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–18 | Final Boss Level ๐Ÿ˜ˆ๐Ÿ†๐Ÿ”ฅ)

171. If PSPACE = NP, which of the following must be true?

A) P = NP
B) NP = co-NP
C) EXP = PSPACE
D) All undecidable problems become decidable

Answer: B) NP = co-NP
(PSPACE is closed under complement)

172. The Cook–Levin Theorem proves that:

A) P = NP
B) SAT is NP-Complete
C) Halting Problem is undecidable
D) 3-SAT is polynomial

Answer: B) SAT is NP-Complete

173. If L₁ and L₂ are NP-Complete, then L₁ ∩ L₂ is:

A) Always NP-Complete
B) Always in P
C) Not necessarily NP-Complete
D) Undecidable

Answer: C) Not necessarily NP-Complete

174. In distributed systems, Byzantine Generals Problem tolerates at most:

A) f faulty nodes in system of 2f
B) f faulty nodes in system of 3f + 1
C) f faulty nodes in system of 2f + 1
D) Unlimited faults

Answer: B) f faulty nodes in system of 3f + 1

175. If a language is both RE and co-RE, then it is:

A) Undecidable
B) Recursive
C) NP-Complete
D) PSPACE

Answer: B) Recursive

176. The space complexity of Depth-First Search on a graph with V vertices is:

A) O(V²)
B) O(V)
C) O(E)
D) O(log V)

Answer: B) O(V)

177. In cryptographic hash functions, collision resistance means:

A) Hard to find any preimage
B) Hard to find two distinct inputs with same hash
C) Hash output is reversible
D) Encryption key is hidden

Answer: B) Hard to find two distinct inputs with same hash

178. In learning theory, PAC learning guarantees:

A) Exact learning
B) Learning with high probability and small error
C) Deterministic classification
D) Zero training error

Answer: B) Learning with high probability and small error

179. The time complexity of Karatsuba multiplication is:

A) O(n²)
B) O(n log n)
C) O(n^1.585)
D) O(n³)

Answer: C) O(n^1.585)

180. The hierarchy theorem implies that:

A) More time allows solving strictly more problems
B) P = NP
C) NP = PSPACE
D) All languages are decidable

Answer: A) More time allows solving strictly more problems

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