Try to initialize your RadioButton
as below:
correctChoice1= (RadioButton )findViewById(R.id.correct1);
correctChoice1.setOnClickListener(new OnClickListener() {
@Override
public void onClick(View v) {
if(AppSingleton.score <=5)
AppSingleton.score++;
Intent intent = new Intent(MainActivity.this, Page_two.class);
startActivity(intent);
}
});