JUNE 2012 - PAPER III

4. What is Granularity ?

(A) The size of database
(B) The size of data item
(C) The size of record
(D) The size of file

Ans:-B

Explanation:- Granularity refers to the size of any data item. It could be a tuple, relation, database,anything. So the option is B.

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5. Suppose that a given application is run on a 64-processor machine and that 70 percent of the application can be parallelized. Then the expected performance improvement using Amdahl’ s law is

(A) 4.22
(B) 3.22
(C) 3.32
(D) 3.52

Ans:-B

Explanation:-
According to Amdahl's law, in case of parallelization,if P is the proportion of the program that can be made parallel, then (1-P) is the proportion that cannot be parallelized. Then the maximum speedup that can be achieved by using N processor is, S(N)=1/(1-P)+P/N where N refers to the no of processors, and P refers to the proportion that can be parallelized.
In the question above, no of processor, N=64
The proportion of the program that can be made parallel, P = 70%=0.7
So, substituting in the formula, we get, 1/(1-0.7)+0.7/64=1/0.3+0.0109375=1.0.310975
=3.215
=3.22
Therefore, the option is B.

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6. If two fuzzy sets A and B are given with membership functions μA(x) = {0.2, 0.4, 0.8, 0.5, 0.1} μB(x) = {0.1, 0.3, 0.6, 0.3, 0.2} Then the value of μ ––– willbe A∩B

(A) {0.9, 0.7, 0.4, 0.8, 0.9}
(B) {0.2, 0.4, 0.8, 0.5, 0.2}
(C) {0.1, 0.3, 0.6, 0.3, 0.1}
(D) {0.7, 0.3, 0.4, 0.2, 0.7}

Ans:-A

Explanation:-
The fuzzy intersection of two fuzzy sets A and B on universe of discourse X: μA∩B(x) = min [μA(x), μB(x)] , where x∈X
But here in the question, they are asking for complement of AintersectionB and so the answer would be 1-min[A(x),B(x)]. The minimum of 0.2 and 0.1 will be 0.1, and 1-0.1 will be 0.9. The second value is min(0.4,0.3)=0.3 and 1-0.3=0.7
The third value is min(0.8,0.6)=0.6 and 1-0.6=0.4
The fourth value is min(0.5,0.3)=0.3 and 1-0.3=0.7
The last value is min(0.1,0.2)=0.1 and 1-0.1=0.9
The only option which has got the values 0.9,0.7,0.4,0.7 and 0.9, although the fourth value is given as 0.8 instead of 0.7 is option A. So the answer is option A.

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