61.
Which of the following statements is not
correct?

(1) Every
recursive language is recursively enumerable.

(2) L = {0

^{n}1^{n}0^{n}| n=1, 2 , 3, ....} is recursively enumerable.
(3)
Recursive languages are closed under intersection.

(4)
Recursive languages are not closed under intersection.

Answer: 4

62. Context
free grammar is not closed under :

(1)
Concatenation

(2)
Complementation

(3) Kleene
Star

(4) Union

Answer: 2

63. Consider
the following languages :

L

_{1}= {a^{m}b^{n }| m ≠ n}
L

_{2}= {a^{m}b^{n }| m = 2n+1}
L

_{3}= {a^{m}b^{n }| m ≠ 2n}
Which one of
the following statement is correct?

(1) Only L

_{1}and L_{2}are context free languages
(2) Only L

_{1}and L_{3}are context free languages
(3) Only L

_{2}and L_{3}are context free languages
(4) L

_{1}, L_{2}and L_{3}are context free languages
Answer: 4

64. A
4×4 DFT matrix is given by :

(j

^{2}=−1)
Where values
of x and y are ..........., ............. respectively.

(1) 1, −1

(2) −1, 1

(3) −j, j

(4) j, −j

Answer: 4

65. Entropy
of a discrete random variable with possible values {x

_{1}, x_{2}, ..., x_{n}} and probability density function P(X) is :
The value of
b gives the units of entropy. The unit for b=10 is :

(1) bits

(2) bann

(3) nats

(4) deca

Answer: Marks to all

66. For
any binary (n, h) linear code with minimum distance (2t+1) or greater

(1) 2t+1

(2) t+1

(3) t−1

(4) t

Answer: 4

67. Which
of the following is a valid reason for causing degeneracy in a transportation problem?
Here m is no. of rows and n is no. of columns in transportation table.

(1) When the
number of allocations is m+n−1.

(2) When two
or more occupied cells become unoccupied simultaneously.

(3) When the
number of allocations is less than m+n−1.

(4) When a
loop cannot be drawn without using unoccupied cells, except the starting cell of
the loop.

Answer: 3

68. Consider
the following LPP :

Max Z=15x

_{1}+10x_{2}
Subject to
the constraints

4x

_{1}+6x_{2}≤ 360
3x

_{1}+0x_{2}≤ 180
0x

_{1}+5x_{2}≤ 200
x

_{1}, x_{2}≥ 0
The solution
of the LPP using Graphical solution technique is :

(1) x

_{1}=60, x_{2}=0 and Z=900
(2) x

_{1}=60, x_{2}=20 and Z=1100
(3) x

_{1}=60, x_{2}=30 and Z=1200
(4) x

_{1}=50, x_{2}=40 and Z=1150
Answer: 2

69. Consider
the following LPP :

Min Z=2x

_{1}+x_{2}+3x_{3}
Subject to :

x

_{1}−2x_{2}+x_{3}≥ 4
2x

_{1}+x_{2}+x_{3}≤ 8
x

_{1}−x_{3}≥ 0
x

_{1}, x_{2}, x_{3}≥ 0
The solution
of this LPP using Dual Simplex Method is :

(1) x

_{1}=0, x_{2}=0, x_{3}=3 and Z=9
(2) x

_{1}=0, x_{2}=6, x_{3}=0 and Z=6
(3) x

_{1}=4, x_{2}=0, x_{3}=0 and Z=8
(4) x

_{1}=2, x_{2}=0, x_{3}=2 and Z=10
Answer: 3

70. Consider
a Takagi - Sugeno - Kang (TSK) Model consisting of rules of the form :

If x

_{1}is A_{i1}and ... and x_{r}is A_{ir}
THEN y =f

_{i}(x_{1}, x_{2}, ..., x_{r}) = b_{i0}+b_{i1}x_{1}+...+b_{ir }x_{r}
assume, Î±

_{i}is the matching degree of rule i, then the total output of the model is given by:
Answer: 2

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