1
GATE CSE 1998
+1
-0.3
If the regular set $$A$$ is represented by $$A = {\left( {01 + 1} \right)^ * }$$ and the regular set $$'B'$$ is represented by $$B = \left( {{{\left( {01} \right)}^ * }{1^ * }} \right),$$ which of the following is true?
A
$$A \subset B$$
B
$$B \subset A$$
C
$$A$$ and $$B$$ are incomparable
D
$$A=B$$
2
GATE CSE 1998
+1
-0.3
Which of the following sets can be recognized by a Deterministic Finite-state Automation?
A
The numbers $$1, 2, 4, 8,$$ ...... $${2^n},$$ ............. written in binary.
B
The numbers $$1, 2, 4, .....$$ $${2^n},$$ $$.....$$ written in unary.
C
The set of binary strings in which the numbers of zeros is the same as the numbers of ones.
D
The set $$\left\{ {1,101,11011,1110111,...} \right\}.$$
3
GATE CSE 1998
MCQ (More than One Correct Answer)
+1
-0.3
The string $$1101$$ does not belong to the set represented by
A
$${110^ * }\,\,\left( {0 + 1} \right)$$
B
$$\,1\,{\left( {0 + 1} \right)^ * }101$$
C
$${\left( {10} \right)^ * }\,{\left( {01} \right)^ * }\,{\left( {00 + 11} \right)^ * }$$
D
$${\left( {00 + {{\left( {11} \right)}^ * }0} \right)^ * }$$
4
GATE CSE 1998
+1
-0.3
How many substrings of different lengths (non-zero) can be formed from a character string of length $$n$$ ?
A
$$n$$
B
$${n^2}$$
C
$${2^n}$$
D
$$n\left( {n + 1} \right)/2$$
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