Answer
The smallest oscillation frequency is the circuit with the capacitors in parallel combined with the inductor.
Work Step by Step
$\omega = \frac{1}{\sqrt{LC}}$
We can write an expression for the frequency:
$f = \frac{\omega}{2\pi} = \frac{1}{2\pi~\sqrt{LC}}$
To minimize the frequency for a given inductance $L$, we should maximize the capacitance $C$
We can find the capacitance for the four possible combinations:
Combination 1: the capacitors in parallel combined with the inductor
$C_{eq} = 2.0~\mu F+5.0~\mu F = 7.0~\mu F$
Combination 2: the $5.0~\mu F$ capacitor combined with the inductor
$C = 5.0~\mu F$
Combination 3: the $2.0~\mu F$ capacitor combined with the inductor
$C = 2.0~\mu F$
Combination 4: the capacitors in series combined with the inductor
$\frac{1}{C_{eq}} = \frac{1}{2.0~\mu F}+\frac{1}{5.0~\mu F}$
$\frac{1}{C_{eq}} = \frac{5.0}{10~\mu F}+\frac{2.0}{10~\mu F}$
$C_{eq} = 1.4~\mu F$
The largest capacitance is the circuit with the capacitors in parallel combined with the inductor.
Therefore, the smallest oscillation frequency is the circuit with the capacitors in parallel combined with the inductor.
