The total income of $A$ and $B$ is greater than the total income of $C$ and $D$. The total income of $A$ and $C$ is equal to the total income of $B$ and $D$. Furthermore,the income of $A$ is equal to half the total income of $B$ and $D$. Which of the following statements is $NOT$ true?

There are five different houses,$A$ to $E$,in a row. $A$ is to the right of $B$,and $E$ is to the left of $C$ and right of $A$. $B$ is to the right of $D$. Which of the houses is in the middle?

$A$ is elder to $B$ while $C$ and $D$ are elder to $E$ who lies between $A$ and $C$. If $C$ is elder to $B$,which one of the following statements is necessarily true?

There are six persons $A, B, C, D, E,$ and $F$ in a school. Each of the teachers teaches two subjects: one compulsory subject and the other optional subject. $D's$ optional subject was History,while three others have it as a compulsory subject. $E$ and $F$ have Physics as one of their subjects. $F's$ compulsory subject is Mathematics,which is an optional subject for both $C$ and $E.$ History and English are $A's$ subjects,but in terms of compulsory and optional subjects,they are the reverse of those of $D's.$ Chemistry is an optional subject for only one of them. The only female teacher in the school has English as her compulsory subject. Which of the following has the same compulsory and optional subjects as those of $F$? (Note: The question asks for the person with the same subject distribution as $F$.)

Seven executives $P, Q, R, S, T, U$ and $W$ reach office in a particular sequence. $U$ reaches immediately before $P$ but does not immediately follow $S.$ $R$ is the last one to reach office. $T$ follows immediately after $P$ and is subsequently followed by $W.$
Who ranks fourth in the sequence of reaching office?

Five children were administered psychological tests to know their intellectual levels. In the report,psychologists pointed out that the child $A$ is less intelligent than the child $B$. The child $C$ is less intelligent than the child $D$. The child $B$ is less intelligent than the child $C$ and child $A$ is more intelligent than the child $E$. Which child is the most intelligent?