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For Ξ£ = {π‘Ž, 𝑏}, let us consider the regular language 𝐿 = { π‘₯ |π‘₯ = π‘Ž2+3π‘˜ or π‘₯ = 𝑏10+12π‘˜, π‘˜ β‰₯ 0}. Which one of the following

Q. For Ξ£ = {π‘Ž, 𝑏}, let us consider the regular language 𝐿 = { π‘₯ |π‘₯ = π‘Ž2+3π‘˜ or π‘₯ = 𝑏10+12π‘˜, π‘˜ β‰₯ 0}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for 𝐿 ? (A) 3 (B) 5 (C) 9 (D) 24 Ans: 24 Solution: According to Pumping lemma, ...

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Let 𝐺 be an undirected complete graph on 𝑛 vertices, where 𝑛 > 2. Then, the number of different Hamiltonian cycles in 𝐺 is equal to

Q. Let 𝐺 be an undirected complete graph on 𝑛 vertices, where 𝑛 > 2. Then, the number of different Hamiltonian cycles in 𝐺 is equal to Ans: Option D Solution: A simple circuit in a graph G that passes through every vertex exactly once is called a Hamiltonian circuit. In Hamiltonian ...

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Let 𝐺 be an arbitrary group. Consider the following relations on 𝐺

Q. Let 𝐺 be an arbitrary group. Consider the following relations on 𝐺: 𝑅1: βˆ€π‘Ž, 𝑏 ∈ 𝐺, π‘Ž 𝑅1𝑏 if and only if βˆƒπ‘” ∈ 𝐺 such that π‘Ž = π‘”βˆ’1𝑏𝑔 𝑅2: βˆ€π‘Ž, 𝑏 ∈ 𝐺, π‘Ž 𝑅2𝑏 if and only if π‘Ž = π‘βˆ’1 Which of the above is/are equivalence relation/relations? (A) 𝑅1 and 𝑅2 (B) 𝑅1 only (C) 𝑅2 only (D) ...

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If 𝐿 is a regular language over Ξ£ = {π‘Ž, 𝑏}, which one of the following languages is NOT regular ?

Q. If 𝐿 is a regular language over Ξ£ = {π‘Ž, 𝑏}, which one of the following languages is NOT regular ? (A) 𝐿 β‹… 𝐿𝑅 = {π‘₯𝑦 | π‘₯ ∈ 𝐿, 𝑦𝑅 ∈ 𝐿} (B) {𝑀𝑀𝑅 | 𝑀 ∈ 𝐿} (C) Prefix (𝐿) = {π‘₯ ∈ π›΄βˆ—|βˆƒπ‘¦ ∈ π›΄βˆ— such that π‘₯𝑦 ∈ 𝐿} (D) Suffix (𝐿) = {𝑦 ∈ π›΄βˆ—|βˆƒπ‘₯ ∈ π›΄βˆ— such that π‘₯𝑦 ∈ 𝐿} Ans:{𝑀𝑀𝑅 | 𝑀 ∈ 𝐿} ...

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Let π‘ˆ = {1,2, … , 𝑛}. Let 𝐴 = {(π‘₯, 𝑋)|π‘₯ ∈ 𝑋, 𝑋 βŠ† π‘ˆ}. Consider the following two statements on |𝐴|

Q.Let π‘ˆ = {1,2, … , 𝑛}. Let 𝐴 = {(π‘₯, 𝑋)|π‘₯ ∈ 𝑋, 𝑋 βŠ† π‘ˆ}. Consider the following two statements on |𝐴|. I. |𝐴| = 𝑛2π‘›βˆ’1 II. |𝐴| = βˆ‘π‘›π‘˜=1 π‘˜(𝑛) Which of the above statements is/are TRUE?Β (A) Only I(B) Only IIΒ (C) Both I and II(D) Neither I nor IIAns: Both I and ...

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The chip select logic for a certain DRAM chip in a memory system design is shown below. AssumeΒ thatΒ the memory system has 16 address lines denoted by A15 to A0

Q. The chip select logic for a certain DRAM chip in a memory system design is shown below. AssumeΒ thatΒ the memory system has 16 address lines denoted by A15 to A0. What is the range of addresses (in hexadecimal) of the memory system that can get enabled by the chip select (CS) signal? (A) ...

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