# CBSE UGC NET Computer Science Paper III Solved November 2017 - Part 7

61.       Which of the following statements is not correct?
(1) Every recursive language is recursively enumerable.
(2) L = {0n 1n 0n | n=1, 2 , 3, ....} is recursively enumerable.
(3) Recursive languages are closed under intersection.
(4) Recursive languages are not closed under intersection.
62.       Context free grammar is not closed under :
(1) Concatenation
(2) Complementation
(3) Kleene Star
(4) Union
63.       Consider the following languages :
L1 = {am bn | m ≠ n}
L2 = {am bn | m = 2n+1}
L3 = {am bn | m ≠ 2n}
Which one of the following statement is correct?
(1) Only L1 and L2 are context free languages
(2) Only L1 and L3 are context free languages
(3) Only L2 and L3 are context free languages
(4) L1, L2 and L3 are context free languages
64.       A 4×4 DFT matrix is given by :
(j2=−1)
Where values of x and y are ..........., ............. respectively.
(1) 1, −1
(2) −1, 1
(3) −j, j
(4) j, −j
65.       Entropy of a discrete random variable with possible values {x1, x2, ..., xn} 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
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
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.
68.       Consider the following LPP :
Max Z=15x1+10x2
Subject to the constraints
4x1+6x2 ≤ 360
3x1+0x2 ≤ 180
0x1+5x2 ≤ 200
x1, x2 ≥ 0
The solution of the LPP using Graphical solution technique is :
(1) x1=60, x2=0 and Z=900
(2) x1=60, x2=20 and Z=1100
(3) x1=60, x2=30 and Z=1200
(4) x1=50, x2=40 and Z=1150
69.       Consider the following LPP :
Min Z=2x1+x2+3x3
Subject to :
x1−2x2+x3 ≥ 4
2x1+x2+x3 ≤ 8
x1−x3 ≥ 0
x1, x2, x3 ≥ 0
The solution of this LPP using Dual Simplex Method is :
(1) x1=0, x2=0, x3=3 and Z=9
(2) x1=0, x2=6, x3=0 and Z=6
(3) x1=4, x2=0, x3=0 and Z=8
(4) x1=2, x2=0, x3=2 and Z=10