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PREVIOUS YEAR SOLVED PAPERS - July 2016 Paper 3

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56. Let L = {0n1n|n ≥ 0} be a context free language. Which of the following is correct ?

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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(q3, b) = (q3, b, R) The language L(M) accepted by the Turing Machine is given as:

  • Option : C
  • Explanation :
    According to given question, we have transtion: δ(q0, a) = (q1, a, R) δ(q1, b) = (q2, b, R) δ(q2, a) = (q2, a, R) δ(q3, b) = (q3, b, R) We can draw a DFA:

    Language will be aba*b. So, option (C) is correct.
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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?

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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 ?

  • Option : B
  • Explanation :

    Bits required per symbol: A - 0 (1 bit) B - 10 (2 bit) C - 110 (3 bit) D - 111 (3 bit) Average number of bits per symbol = 1 * 1 / 2 + 2 * 1 / 4 + 3 * 1 / 8 + 3 * 1 / 8 = 7 / 4 = 1.75. So, option (B) is correct.
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60. Which of the following is used for the boundary representation of an image object?

  • Option : D
  • Explanation :
  • Chain codes is used for the boundary representation of an image object
  • A quad tree is a tree data structure in which each internal node has exactly four children.
  • Projection is the presentation of an image on a surface
  • Run-length encoding (RLE) is a very simple form of lossless data compression
    • So, option (D) is correct.
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