$1.$ There is a group of six persons $A, B, C, D, E$ and $F$ from a family. They are Professor,Manager,Lawyer,Jeweller,Doctor,and Engineer.
$2.$ The Doctor is the grandfather of $F$,who is a Professor.
$3.$ The Manager $D$ is married to $A$.
$4.$ $C$,the Jeweller,is married to the Lawyer.
$5.$ $B$ is the mother of $F$ and $E$.
$6.$ There are two married couples in the family.
What is the profession of $A$?

$(i)$ There are six friends $A, B, C, D, E$ and $F$.
$(ii)$ Each one is proficient in one of the games,namely Badminton,Volleyball,Cricket,Hockey,Tennis and Polo.
$(iii)$ Each owns a different coloured car,namely yellow,green,black,white,blue and red.
$(iv)$ $C$ does not play either Tennis or Hockey and owns neither blue nor yellow coloured car.
$(v)$ $D$ plays Polo and owns a yellow coloured car.
$(vi)$ $E$ owns a white car and plays Badminton.
$(vii)$ $B$ does not play Tennis,he owns a red coloured car.
$(viii)$ $A$ plays Cricket and owns a black car.
Which of the following combinations of colour of car and game played is not correct?

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?

Madhu and Shobha are good in Dramatics and Computer Science. Anjali and Madhu are good in Computer Science and Physics. Anjali,Poonam and Nisha are good in Physics and History. Nisha and Anjali are good in Physics and Mathematics. Poonam and Shobha are good in History and Dramatics. Who is good in History,Physics,Computer Science and Mathematics?

$300$ persons are participating in a meeting,out of which $120$ are foreigners and the rest are Indians. Out of the Indians,there are $110$ men who are not judges,$160$ are men or judges,and $35$ are women judges. There are no foreign judges. How many Indian women attended the meeting?

$(i)$ $P, Q, R, S, T$ and $U$ are six students pursuing their Master's degree in six different subjects $-$ English,History,Philosophy,Physics,Statistics and Mathematics.
$(ii)$ Two of them stay in a hostel,two stay as paying guests $(PG)$ and the remaining two stay at their home.
$(iii)$ $R$ does not stay as a $PG$ and studies Philosophy.
$(iv)$ The students studying Statistics and History do not stay as $PG$.
$(v)$ $T$ studies Mathematics and $S$ studies Physics.
$(vi)$ $U$ and $S$ stay in a hostel. $T$ stays as a $PG$ and $Q$ stays at home.
Which of the following combinations of subject and place of stay is not correct?