GATE CSE 2021 Set 2 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2021 Set 2

MCQ (More than One Correct Answer)

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For a string w, we define wR to be the reverse of w. For example, if w = 01101 then wR = 10110.

Which of the following languages is/are context-free?

{wxwRxR | w, x ∈ {0, 1}*}

{wwRxxR | w, x ∈ {0, 1}*}

{wxwR | w, x ∈ {0, 1}*}

{wxxRwR | w, x ∈ {0, 1}*}

GATE CSE 2021 Set 2

MCQ (More than One Correct Answer)

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Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string ∈ divisible by three.

(0 + 1(01*0)*1)*

(0*(1(01*0)*1)*)*

(0 + 11 + 10(1 + 00)*01)*

( 0+ 11 + 11(1 + 00)*00)*

GATE CSE 2021 Set 2

Numerical

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Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps (= 106 bits per second). The aggregate number of transmissions across all the nodes (in-cluding new frame transmissions and retransmitted frames due to collisions) is modelled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is

Your input ____

GATE CSE 2021 Set 2

MCQ (More than One Correct Answer)

-0

Let L₁ be a regular language and L₂ be a context-free language. Which of the following languages is/are context-free?

L₁ ∩ L̅₂

L₁ ∪ (L₂ ∪ L̅₂)

$$\overline {{{\bar L}_1} \cup {{\bar L}_2}} $$

(L₁∩ L₂) ∪ (L̅₁ ∩ L₂)

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