# GATE Papers >> CSE >> 2015 >> Question No 244

Question No. 244

Which of the following languages are context-free?

L1 = {ambnanbm |m, n$\ge$1}
L2 = {ambnambn|m, n $\ge$1}
L3 = {ambn|m = 2n+1}

##### Answer : (B)  L1and L3 only

Solution of Question No 244 of GATE 2015 CSE Paper

$L_1=\left\{a^m\;b^n\;a^n\;b^m\;\vert\;m,\;n\geq1\right\}$ is CFL (push "a" and "b" and then first "a" pops "b" and then "b" pops "a").

$L_2=\left\{a^m\;b^n\;a^m\;b^n\;\vert\;m,\;n\geq1\right\}$ is non-CFL (Alternate comparison not possible in a PDA)

$L_3=\left\{a^m\;b^n\;\vert\;m=2n+1\right\}$ is CFL (Single comparison is possible in a PDA)

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