Match the counting statements in List-I with the numbers in List-II. List-I (P) Number of real solutions of |x^2-4|=x+2 (Q) Number of ordered pairs…

(P) $x^2-4=x+2$ gives $x=-2,3$; $x^2-4=-(x+2)$ gives $x=-2,1$; the distinct solutions are $-2,1,3$: three (2). (Q) $(m-6)(n-6)=36$ with both factors positive (negative factors would give $m<6$ or $n<6$ and are impossible since $\frac1m<\frac16$ is required): $\tau(36)=9$ pairs (3). (R) Multiples of $7$ with digit sum $10$: $154,217,280,343,406,532,721,910$: eight (4). (S) Solutions need $|x|\le4\pi$. For $x>0$: one crossing in $(0,\pi)$, and two in $(2\pi,3\pi)$ where the hump of height $1$ exceeds the line value at most $\frac{3}{4}$; none beyond. That gives $3$ positive, $3$ negative and $x=0$: seven (1). So P→2, Q→3, R→4, S→1.