[QUE/QM-08002]

State if the combinations of $j,m$ values, in the table given below, are allowed or not. Complete the table by writing ALLOWED/NOT ALLOWED in the second column and specifying a reason in support of your answer selecting a reason from the list, $(R1)-(R5)$, given below. In case you do not find a valid or appropriate reason listed below, feel free to select option (R6) and specify your reason.\footnote{This question requires knowledge of angular momentum eigenvalues.}\\ {\bf{List of Possible Reasons:}}

1. [(R1)]All values of $jm$ are allowed.
2. [(R2)]Not allowed because $m$ is not an integer
3. [(R3)]Allowed because all vales of $m$ in the range $-j$ to $+j$ are allowed
4. [(R4)]Not allowed because $j,m$ must be an integers
5. [(R5)]Not allowed because both $j,m$ must be integers, or half integers.
6. [(R6)]Any other reason, please specify for each case separately