What are the allowed total angular momentum quantum numbers

What are the allowed total angular momentum quantum numbers of a composite system in which j_1 = 2 and j_2 = 1?

Solution

j ₁ = 2

j ₂ = 1

The allowed total angular momentum quantum numbers of a composite system are ( j ₁ - j ₂ ) to ( j ₁+ j ₂)   (only integer values)

i.e., ( 2-1) to (2+1)

i.e., 1 to 3

Answer is 1, 2, 3