______ method is used to map logical addresses of variable length onto…

Concept

A memory-management scheme is defined by the SIZE of the logical unit it translates into a physical address. A scheme that divides the logical address space into FIXED-size blocks cannot natively represent a unit of arbitrary length -- it must round the unit up to a whole number of blocks. A scheme built around segments of VARIABLE size, where each segment carries its own base address and limit (length), can map a logical unit of any length directly onto physical memory. Mapping logical addresses of variable length onto physical memory is exactly this second kind of scheme -- segmentation.

Application to this question

Checking each option against this idea: only a scheme whose address-mapping unit can itself be of arbitrary, varying length qualifies. Segmentation splits the logical address space into segments -- one per function, array, or stack -- and each segment's table entry stores exactly that segment's own base and limit, so a segment of any length maps directly to physical memory. That is precisely the variable-length mapping the question describes, so Segmentation is the correct method.

Why the other options don't fit

• Paging: divides both logical and physical memory into FIXED-size pages and frames. Every logical address is forced into whole pages regardless of how large or small the actual data unit is, so paging cannot natively express a segment of a specific, variable length -- it needs padding, causing internal fragmentation.

• Overlays: a run-time technique for fitting a program larger than available physical memory by swapping mutually exclusive code/data sections in and out. It is not an address-translation scheme at all, so it does not map logical addresses to physical memory the way segmentation does.

• More than one of the above / None of the above: exactly one of the listed techniques is built around variable-length logical units, so neither "more than one" nor "none" fits.

Cross-check

Paging does translate logical addresses to physical addresses too, so it can look like a fit at first glance. But the question specifically asks about VARIABLE-length mapping, and paging's page size is fixed by the operating system, not variable per unit. Segmentation is the scheme whose mapping unit is variable-length by definition -- that is the distinguishing feature the question is testing, not the general idea of address translation.

Answer

Segmentation is the method that maps logical addresses of variable length onto physical memory.