UGC NET Computer Science and Applications Paper III December 2012 - Part 2

11.       The time complexities of some standard graph algorithms are given. Match each algorithm with its time complexity? (n and m are no. of nodes and edges respectively)
List - I
a. Bellman Ford algorithm
b. Kruskals algorithm
c. Floyd Warshall algorithm
d. Topological sorting
List - II
1. O (m log n)
2. O (n3)
3. O(mn)
4. O(n + m)
Codes :
      a   b   c   d
(A) 3   1   2   4
(B) 2   4   3   1
(C) 3   4   1   2
(D) 2   1   3   4
Answer: A
12.       Let V1 = 2I – J + K and V2 = I + J – K, then the angle between V1 & V2 and a vector perpendicular to both V1 & V2 shall be :
(A) 90 and (–2I+J–3K)
(B) 60 and (2I+J+3K)
(C) 90 and (2I+J–3K)
(D) 90 and (–2I–J+3K)
Answer: Marks to All
Explanation:
V1.V2=(2I – J + K)(I + J – K)=2-1-1=0
Hence angle between V1 and V2 is 900
Correct answer is 90 and (3J+3K)
13.       Consider a fuzzy set A defined on the interval X=[0,10] of integers by the membership function
µA(x)=x/(x+2)
Then the α cut corresponding to α=0.5 will be
(A) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(B) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(C) {2, 3, 4, 5, 6, 7, 8, 9, 10}
(D) { }
Answer: C
Explanation:
An alpha-cut of the membership function A (denoted aA) is the set of all x such that A(x) is greater than or equal to alpha. Similarly, a strong alpha-cut (denoted a+A) is the set of all x such that A(x) is strictly greater than alpha.
A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
µA(x)=x/(x+2)
µA = {0, 1/3, 2/4, 3/5, 4/6, 5/7, 6/8, 7/9, 8/10, 9/11, 10/12}
    = {0, .33, .5, .6, .66, .71, .75, .77, .8, .81, .83}
Hence, α cut where α =0.5 is membership value greater or equal to 0.5
    = {2, 3, 4, 5, 6, 7, 8, 9, 10}
14.       Let T(n) be the function defined by T(n)=1 and T(n)=2T(n/2)+√n, which of the following is TRUE?
(A) T(n)=O(√n) 
(B) T(n)=O(log2n)
(C) T(n)=O(n)
(D) T(n)=O(n2)
Answer: C
Explanation:
According to Master theorem
T(n) =aT(n/b) + nc
a=2, b=2
nc = √n => nc = n1/2 => c=1/2
1. if logba < c, T(n) = Θ(nc),
2. if logba = c, T(n) = Θ(nc log n),
3. if logba > c, T(n) = Θ(nlogba).
Here logba > c, So T(n)= Θ(nlogba)= Θ(n1)= Θ(n)
15.       In classful addressing, an IP address 123.23.156.4 belongs to …………. class format.
(A) A
(B) B
(C) C
(D) D
Answer: A

16.       The Mandelbrot set used for the construction of beautiful images is based on the following transformation :
xn+1=x2n+z
Here,
(A) Both x & z are real numbers.
(B) Both x & z are complex numbers.
(C) x is real & z is complex.
(D) x is complex & z is real.
Answer: B
17.       Which of the following permutations can be obtained in the output using a stack of size 3 elements assuming that input, sequence is 1, 2, 3, 4, 5?
(A) 3, 2, 1, 5, 4
(B) 5, 4, 3, 2, 1
(C) 3, 4, 5, 2, 1
(D) 3, 4, 5, 1, 2
Answer: A, C
Explanation:
Initially 1, 2, 3 are pushed into stack after that if you want to push 4 in stack then pop 3 then push 4. If you want to push 5 then pop 4 and push 5. After that elements are poped from stack are 5, 2, 1.
Hence, the sequence is 3, 4, 5, 2, 1.
18.       In a Linear Programming Problem, suppose there are 3 basic variables and 2 non-basic variables, then the possible number of basic solutions are
(A) 6
(B) 8
(C) 10
(D) 12
Answer: C
Explanation:
Number of basic solutions are
nCm = 5C3 = 5C2 = 5x4/1x2 = 10
19.       Identify the following activation function :
Z, X, Y are parameters
(A) Step function
(B) Ramp function
(C) Sigmoid function
(D) Gaussian function
Answer: C
Explanation:
A sigmoid function(or logistic function) is a mathematical function having an "S" shape (sigmoid curve) is defined by the formula
20.    The no. of ways to distribute n distinguishable objects into k distinguishable boxes, so that ni objects are placed into box i, i = 1, 2, …. k equals which of the following?
Answer: C
Theorem:
The number of ways to distribute n distinguishable objects into k distinguishable boxes such that ni objects are placed into box i, i = 1, 2, . . . , k, equals


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