Which is the most serious ongoing challenge for modern pakistan? entrenched communist government ethnic and religious conflict ongoing war against china an ineffective military

Entrenched communist government - this is false. Pakistan has a communist party, but this is not in the goverment. Pakistan in led by the Pakistan Muslim League.
   

ethnic and religious conflict - this is the correct option, Pakistan is predominantly Muslim, and in fact in was created as a country for the Muslims (who were before discriminated against in India). This led to a religious conflict, in which all the minorities, and especially Hindus and Christians are prosecuted( by individuals, much less by the government). Additionally, there are many ethnicities in Pakistan, and there is also a conflict between those.
   
ongoing war against China - this is false. Pakistan generally has good relations with China. They had a small border dispute, but it's settled now. an 

ineffective military - well, this is true, but is this the biggest challenge? if you have generally peace in the country, the military isn't really needed that much. That's why the second option is the best.