Answer
The second largest oscillation frequency is the circuit with the $2.0~\mu F$ capacitor 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 maximize the frequency for a given inductance $L$, we should minimize 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 second smallest capacitance is the circuit with the $2.0~\mu F$ capacitor combined with the inductor.
Therefore, the second largest oscillation frequency is the circuit with the $2.0~\mu F$ capacitor combined with the inductor.
