Summary: ``A finite group $G$ is called $(l, m, n)$-{\it generated}, if it is a quotient group of the triangle group $T(l, m, n) = \langle x, y, z|x^l = y^m = z^n = xyz = 1\rangle$. Moori posed the question of finding all the $(p, q, r)$ triples, where $p$, $q$, and $r$ are prime numbers, such that a non-abelian finite simple group $G$ is a $(p, q, r)$- generated. In this paper, we establish all the $(p, q, r)$-generations of the alternating group $A_{11}$. The Groups, Algorithms and Programming and the Atlas of finite group representations are used in our computations.''