Identify what is being asked

We need the test that gives a positive result for a phenolic group.

Check each option

A: Tollen's test

• Tollen's reagent is used mainly to detect aldehydes.
• It gives a silver mirror with aldehydes.
• Phenols do not generally give Tollen's test.

Therefore, A is incorrect.

B: Phthalein dye test

• Phenols react with phthalic anhydride in presence of concentrated $\mathrm{H_2SO_4}$ to form phthalein dyes.
• This is a characteristic test for phenolic compounds.

Therefore, B is correct.

C: Carbylamine test

• Carbylamine test is given by primary amines.
• It produces foul-smelling isocyanides.
• Phenols do not respond to this test.

Therefore, C is incorrect.

D: Lucas test

• Lucas test distinguishes primary, secondary, and tertiary alcohols.
• It is not a test for phenols.

Therefore, D is incorrect.

Conclusion

The phenolic group is identified by a positive phthalein dye test.

Hence, the correct option is: $\boxed{\text{B}}$

Comparison with stored correct answer

• Derived answer: B
• Stored correct answer: B

Both match.