Part (a) — fuming sulfuric acid, if discarded. YES if/when it becomes a waste. Fuming sulfuric acid (oleum) is extremely corrosive (pH far below 2), meeting the corrosivity characteristic outright; it is also a strong oxidizer, relevant to reactivity. As a virgin, in-spec product still in commerce it is a regulated hazardous MATERIAL (shipping/transport rules) rather than a waste, but the instant it is discarded, spilled, or off-specification (unusable for its intended purpose), it becomes a RCRA hazardous waste by the corrosivity characteristic.
Part (b) — spent cleaning solvents. YES. Once used, spent halogenated and non-halogenated solvents are specifically identified as LISTED hazardous wastes under RCRA's F-list (e.g. F001–F005, spent solvents from degreasing/cleaning operations) regardless of whether they still exhibit a characteristic — the listing alone is sufficient, which is why this is a clean "yes" even without running a flash-point or toxicity test on the specific batch.
Part (c) — radioactive tracers after lab use. A MIXED-waste question. The radioactive component itself is regulated separately, under the Atomic Energy Act (via the NRC), not RCRA — source, special nuclear, and by-product material are specifically excluded from the RCRA hazardous-waste definition. However, if the SAME waste also exhibits a RCRA characteristic (e.g. the tracer is carried in an ignitable or toxic organic solvent, as is common in liquid scintillation counting), it is regulated as "mixed waste" under BOTH RCRA (for the chemical hazard) and the AEA/NRC (for the radioactivity) simultaneously — so the answer is "yes, for the chemical component" whenever a hazardous carrier or contaminant is present, independent of the radioactivity.
Part (d) — mercury. YES. Mercury is a RCRA-listed toxic heavy metal; discarded elemental mercury and mercury-containing wastes (e.g. spent thermometers, switches, lamps) are specifically listed (e.g. U151) and/or would exceed the TCLP toxicity threshold for mercury, making it hazardous essentially without exception once discarded.
Part (e) — gasoline-contaminated soil. YES, generally. Gasoline is ignitable (flash point well below 60°C) and contains listed/regulated constituents (benzene, toluene, ethylbenzene, xylenes — BTEX), so soil visibly contaminated with fresh gasoline typically exhibits the ignitability characteristic and/or exceeds toxicity thresholds for BTEX constituents, making the contaminated soil itself a RCRA hazardous waste once excavated. (In practice, many jurisdictions apply a "contained-in" policy: once remediated soil no longer exhibits a hazardous characteristic, e.g. after volatilization/biodegradation has reduced BTEX and raised the flash point, it may be reclassified as non-hazardous for disposal purposes — but AS SPILLED, freshly contaminated soil is hazardous.)
Check: part (c) is presented as a mixed-waste analysis (RCRA excludes source/special-nuclear/by-product material outright; a co-located RCRA characteristic in the carrier solvent is what brings the chemical component back under RCRA) rather than a simple yes/no, since the regulatory answer genuinely depends on the tracer's chemical carrier, which the question does not specify.