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Question

Nobody knows why people walk or talk in their sleep 
a) know b) knows c)knew d) is knowing 
2.Where have been you last night at the time of the burglary 
a) were d) have been 
3.John a new job was been offered 
a)have offered b) has been offered c) has offering d) was been offered 
4. The boy may to go for a walk after he does all lessons 
 a) may b) was allowed c) will be allowed d)might 
5) The proposal is reported to have been approved by the committee 
a) to be approved b) to have been approved c) to approve 
6) William the Conqueror is famous for conquering 
a) having been conquered b) conquering c) having conquered 
7) I hate him to laugh at 
a) to laugh at b) to be laughed c) laughed at

Ник · Accepted Answer

Nobody knows why people walk or talk in their sleep - Правильно, то есть b) knows. 
2.Where have been you last night at the time of the burglary - Неправильно, нужно a) were. 
3. b) has been offered (Конечно, если это Джону предложили новую работу, а не он сам кому-то её предложил. ) 
4. The boy may to go for a walk after he does all lessons - Неправильно, нужно c) will be allowed. 
5) The proposal is reported to have been approved by the committee - Правильно, то есть b) to have been approved. 
6) William the Conqueror is famous for conquering - Скорее правильно, то есть b) conquering - если этим conquering предложение и ограничивается, то есть если имеется в виду "...известен своими завоеваниями (вообще, в целом) ", а не "...завоеванием чего-то определённого". 
7) I hate him to laugh at - Неправильно, то есть b) to be laughed - и, по-моему, здесь не хватает at, то есть нужно to be laughed at.