July 2016 - Paper 3

56:

Let L = {0n1n|n ≥ 0} be a context free language.

Which of the following is correct ?

A.	L' is context free and L^k is not context free for any k ≥ 1.
B.	L' is not context free and L^k is context free for any k ≥ 1.
C.	Both L' and L^k is for any k ≥ 1 are context free.
D.	Both L' and L^k is for any k ≥ 1 are not context free.
	Answer Report Discuss
	Option: C Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

57:

Given a Turing Machine

M = ({q0, q1, q2, q3}, {a, b}, {a, b, B}, δ, B, {q3})

Where δ is a transition function defined as

δ(q0, a) = (q1, a, R)

δ(q1, b) = (q2, b, R)

δ(q2, a) = (q2, a, R)

δ(q2, b) = (q3, b, R)

The language L(M) accepted by the Turing Machine is given as :

A.	aa*b
B.	abab
C.	aba*b
D.	aba*
	Answer Report Discuss
	Option: C Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

58:

Consider a discrete memoryless channel and assume that H(x) is the amount of information per symbol at the input of the channel; H(y) is the amount of information per symbol at the output of the channel; H(x|y) is the amount of uncertainty remaining on x knowing y; and I (x; y) is the information transmission. Which of the following does not define the channel capacity of a discrete memoryless channel ?

A.	max I (x; y) p(x)
B.	max [H(y) – H(y\|x)] p(x)
C.	max [H(x) – H(x\|y)] p(x)
D.	max H(x\|y) p(x)
	Answer Report Discuss
	Option: D Explanation : The channel capacity of a discrete memoryless channel is defined by: C = max I(X; Y ) p(x) = max [H(Y ) − H(Y \|X)] p(x) = max [H(X) − H(X\| p(x) Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

59:

Consider a source with symbols A, B, C, D with probabilities 1/2, 1/4, 1/8, 1/8 respectively. What is the average number of bits per symbol for the Huffman code generated from above information ?

A.	2 bits per symbol
B.	1.75 bits per symbol
C.	1.50 bits per symbol
D.	1.25 bits per symbol
	Answer Report Discuss
	Option: B Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

60: Which of the following is used for the boundary representation of an image object ?

A.	Quad Tree
B.	Projections
C.	Run length coding
D.	Chain codes
	Answer Report Discuss
	Option: D Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

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