Step 1: Understand why a direct pull test is avoided.
Gripping a brittle rock specimen firmly enough to pull it apart in pure tension is practically very hard, the grips tend to crush the rock locally before a clean tensile failure can occur, so engineers look for a smarter, indirect way.
Step 2: See how compressing a disc sideways can create tension.
If you take a thin circular disc of rock and squeeze it diametrically between two flat platens, the loading actually generates a fairly uniform tensile stress acting across the vertical diameter inside the disc, even though the applied load itself is compressive.
Step 3: Connect the failure mode to the tensile strength.
As the compressive load increases, the disc eventually splits cleanly along that loaded diameter, and from the load at which this split occurs, along with the disc dimensions, we can back calculate the tensile strength, this clever indirect approach is known as the Brazilian test.
Step 4: Rule out the other options.
The confined and unconfined compressive strength tests measure compressive behaviour, and the Protodyaknov index is an impact based drillability indicator, neither of them targets tensile strength.
\[ \boxed{\text{Brazilian test}} \]