Let $S = \{4, 6, 9\}$ and $T = \{9, 10, 11, \ldots, 1000\}$. If $A = \{a_{1} + a_{2} + \ldots + a_{k} : k \in N, a_{1}, a_{2}, \ldots, a_{k} \in S\}$,then the sum of all the elements in the set $T - A$ is equal to:

In a class of $55$ students,the number of students studying different subjects are $23$ in Mathematics,$24$ in Physics,$19$ in Chemistry,$12$ in Mathematics and Physics,$9$ in Mathematics and Chemistry,$7$ in Physics and Chemistry,and $4$ in all the three subjects. The total number of students who have taken exactly one subject is

In a class of $30$ pupils,$12$ take needle work,$16$ take physics,and $18$ take history. If all the $30$ students take at least one subject and no one takes all three,then the number of pupils taking exactly $2$ subjects is:

In a school,there are $21$ students in the cricket team,$26$ in the hockey team,and $29$ in the football team. Among these,$14$ play both hockey and cricket,$15$ play both hockey and football,and $12$ play both football and cricket. If $8$ students play all three games,find the total number of students in the three athletic teams.

In a class of $60$ students,$25$ students play cricket and $20$ students play tennis,and $10$ students play both the games. The number of students who play neither is:

In a certain test,$a_i$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, 3, \dots, k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is: