from one place to another while preserving correctness . What is the minimum number of spills to memory in the compiled code? [GATE – 2013]

a. 0
b. 1
c. 2
d. 3