Graph Theory And State Equations Practice Questions

Different trees (P) are shown below Different cut-sets (Q) are shown below:

It is forming a closed loop. So it can't be a tree.

Applying KVL, $\sin t=i(t) \times 2+L \frac{d i(t)}{d t}+\frac{1}{c} \int i(t) d t$ $\sin t=2 i(t)+2 \frac{d i(t)}{d t}+\int i(t) d t$ Differentiating with respect to t $\cos (t)=\frac{2 d i(t)}{d t}+\frac{2 d^{2} i(t)}{d t^{2}}+i(t)$