Bihar STET – TOC Practice Test | Set 2 ⋆ CSE Study247

Question 1

MCQ · Single Correct 1 mark

Previous Year Question Bihar STET C.S. 18.09.2023 (Shift-I) PYQ

In the Myhill-Nerode Theorem, two strings x and y are defined to be equivalent with respect to a language L (x $R_L$ y) if -

A x and y have the same length B x and y are both in L C x and y start with the same symbol D For all strings z, xz ∈ L if and only if yz ∈ L

Question 2

MCQ · Single Correct 1 mark

Previous Year Question Bihar STET C.S. 12.06.2024 (Shift-I) PYQ

What does the 'Index' of the Myhill-Nerode equivalence relation $R_L$ represent for a regular language L?

A The depth of the parse tree B The alphabet size |$\Sigma |$ C The total length of the shortest string in L D The exact number of states in the MINIMAL Deterministic Finite Automaton (DFA) accepting L

Question 3

MCQ · Single Correct 1 mark

Previous Year Question Bihar STET C.S. 03.11.2025 (Shift-I) PYQ

In the Table-Filling Algorithm (Marking Algorithm) for DFA minimization, two states p and q are distinguished in the base step if -

A p and q have identical outgoing edges B Both states have self-loops C One state is an accepting state (p ∈ F) and the other is a non-accepting state (q ∉ F) D Both states are initial states

Question 4

MCQ · Single Correct 1 mark

Previous Year Question Bihar STET C.S. 04.11.2025 PYQ

In the Table-Filling DFA minimization algorithm, when is a state pair (p, q) marked as distinguishable in an inductive step on input symbol 'a'?

A If p and q have the same state number B If $\delta (p, a) == \delta (q, a)$ C If 'a' is the empty string $\epsilon$ D If the pair of target states ($\delta (p, a), \delta (q, a)) has ALREADY been marked as distinguishable$

Question 5

MCQ · Single Correct 1 mark

Previous Year Question Bihar STET C.S. 2020 PYQ

According to the Pumping Lemma for Regular Languages, for any regular language L with pumping length p, every string w ∈ L with |w| $\ge p can be split$ into $w = xyz satisfying$ which THREE conditions?

A 1) |xy| $\ge p, 2) |y| = 1$, and 3) xyz^i ∈ L B 1) |x| $\le p, 2) |y| = 0$, and 3) xy z ∈ L C 1) |z| $\le p, 2) |y| \ge p$, and 3) $x^i$ y z ∈ L D 1) |xy| $\le p, 2) |y| \ge 1$, and 3) xy^i z ∈ L for all i $\ge 0$