In the datasheet for a MCU, it is mentioned that TM "Test Mode" pin require an external pull down device.
But there is no details: If I will put pull down resistor, what value should I choose then ?
The exact value may not be critical. Typical ballpark values range from 1k to 100k.
With a 1k resistor, lots of current flows through so it is considered "strong" or more immune to noise. This is at the expense of efficiency.
With a 100k resistor, little current flows through so it is considered "weak" or more susceptible to noise. In this case efficiency is improved.
If the device is used in a noisy environment you would typically favor a lower value pull down but if you have a low power battery operated device you would favor a higher value pull down resistor.
10k is a very commonly used value since its easily available and balances both of these concerns.