1.It is none of your business what other people think about you.Believe yourself.
是名词性从句.what 不能引导定语从句,定语从句用来修饰一个名词.
2.选 B that
这句话含名词性从句(宾语从句),补充完整后的句子是
Having checked that the doors were closed,and that all the lights were off,the boy opened the door to his bedroom.
男孩查看门关好了,所有的灯也关了,就开了他卧室的门