# CBSE UGC NET Computer Science Paper III Solved June 2015 - Part 7

61.       A context free grammar for L={w|n0(w)>n1(w)} is given by:
(A) S→0|0S|1SS                      (B) S→0S|1S|0SS|1SS|0|1
(C) S→0|0S|1SS|S1S|SS1    (D) S→0S|1S|0|1
62.       Given the following two statements:
S1: If L1 and L2 are recursively enumerable languages over ∑, then L1L2 and L1L2 are also recursively enumerable.
S2: The set of recursively enumerable languages is countable.
Which of the following is correct?
(A) S1 is correct and S2 is not correct
(B) S1 is not correct and S2 is correct
(C) Both S1 and S2 are not correct
(D) Both S1 and S2 are correct
63.       Given the following grammars:
G1:          S→AB|aaB
A→aA|ϵ
B→bB|ϵ
G2:          S→A|B
A→aAb|ab
B→abB|ϵ
Which of the following is correct?
(A) G1 is ambiguous and G2 is unambiguous grammars
(B) G1 is unambiguous and G2 is ambiguous grammars
(C) Both G1 and G2 are ambiguous grammars
(D) Both G1 and G2 are unambiguous grammars
64.       Given the symbols A, B, C, D, E, F, G and H with the probabilities 1/30, 1/30, 1/30, 2/30, 3/30, 5/30, 5/30 and 12/30 respectively. The average Huffman code size in bits per symbol is:
(A) 67/30           (B) 70/34
(C) 76/30           (D) 78/30
65.       The redundancy in images stems from:
(A) pixel decorrelation                        (B) pixel correlation
(C) pixel quantization             (D) image size

66.       In a binary Hamming code the number of check digits is r then number of message digits is equal to:
(A) 2r-1               (B) 2r-r-1
(C) 2r-r+1           (D) 2r+r-1
67.       In the Hungarian method for solving assignment problem, an optimal assignment requires that the maximum number of lines that can be drawn through squares with zero opportunity cost be equal to the number of:
(A) rows or columns    (B) rows+columns
(C) rows+columns-1   (D) rows+columns+1
68.       Consider the following transportation problem:
The initial basic feasible solution of the above transportation problem using Vogel’s Approximation Method(VAM) is given below:
The solution of the above problem:
(A) is degenerate solution     (B) is optimum solution
(C) needs to improve              (D) is infeasible solution
69.       Given the following statements with respect to linear programming problem:
S1: The dual of the dual linear programming problem is again the primal problem
S2: If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution
S3: If either the primal or dual problem has a finite optimal solution, the other one also possesses the same, and the optimal value of the objective functions of the two problems are equal.
Which of the following is true?
(A) S1 and S2     (B) S1 and S3
(B) S2 and S3    (D) S1, S2 and S2