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–16 | Ultimate Challenge – PhD Level ๐Ÿ˜ˆ๐Ÿ”ฅ)

151. If P = NP, which of the following would immediately follow?

A) All undecidable problems become decidable
B) All NP-Complete problems can be solved in polynomial time
C) PSPACE = EXPTIME
D) Halting problem becomes solvable

Answer: B) All NP-Complete problems can be solved in polynomial time

152. The complement of a recursive language is:

A) Recursive
B) Recursively Enumerable only
C) Not decidable
D) Context-Free

Answer: A) Recursive

153. A language is recursively enumerable but not recursive if and only if:

A) Both L and L̅ are RE
B) Neither L nor L̅ are RE
C) L is RE but L̅ is not RE
D) L is regular

Answer: C) L is RE but L̅ is not RE

154. In parameterized complexity, FPT stands for:

A) Fully Polynomial Time
B) Fixed Parameter Tractable
C) Fast Polynomial Theorem
D) Finite Processing Time

Answer: B) Fixed Parameter Tractable

155. The communication complexity of equality problem with deterministic protocol (n-bit input) is:

A) O(1)
B) O(log n)
C) O(n)
D) O(n²)

Answer: C) O(n)

156. In randomised algorithms, Monte Carlo algorithms:

A) Always give correct result
B) May give incorrect result with bounded probability
C) Never terminate
D) Are deterministic

Answer: B) May give incorrect result with bounded probability

157. The VC-dimension of a linear classifier in 2D is:

A) 2
B) 3
C) 4
D) Infinite

Answer: B) 3

158. In cryptography, a one-way function is:

A) Easily invertible
B) Hard to compute
C) Easy to compute but hard to invert
D) Symmetric encryption

Answer: C) Easy to compute but hard to invert

159. If NP ⊆ P/poly, then:

A) P = NP
B) Polynomial hierarchy collapses
C) PSPACE = NP
D) EXP = NP

Answer: B) Polynomial hierarchy collapses

160. In quantum computing, Shor’s algorithm solves:

A) Search problem
B) Graph coloring
C) Integer factorization in polynomial time
D) Sorting

Answer: C) Integer factorization in polynomial time

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