= Solution
\b[All the listed modes are Raman active; only $A_1$ and $E$ are infrared active.] For the <C4v molecular point group>, with vertical planes through the outer atoms:
|| Symmetry
|| Number of modes of this symmetry
|| Infrared
|| Raman
| $A_1$
| 2
| \b[Parallel], $z$
| Yes: $x^2+y^2,z^2$
| $B_1$
| 2
| No
| Yes: $x^2-y^2$
| $B_2$
| 1
| No
| Yes: $xy$
| $E$
| 2, each doubly degenerate
| \b[Perpendicular], $(x,y)$
| Yes: $(xz,yz)$
There is no inversion centre, so <infrared and Raman mutual exclusion> does not apply.
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