Q.A rheostat is used (A) to bring on a known change of resistance in the circuit to alter the current (B) to continuously change the resistance in any arbitrary manner and thereby alter the current (C) to make and break the circuit at any instant (D) neither to alter the resistance nor the current

[!TLDR] A rheostat's whole purpose is CONTINUOUS, arbitrary adjustment of resistance (and hence current), not a single fixed jump. [!ANSWER] (B) to continuously change the resistance in any arbitrary manner and thereby alter the current

As section 11.8.1 describes, a rheostat is an ADJUSTABLE resistor with a sliding contact that can be moved anywhere along its resistive element, allowing its effective resistance to be varied smoothly and continuously over its whole range -- used for dimming lights, controlling motor speed, or volume control. Option (A) describes only a single, predetermined, discrete change (not the rheostat's actual continuous-adjustment capability). Option (C) describes a switch, not a rheostat (a rheostat does not make/break the circuit; it always keeps the circuit closed while varying resistance). Option (D) is simply false, since altering resistance is precisely a rheostat's function. [!ANSWER] (B) to continuously change the resistance in any arbitrary manner and thereby alter the current

Recall the defining feature of a rheostat from section 11.8.1: a sliding-contact resistor built for smooth, continuous, arbitrary adjustment of resistance (and hence current), not for a fixed jump or for opening/closing the circuit.

Confusing a rheostat (continuously variable resistance) with a switch (which only makes or breaks the circuit) or with a fixed resistor swapped for another fixed value.