1
GATE CSE 2014 Set 2
+1
-0.3
If $${L_1} = \left\{ {{a^n}\left| {n \ge \left. 0 \right\}} \right.} \right.$$ and $${L_2} = \left\{ {{b^n}\left| {n \ge \left. 0 \right\}} \right.} \right.,$$ consider
$$\left. {\rm I} \right)$$ $$\,\,\,{L_{1 \bullet }}{L_2}$$ is a regular language
$$\left. {\rm II} \right)$$ $$\,\,\,{L_{1 \bullet }}{L_2} = \left\{ {{a^n}{b^n}\left| {n \ge \left. 0 \right\}} \right.} \right.$$
Which one of the following is CORRECT?
A
Only $$\left( {\rm I} \right)$$
B
Only $$\left( {\rm II} \right)$$
C
Both $$\left( {\rm I} \right)$$ and $$\left( {\rm II} \right)$$
D
Neither $$\left( {\rm I} \right)$$ nor $$\left( {\rm II} \right)$$
2
GATE CSE 2014 Set 3
Numerical
+1
-0
The length of the shortest string NOT in the language (over $$\sum { = \left\{ {a,\,\,b} \right\}}$$) of the following regular expression is ____________. $$a{}^ * b{}^ * \left( {ba} \right){}^ * a{}^ *$$\$
3
GATE CSE 2014 Set 1
+1
-0.3
Which one of the following is TRUE?
A
The language $$L = \left\{ {{a^n}\,{b^n}\left| {n \ge 0} \right.} \right\}$$ is regular.
B
The language $$L = \,\,\left\{ {{a^n}\,\left| n \right.\,} \right.$$ is prime$$\left. \, \right\}$$ is regular.
C
The language $$L = \left\{ {w\left| {w\,\,} \right.} \right.$$ has $$3k+1$$ $$b'$$ $$s$$ for some $$k \in N$$ with $$\sum { = \left\{ {a,\,\,b} \right\}\left. \, \right\}}$$ is regular.
D
The language $$L = \left\{ {ww\,\left| {w \in \sum {{}^ * } } \right.} \right.$$ with $$\sum { = \left. {\left\{ {0,\,\,1} \right\}} \right\}}$$ is regular.
4
GATE CSE 2014 Set 1
+1
-0.3
Consider the finite automation in the following figure.

What is the set of reachable states for the input string $$0011?$$

A
$$\left\{ {{q_0},\,{q_1},\,{q_2}} \right\}$$
B
$$\left\{ {{q_0},\,{q_1}} \right\}$$
C
$$\left\{ {{q_0},\,{q_1},\,{q_2},\,{q_3}} \right\}$$
D
$$\left\{ {{q_3}} \right\}$$
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