Using pascal triangle
We can see that that the 6th row is $1,5,{\color{Red} {10}},{\color{Blue} {10}},5,1$ so
$11^5 = 1(5+{\color{Red} 1})({\color{Red} 0}+{\color{Blue} {1}}){\color{Blue} {0}}51 = 161051$ $\implies (1.1)^5 = 1.61051$
$(1.1)^{10} = (1.1)^5*(1.1)^5 = 1.61051*1.61051 \approx 1.61*1.61 = 2.5921$
$\therefore$ Option $C.$ is the correct answer