The largest number of 4 digits exactly divisible by 13 is

1. 9,996

2. 9,997

3. 9,995

4. 9,984

The largest 4-digit number = 9,999.

To find the largest 4-digit number exactly divisible by 13, we divide 9,999 by 13 and subtract the remainder to get the largest multiple.

$\begin{array}{l} \phantom{x^2}{769} \ 13\overline{\smash{\big)}9999} \ \phantom{x}\phantom{)}\underline{-91} \ \phantom{{x^2 } +} 89 \ \phantom{{x))} }\underline{-78} \ \phantom{{x^2 } + 2} 119 \ \phantom{{x} +)}\underline{-117} \ \phantom{{x^2 + 3)}} 2 \ \end{array}$

The remainder when 9,999 is divided by 13 is 2.

Therefore, 9,999 − 2 = 9,997.

Hence, option 2 is the correct option.