Condition for parallel lines is

a₁/a₂ = b₁/b₂ c₁/c₂ …(i)

Given lines, 3x + 2ky - 2 = 0

and 2x + 5y - 1 = 0;

Comparing with ax + by + c = 0;

Here, a₁ = 3, b₁ = 2k, c₁ = - 2

and a₂ = 2, b₂ = 5, c₂ = - 1

From Eq. (i), 3/2 = 2k/5

k = 15/4