= Solution
{c}
Write $R=e^r$, $u=1.2$ and $d=0.9$. In a one-step <binomial options pricing model>, absence of <arbitrage> requires $d<R<u$. If $R\leq d$, borrowing to buy the stock gives a nonnegative gain in either state and a positive gain in at least one. If $R\geq u$, shorting the stock and investing the proceeds does the same. Conversely, strict inequalities give the <risk-neutral probability> $q=(R-d)/(u-d)\in(0,1)$, under which the discounted stock is a martingale; this excludes arbitrage at each node. Hence
$$
\boxed{\log0.9<r<\log1.2.}
$$
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