Step 1: Note the claims.
Assertion: the NCTE is a statutory body of the Government of India. Reason: it began on 17 August 1995 under the NCTE Act, 1993.
Step 2: Define a statutory body.
A statutory body is one created by an Act of the legislature, which defines its powers and functions.
Step 3: Verify the Assertion.
The NCTE regulates teacher education and draws its authority from a parliamentary Act, so it is statutory and the Assertion is true.
Step 4: Verify the Reason.
The NCTE Act was passed in 1993 and the council became functional as a statutory body on 17 August 1995, so the Reason is true.
Step 5: Link them.
A body is statutory only because an Act establishes it, so the 1993 Act is precisely why the NCTE is statutory; the Reason explains the Assertion.
Step 6: Choose the label.
Both true and Reason explains Assertion, which is option A.
\[ \boxed{\text{Both [As] and [R] are true, and [R] is the correct explanation of [As].}} \]