In a car exhibition,seven cars of seven different companies viz. Cardilac,Ambassador,Fiat,Maruti,Mercedes,Bedford and Fargo were displayed in a row,facing east such that:
$(1)$ Cardilac car was to the immediate right of Fargo.
$(2)$ Fargo was fourth to the right of Fiat.
$(3)$ Maruti car was between Ambassador and Bedford.
$(4)$ Fiat,which was third to the left of Ambassador car,was at one of the ends.
Which of the following groups of cars is to the right of the Ambassador car?

Six persons $A, B, C, D, E$ and $F$ are sitting in two rows,three in each. $E$ is not at the end of any row.
$D$ is second to the left of $F$.
$C$,the neighbour of $E$,is sitting diagonally opposite to $D$.
$B$ is the neighbour of $F$.
Who is facing $B$?

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 of 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 $D$. Chemistry is an optional subject of only one of them. The only female teacher in the school has English as her compulsory subject. Which of the following groups has History as the compulsory subject?

In the Olympic Games,the flags of six nations were flown on the masts in the following way:
The flag of America was to the left of the Indian tricolour and to the right of the flag of France. The flag of Australia was on the right of the Indian flag but was to the left of the flag of Japan,which was to the left of the flag of China.
Find the two flags which are in the centre.

Rohit,Kunal,Ashish,and John are students of a school. Three of them stay far from the school and one near it. Two study in class $IV$,one in class $V$,and one in class $VI$. They study Hindi,Mathematics,Social Science,and Science. One is good at all the four subjects while another is weak in all of these. Rohit stays far from the school and is good at Mathematics only,while Kunal is weak in Mathematics only and stays close to the school. Neither of these two nor Ashish studies in class $VI$. One who is good at all the subjects studies in class $V$. Which two boys are good at Mathematics?

$(A)$ $P, Q, R, S$ and $T$ are sitting in a circle facing the centre.
$(B)$ $R$ is immediate left of $T.$
$(C)$ $P$ is between $S$ and $T.$
To find the answer to the above question,which of the following statements can be dispensed with?