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
Answer: C
62. Given
the following two statements:
S1: If L1 and L2
are recursively enumerable languages over ∑, then L1⋃L2 and L1⋂L2 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
Answer: D
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
Answer: C
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
Answer: C
65. The
redundancy in images stems from:
(A) pixel decorrelation (B) pixel correlation
(C) pixel quantization (D) image size
Answer: B
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
Answer: B
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
Answer: A
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
Answer: B
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
Answer: D
70. Consider
the two class classification task that consists of the following points:
Class C1: [1 1.5] [1 -1.5]
Class C2: [-2 2.5] [-2 -2.5]
The decision boundary between the two classes
using single perceptron is given by:
(A) x1+x2+1.5=0 (B) x1+x2-1.5=0
(C) x1+1.5=0 (D) x1-1.5=0
Answer: C
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