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# GATE 2022 Rapid Revision Quiz 4

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Question 1

Let f be a substitution function which is used for mapping every input symbol of language to some symbol. The language L = (bc)*a + b is over Σ = {a, b, c} and following substitutions are provided.

f(a) = ε, f(b) = Φ.(a + b)*, f(c) = Φ.a*

Which of the following represents f(L)?

Question 2

Consider a system which has 28 instances of a resource P such that 4 + n processes share them, 4 process request 5 instances of ‘P’. If n processes request 5 instances of same resources what is the maximum value of n such that system is in safe state ________

Question 3

The following is a scheme for floating-point number representation using 16 bits.

Bit position-

Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields, respectively. Then the floating-point number represented is {( -1)8(1 + m x 2-9)2e-31 if the exponent ≠ [111111] otherwise 0. What is the maximum difference between two successive real numbers representable in this system?

Question 4Multiple Correct Options

Consider BFS algorithm. The starting vertex is 3, which of the following is/are valid BFS sequences?

[Multi-select Question]

Question 5

One server sends 15 packets to its remote client through parallel packet switched network at distance 10 km, each packet size 50 bits. Network has propagation speed 2*105 meter and bandwidth 2 Mbps and 5 Hops. What is total time taken to send all packet successfully? Assume processing delay and queueing delay as zero.

Question 6

Let <M> be the encoding of Turing machine as a string over Σ = {0, 1}. Let L = {<M> | M is TM on input w will visit some state P}.

The language L is

Question 7

Given a Turing machine M, what is the language accepted by M?

Question 8

A min heap having 1024 distinct elements with keys ranging from 0 to 1023 is stored in array of 1024 indices. The maximum difference between element 512 present at maximum level and minimum level is ________. [Assume root is present at level-1]
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