December 2014 - Paper 3

61:  
According to pumping lemma for context free languages:
Let L be an infinite context free language, then there exists some positive integer m such that any w ∈ L with
I w I ≥ m can be decomposed as w = u v x y z
A.

with I vxy I ≤ m such that uvi xyi z ∈ L for all i = 0,1,2

B.

with I vxy I ≤ m and I vy I ≥ 1 such that uvi xyi z ∈ L for all i = 0,1,2,.....

C.

with I vxy I ≥ m and I vy I ≤ 1 such that uvi xyi z ∈ L for all i = 0,1,2,.....

D.

with I vxy I ≥ m and I vy I ≥ 1 such that uvi xyi z ∈ L for all i = 0,1,2,.....

 
 

Option: D

Explanation :

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62:  
Given a simple image of size 10 x 10 whose histogram models the symbol probabilities and is given by

P1

P2

P3

         P4

a

b

c

d

The first order estimate of image entropy is maximum whe

A.

a = 0, b = 0, c = 0, d = 1

B.

a = 1/2, b =1/2, c=0, d=0

C.

a = 1/3, b =1/3, c=1/3, d=0

D.

a = 1/4, b =1/4, c=1/4, d=1/4

 
 

Option: D

Explanation :

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63:  
If an artificial variable is present in the ,'basic variable' column of optimal simplex table, then the solution is
A.

Optimum

B.

Infeasible

C.

Unbounded

D.

Degenerate

 
 

Option: D

Explanation :

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64:  

The occurrence of degeneracy while solving a transportation problem means that

A.

total supply equals total demand

B.

total supply does not equal total demand

C.

the solution so obtained is not feasible

D.

none of these

 
 

Option: D

Explanation :

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65:  
Consider the following statements about a perception :
I. Feature detector can be any function of the input parameters.
II. Learning procedure only adjusts the connection weights to the output layer.
Identify the correct statement out of the following:
A.

I is false and II is false

B.

I is true and II is false .

C.

I is false and II is true

D.

l is true and II is true.

 
 

Option: D

Explanation :

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