Computer Science MCQs (Set–29 | Level — Frontier Open Conjectures & Deep Structural Theory ๐Ÿ˜ˆ๐Ÿ”ฅ)

281. The statement “P ≠ NP” would immediately imply: A) NP ⊄ P B) No NP-Complete problem is solvable in polynomial time C) There exist problems verifiable but not efficiently solvable D) All of the above Answer: D) All of the above 282. The class coNP consists of languages whose complements are in: A) P B) NP C) PSPACE D) EXP Answer: B) NP 283. If PH collapses to level k, then: A) All higher levels equal ฮฃโ‚–^P B) PSPACE collapses C) NP = PSPACE D) EXP collapses Answer: A) All higher levels equal ฮฃโ‚–^P 284. The problem of graph isomorphism is currently known to be in: A) P (proven decades ago) B) NP-Complete C) Quasi-polynomial time D) PSPACE-Complete Answer: C) Quasi-polynomial time 285. The class #P deals with: A) Optimization problems B) Counting accepting paths C) Space-bounded computation D) Quantum proofs Answer: B) Counting accepting paths 286. If #P = FP (polynomial-time computable functions), then: A) P = NP B) PH collapses C) PSPACE = NP D) BQP = P Answer: B) PH collapses ...
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Computer Science MCQs (Set–17 | Proof-Based + Conceptual Trap Level ๐Ÿ˜ˆ๐Ÿ”ฅ)

161. If L is NP-Complete and L ∈ P, then:

A) P ≠ NP
B) P = NP
C) L is undecidable
D) NP = PSPACE

Answer: B) P = NP

162. Which of the following is TRUE?

A) Every decidable language is recursive
B) Every recursive language is regular
C) Every context-free language is recursive
D) Every recursively enumerable language is recursive

Answer: C) Every context-free language is recursive

163. The closure of Context-Free Languages under complement is:

A) Closed
B) Not Closed
C) Depends on grammar
D) Only for deterministic CFL

Answer: B) Not Closed

164. If A ≤p B and B ∈ P, then A is:

A) NP-Complete
B) In P
C) Undecidable
D) In PSPACE only

Answer: B) In P

165. The Chromatic Number problem is NP-Complete for:

A) k = 1
B) k = 2
C) k ≥ 3
D) All k

Answer: C) k ≥ 3

166. In amortized analysis using accounting method, the stored credit must always be:

A) Negative
B) Zero
C) Non-negative
D) Infinite

Answer: C) Non-negative

167. In distributed computing, the FLP impossibility result states that:

A) Consensus is always solvable
B) Deterministic consensus is impossible in asynchronous system with one faulty process
C) Deadlock always occurs
D) Byzantine agreement is easy

Answer: B) Deterministic consensus is impossible in asynchronous system with one faulty process

168. If f(n) = ฮ˜(g(n)) and g(n) = ฮ˜(h(n)), then f(n) is:

A) O(h(n))
B) ฮฉ(h(n))
C) ฮ˜(h(n))
D) None

Answer: C) ฮ˜(h(n))

169. In a fully connected network of n nodes, number of communication links is:

A) n
B) n²
C) n(n−1)/2
D) 2n

Answer: C) n(n−1)/2

170. The Kolmogorov complexity of a truly random string of length n is approximately:

A) log n
B) n
C) √n
D) 1

Answer: B) n

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