UGC NET COMPUTER SCIENCE SOLVED PAPERS 2014-16 - UGC NET Computer Science Paper 3 July 2016

61. The region of feasible solution of a linear programming problem has a _____ property in geometry, provided the feasible solution of the problem exists.

  • Option : B
  • Explanation :
    The region of feasible solution of a linear programming problem has a convexity property in geometry, provided the feasible solution of the problem exists. Convexity is a measure of the curvature in the relationship between prices and yields. Other term doesn't related to linear programming problem. So, option (B) is correct.
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62. Consider the following statements:
(a) Revised simplex method requires lesser computations than the simplex method.
(b) Revised simplex method automatically generates the inverse of the current basis matrix.
(c) Less number of entries are needed in each table of revised simplex method than usual simplex method. Which of these statements are correct?

  • Option : D
  • Explanation :
  • Revised simplex method requires lesser computations than the simplex method.Correct
  • Revised simplex method automatically generates the inverse of the current basis matrix.Correct
  • Less number of entries are needed in each table of revised simplex method than usual simplex method.Correct All statement are correct.
  • So, option (D) is correct.
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63. The following transportation problem:

 ABCSupply
I.50302201
II.90401703
III.250200504
Demand442 

has solution

 ABC
I.1  
II.30 
III. 22

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64. Let R and S be two fuzzy relations defined as :
Then, the resulting relation, T, which relates elements of universe x to elements of universe z using max-min composition is given by
and

  • Option : D
  • Explanation :
    Since x is related to y and y is related to z, to relate universe x and universe z we have to compute max-min composition:
    x1z1= max(min(0.7, 0.9), min(0.5, 0.1))
    = max(0.7 0.1)
    = 0.7
    x1z2= max(min(0.7, 0.6), min(0.5, 0.7))
    = max(0.6, 0.5)
    = 0.6
    x1z3= max(min(0.7, 0.2), min(0.5, 0.5))
    = max(0.2, 0.5)
    = 0.5
    x2z1= max(min(0.8, 0.9), min(0.4, 0.1))
    = max(0.8, 0.1)
    = 0.8
    x2z2= max(min(0.8, 0.6), min(0.4, 0.7))
    = max(0.6, 0.4)
    = 0.6
    x3z3= max(min(0.8, 0.2), min(0.4, 0.5))
    = max(0.2, 0.4)
    = 0.4
    So, option (C) is correct.
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65. Compute the value of adding the following two fuzzy integers : A = {(0.3, 1), (0.6, 2), (1, 3), (0.7, 4), (0.2, 5)} B = {(0.5, 11), (1, 12), (0.5, 13)} Where fuzzy addition is defined as μA+B (z) = max x + y = z(min (μA(x), μB(x))) Then, f (A + B) is equal to

  • Option : D
  • Explanation :
    According to question: A={(0.3, 1), (0.6, 2), (1, 3), (0.7, 4), (0.2, 5)} B={(0.5,11), (1, 12), (0.5, 13)} first add the numbers(x + y = z) and write the min membership value since function is min((μA(x),μB(x)) u will get following 15 terms: {(0.3, 12), (0.3, 13), (0.3, 14), (0.5, 13), (0.6, 14), (0.5, 15), (0.5, 14), (1, 15), (0.5, 16), (0.5, 15), (0.7, 16), (0.5, 17), (0.2, 16), (0.2, 17), (0.2, 18) f(A + B) is equal to {(0.3, 12), (0.5, 13), (0.6, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)} So, option (D) is correct.
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