Step 1: Examine Assertion (A) about drying HCl.
Concentrated $H_2SO_4$ is a powerful dehydrating agent, so passing HCl gas through it removes moisture and dries the gas.
Step 2: Check that the acids do not react.
Concentrated $H_2SO_4$ does not significantly react with HCl gas under ordinary drying conditions, so it is a safe drying agent here. Hence Assertion (A) is correct.
Step 3: Examine Reason (R) about white fumes.
HCl gas reacts with ammonia gas to form solid ammonium chloride, \[ NH_3(g) + HCl(g) \rightarrow NH_4Cl(s) \] which appears as dense white fumes. So Reason (R) is also correct as a statement.
Step 4: Test whether R explains A.
The white fumes reaction is just a test to detect HCl gas. It says nothing about why concentrated $H_2SO_4$ dries the gas.
Step 5: Draw the link.
Drying depends on $H_2SO_4$ absorbing water, a completely separate idea from the $NH_3$ test. So R cannot be the explanation of A.
Step 6: State the verdict.
Both A and R are correct, but R is not the correct explanation of A, which is option 2.
\[ \boxed{\text{Both (A) and (R) are correct and (R) is not the correct explanation of (A)}} \]