JUNE 2012 - PAPER III

1. Consider the following pseudocode segment :
K:=0
for i1:= l to n
for i2:= 1 to i1
:
:
:
for im:= 1 to im–1
K:= K+1
The value of K after the execution of
this code shall be
(A) C(n + m – 1, m)
(B) C(n – m + 1, m)
(C) C(n + m – 1, n)
(D) C(n – m + 1, n)

Ans:-A

In order to understand the solution to this problem let us consider some sample value of n and m. Let us say n=3 and m=2. The value of m also decides the number of inner loops we have. When we say m=2, the total number of loops we have is 2 only. n decides the range of the outer most loop. So the pseudocode can be understood as,
K:=0
for i:= 1 to n
for m:= 1 to i
K:=K+1
For the value of n=3 and m=2, the value of K would be incremented in the following manner.

i	m	K
1	1	1
2	1	2
2	2	3
3	1	4
3	2	5
3	3	6

The value of i ranges from 1 to n where n=3.
The value of K is K:=6 at the end of the iterations.
Substituting the value of n and m in the options given as the answer let us take option A.
C(n+m-1,m)=C(3+2-1,2)=C(4,2)=4!/2!*2!=6.
So the answer for this question is option A.

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2. In Delta Rule for error minimization

(A) weights are adjusted w.r.to change in the output
(B) weights are adjusted w.r.to difference between desired output and actual output
(C) weights are adjusted w.r.to difference between input and output
(D) none of the above

Ans:-B

Explanation:- The topic comes in Artificial Neural Networks(ANN). In this rule weights are adjusted with respect to difference between desired output and actual output.

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3. The concept of pipelining is most effective in improving performance if the tasks being performed in different stages :

(A) require different amount of time
(B) require about the same amount of time
(C) require different amount of time with time difference between any two tasks being same
(D)require different amount of time with time difference between any two tasks being different

Ans:-B

Explanation:-
In the same June 2012 -Paper II, Question No 48 is based on pipelining and i have explained the same there. Please refer to it.