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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
For all real numbers $x$, there exists a real number $y$ such that $x$ is less than $y$.
(A) $L_1 = { w \in {0,1}^* \mid \text{length of } w \text{ is even} }$
(B) $L_2 = { w \in {0,1}^* \mid \text{length of } w \text{ is odd} }$
(C) $L_3 = { w \in {0,1}^* \mid \text{all 0s come before all 1s in } w }$
(D) $L_4 = { w \in {0,1}^* \mid w \text{ contains equal number of 0s and 1s} }$
(E) $L_5 = { w \in {0,1}^* \mid \text{all 1s come before all 0s in } w }$
Choose the correct answer from the options given below :
Solution
Important fact:
NFA and DFA recognize exactly the same class of languages → Regular Languages
So no language exists that can be recognized by NFA but not DFA.
But option (D)
equal number of 0s and 1s → not regular
Option (E)
all 1s before 0s → regular
Hence only (D) is non-regular.
Closest option given:
(4) (D) and (E) Only
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