Q.Kirchhoff's junction rule is a reflection of

Concept: Conservation of Charge (Kirchhoff's Junction Rule)

At any junction, charge cannot pile up in steady state, so the current flowing in must equal the current flowing out: $\sum I_{in} = \sum I_{out}$.

This single fact can be stated two ways: (b) it follows from conservation of charge, the underlying physical law, and (d) it is equivalent to saying no charge accumulates at the junction, which is what that law means at a single point in the circuit. Both are correct descriptions of the same rule. …

Why the rule exists

A junction is just a point where several wires meet. In steady-state current flow, the charge $Q$ sitting at that point cannot be changing with time — if it were, the junction would be continuously gaining or losing charge forever, which never happens once currents settle down. So

Since current is charge per unit time, $\dfrac{dQ}{dt} = \sum I_{in} - \sum I_{out}$. Setting this to zero gives exactly Kirchhoff's junction rule:

Evaluating each option

• (a) Wrong. There is no general law that the current density vector $\vec{J}$ is conserved through a junction — different branches can have different cross-sectional areas and different $\vec J$ magnitudes/directions; it is the current (the integral of $\vec J$ over area, i.e. charge/time), not $\vec J$ itself, that balances.
• (b) Correct. This is the underlying physical law: electric charge can neither be created nor destroyed, so it cannot pile up at a junction — hence $\sum I_{in}=\sum I_{out}$. …

Method: Identifying which physical law a stated circuit rule reflects

This method applies to any question that gives you a circuit rule (junction rule, loop rule, a balance condition, etc.) in words and asks which underlying physical principle(s) it is a restatement of.

Steps

Step 1: Translate the rule into a conservation equation

Start from the rate of change of the conserved quantity at the point/element in question. For a junction, the relevant quantity is the charge $Q$ sitting at that point. In steady state nothing at a junction can be building up or draining away indefinitely, so

Since current is charge per unit time, $\dfrac{dQ}{dt} = \sum I_{in} - \sum I_{out}$, and setting this to zero directly reproduces the stated rule: $\sum I_{in} = \sum I_{out}$.

Step 2: Recognise that a single physical fact can be phrased in more than one equivalent way

Once you have the governing equation from Step 1, check whether the options are just different verbal descriptions of the same equation rather than genuinely distinct claims. "Charge is conserved" (the general law) and "no charge accumulates at the junction" (its consequence at $dQ/dt = 0$) are two phrasings of one fact — both should be marked correct together, not treated as competing choices.

Step 3: Test each remaining option against what the equation actually says …