How many times is be strong and courageous mentioned in the bible?

Answer 1

Twice.

In the King James version the word - courageous - appears five times.

1. Jos 1:7 Only be thou strong and very courageous, that thou mayest observe to do according to all the law, which Moses my servant commanded thee: turn not from it to the right hand or to the left, that thou mayest prosper withersoever thou goest.
2. Jos 23:6 Be ye therefore very courageous to keep and to do all that is written in the book of the law of Moses, that ye turn not aside therefrom to the right hand or to the left;
3. 2 Sam 13:28 Now Absalom had commanded his servants, saying, Mark ye now when Amnon's heart is merry with wine, and when I say unto you, Smite Amnon; then kill him, fear not: have not I commanded you? be courageous, and be valiant.
4. 2 Chr 32:7 Be strong and courageous, be not afraid nor dismayed for the king of Assyria, nor for all the multitude that is with him: for there be more with us than with him:
5. Amo 2:16 And he that is courageous among the mighty shall flee away naked in that day, saith the LORD.

As can be seen, the first and fourth of those use the phrase "strong and courageous".