In ∆ 𝐴𝐵𝐶 , if X and Y are the points on AB and AC respectively such that 𝐴𝑋𝑋𝐵 = 34 ,𝐴𝑌 = 5 and 𝑌𝐶 = 9. State whether 𝑋𝑌 || 𝐵𝐶 or not

The problem seems to be incomplete. The given information is not enough to determine whether XY is parallel to BC or not. In order to determine this, we would need more information, such as the lengths of other sides or the measures of certain angles. For instance, if we knew that AX/AB = AY/AC, then we could use the Converse of the Basic Proportionality Theorem (or Thales' Theorem) to conclude that XY is parallel to BC. But with the given information, we cannot make this determination.