Manipur Board Solutions for Chapter: Number System, Exercise 2: EXERCISE 1.2

Show that for any natural number $n$, the digit in units place of $3^n$ cannot be even.

Find any five consecutive composite numbers.

Find any four consecutive odd composite numbers

Find the least number which when divided by $24, 36, 60$ will leave in each case the same remainder $7$

Find the least number which when divided by $7, 8,$ and $12$ leaves the same remainder $5$ in each case.

Find the least multiple of $13$ which when divided by $5, 8$ and $12$ leaves same remainder $2$ in each case.

By what prime numbers may $319$ be divided so that remainder is $4$?

By what numbers may $24$ be divided so that the remainder is $3$.