Old fashioned TTL logic (that I used 40 years ago) has a max output low current of 16mA so that each output can drive 10 inputs (a fanout of 10).
Therefore the max input low current is 16mA/10= 1.6mA.
It is preferred to have the input pulled down to at most 0.4V (the max allowed input low is 0.8V) so a pull-down resistor is 0.4V/1.6mA= 250 ohms max.
I never lived nor worked in India or in England so I never called anybody SIR. Nobody ever called me a SIR except Indian kids on these forums. Sometimes in old movies people are called SIR.