Let ω be a non-real cube root of unity. Match each entry of List-I with its value in List-II. List-I (P) The number of complex numbers z satisfying…

(P) Taking moduli, $|z|^5=|z|$, so $z=0$ or $|z|=1$. For $|z|=1$, multiplying by $z$ gives $z^6=|z|^2=1$, which has $6$ roots; with $z=0$ there are $7$, so P→5. (Q) $2^x=x^2$ holds at $x=2$ and $x=4$, and also for one negative $x\approx-0.767$, because $2^x-x^2$ changes sign between $-1$ and $0$; for $x>4$, $2^x$ exceeds $x^2$ forever, so there are exactly $3$ solutions: Q→3. (R) Using $1+\omega+\omega^2=0$: $1-\omega+\omega^2=-2\omega$ and $1+\omega-\omega^2=-2\omega^2$, so the product is $4\omega^3=4$: R→4. (S) The six values $\cos\frac{k\pi}3$ are $1,\frac12,-\frac12,-1,-\frac12,\frac12$ and sum to $0$: S→1. The unmatched item (2) is a distractor. A numerical check of each count and value agrees.