(I) is true. In a two-way layout with $n_{ij}$ observations in cell $(i,j)$ , the row and column effects are orthogonal — their estimates are uncorrelated and the sums of squares add up cleanly — exactly when the cell frequencies are proportional:

$n_{ij}=\frac{n_{i\cdot}\,n_{\cdot j}}{n_{\cdot\cdot}} \qquad\text{for all }i,j .$

Equal cell numbers are the familiar special case. When proportionality fails, the design is non-orthogonal, the classification effects are confounded with one another, and one must distinguish sequential from partial sums of squares.

(II) is not a statement at all — as printed it is an incomplete sentence, breaking off after "the maximum number of mutually orthogonal contrasts among them". With no assertion to evaluate, it cannot be true.

The intended completion is almost certainly "… is $n-1$ ", which would be correct: a contrast $\sum a_iy_i$ requires $\sum a_i=0$ , so the contrast vectors live in the $(n-1)$ -dimensional subspace orthogonal to $\mathbf 1$ , and at most $n-1$ of them can be mutually orthogonal. But the item as printed supports only (I).