The maximum number of students among whom $1001$ pens and $910$ pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils is:

Find the least number which when divided by $2, 3, 4, 5$ and $6$ leaves $1, 2, 3, 4$ and $5$ as remainders,respectively,but when divided by $7$ leaves no remainder.

Find the least number which when divided separately by $15, 20, 36$ and $48$ leaves $3$ as remainder in each case.

Find the greatest number of five digits which when divided by $12, 15, 21, 25$ and $28$ leaves $5, 8, 14, 18$ and $21$ as remainders, respectively.

Three different containers contain different quantities of a mixture of milk and water,measuring $403 \ kg$,$434 \ kg$,and $465 \ kg$. What is the largest measure that can measure all these quantities exactly? (in $kg$)

Let $N$ be the greatest number that will divide $1305, 4665,$ and $6905,$ leaving the same remainder in each case. Then the sum of the digits in $N$ is: