Correct option is C
Introduction
Radioactive minerals contain unstable isotopes of uranium or thorium that emit ionising radiation as they decay.
Several rare-earth and phosphate minerals carry these elements within their crystal lattice, making them naturally radioactive.
Information Booster
The intended answer is — Allanite, Monazite, and Autunite.
A. Allanite is a complex calcium–rare-earth aluminium–iron silicate that typically contains radioactive thorium and uranium, and some allanite transforms into less crystalline metamict allanite during alteration as thorium and uranium leach out. Its radioactivity is a recognised field indicator.
B. Monazite is a rare-earth phosphate that is a classic radioactive/thorium-bearing mineral.
It contains 5–12% (typically about 7%) thorium, and is a major source of thorium from beach-sand (monazite placer) deposits, highly relevant to India's coastal thorium reserves.
E. Autunite is a uranium mineral — a radioactive mineral whose uranium in its chemical formula Ca(UO₂)₂(PO₄)₂·10–12H₂O provides its radioactivity, and it is one of the most popular uranium minerals among collectors.
Additional knowledge
C. Sillimanite — Correctly excluded. Sillimanite is an aluminosilicate (Al₂SiO₅) refractory mineral containing no uranium or thorium; it is entirely non-radioactive and is used industrially in high-temperature ceramics.
· D. Xenotime — Here is the important caveat: xenotime is actually a radioactive mineral. It is an yttrium phosphate with traces of uranium and thorium, appears in the standard list of radioactive minerals, and is mined alongside monazite.