Step 1: Understand the format.
We have an Assertion (A) and a Reason (R). We must judge if each is true and whether R explains A.
Step 2: Read the Assertion.
A says the right to privacy has been judicially recognised as part of Article 21. This is true. In the Puttaswamy case (2017), the Supreme Court held privacy to be part of the right to life and personal liberty under Article 21.
Step 3: Read the Reason.
R says privacy is expressly written as a separate Fundamental Right in Part III of the Constitution. This is false. Privacy is not written down as its own listed right. It was recognised through court interpretation, not by an express clause.
Step 4: Match the truth values.
So A is true and R is false. We look for the option that says exactly this.
Step 5: Reject the other options.
Any option saying both are true cannot be right because R is false. The option saying A is false but R is true is the opposite of the real position, so it is wrong.
Step 6: State the answer.
A is true, but R is false.
\[ \boxed{\text{(A) is true, but (R) is false.}} \]