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 (n

^{3})
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 90

^{0}
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

Âµ

_{A}(x)=x/(x+2)
Then the Î± cut corresponding to Î±=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}

Âµ

_{A}(x)=x/(x+2)
Âµ

_{A}= {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, Î± cut where Î± =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(log

_{2}n)
(C) T(n)=O(n)

(D) T(n)=O(n

^{2})
Answer: C

__Explanation:__
According to Master theorem

T(n) =aT(n/b) + n

^{c}
a=2, b=2

n

^{c}= √n => n^{c}= n^{1/2}=> c=1/2
1. if log

_{b}a < c, T(n) = Î˜(n^{c}),
2. if log

_{b}a = c, T(n) = Î˜(n^{c}log n),
3. if log

_{b}a > c, T(n) = Î˜(n^{log}_{b}^{a}).
Here log

_{b}a > c, So T(n)= Î˜(n^{log}_{b}^{a})= Î˜(n^{1})= Î˜(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 :

x

_{n+1}=x^{2}_{n}+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

^{n}C

_{m}=

^{5}C

_{3}=

^{5}C

_{2}= 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 n

_{i}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 n

_{i}objects are placed into box i, i = 1, 2, . . . , k, equals
## 1 Comments

For Question 57 answer must be A

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