1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Language $${L_1}$$ is polynomial time reducible to language $${L_2}$$ . Language $${L_3}$$ is polynomial time reducible to $${L_2}$$ , which in turn is polynomial time reducible to language $${L_4}$$ . Which of the following is/are true?

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_4} \in P,$$ then $$\,\,\,{L_2} \in P$$
$$\,\,\,\,\,\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_1} \in P$$ or $$\,\,\,{L_3} \in P,$$ then $$\,\,\,{L_2} \in P$$
$$\,\,\,\,\,\,\,\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_1} \in P,$$ and only $$\,\,\,{L_3} \in P$$
$$\,\,\,\,\,\,\,\,\,\,{\rm I}V.\,\,\,\,$$ if $$\,\,\,{L_4} \in P,$$ then $$\,\,\,{L_1} \in P$$ and $$\,\,\,{L_3} \in P$$

A
$${\rm I}$$$${\rm I}$$ only
B
$${\rm III}$$ only
C
$${\rm I}$$ and $${\rm IV}$$ only
D
$${\rm I}$$ only
2
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Which of the following languages are context-free? $$$\eqalign{ & {L_1} = \left\{ {{a^m}{b^n}{a^n}{b^m}|m,n \ge 1} \right\} \cr & {L_2} = \left\{ {{a^m}{b^n}{a^m}{b^n}|m,n \ge 1} \right\} \cr & {L_3} = \left\{ {{a^m}{b^n}|m = 2n + 1} \right\} \cr} $$$
A
$${L_1}$$ and $${L_2}$$ only
B
$${L_1}$$ and $${L_3}$$ only
C
$${L_2}$$ and $${L_3}$$ only
D
$${L_3}$$ only
3
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
In a web server, ten WebPages are stored with the URLs of the form
http://www.yourname.com/$$var$$.html; where, $$var$$ is a different number from $$1$$ to $$10$$ for each Webpage. Suppose, the client stores the Webpage with $$var = 1$$ (say $$W1$$) in local machine, edits and then tests. Rest of the WebPages remains on the web server. $$W1$$ contains several relative URLs of the form “$$var$$.html” referring to the other WebPages. Which one of the following statements needs to be added in $$W1,$$ so that all the relative URLs in $$W1$$ refer to the appropriate WebPages on the web server?
A
< a href: “http://www.yourname.com/”, href: “... $$var$$.html”>
B
< base href: “http://www.yourname.com/”>
C
< a href: “http://www.yourname.com/”>
D
< base href: “http://www.yourname.com/”, range:“…$$var$$.html”>
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