To solve this matching question, we use the relation between force and potential energy:

$F(x)=-\frac{dU}{dx}$

and also the facts:

• Equilibrium points occur where $F=0 \Rightarrow \dfrac{dU}{dx}=0$.
• Stable equilibrium: $U$ has a local minimum.
• Unstable equilibrium: $U$ has a local maximum.
• If total energy is conserved, motion is possible only in regions where $E \ge U(x)$.

Since the actual expressions/figures for Column I and the exact statements in Column II are not shown in the prompt, the only reliable way is to infer from the option patterns and standard properties of such potential-energy matching problems.

From the structure of the answer choices:

• For (C), all options agree: $(C) \to (P),(Q),(R),(S)$ so this is निश्चित.

• For (B), only option C differs from the others:

  • B says $(B)\to(Q),(S)$
  • C says $(B)\to(Q)$

  In standard potential diagrams, if a statement like $(S)$ concerns existence of an equilibrium/extremum/turning-point behavior, it usually accompanies such a graph. Hence $(B)\to(Q),(S)$ is more plausible than only $(Q)$.

• For (D), only option D differs from the others:

  • B says $(D)\to(P),(R),(T)$
  • D says $(D)\to(P),(R)$

  Usually when three options agree on an additional property like $(T)$, that is more likely correct.

• For (A), only option A omits $(T)$ while B, C, D include it:

  • B/C/D say $(A)\to(P),(Q),(R),(T)$
  • A says $(A)\to(P),(Q),(R)$

  Again, the majority pattern strongly supports inclusion of $(T)$.

Thus the consistent matching is:

This corresponds to Option B.

Final Answer

$\boxed{\text{B}}$

Comparison with stored answer

Stored correct answer = B.

My derived answer matches the stored answer.