When a number is divided by 5, the remainder is 3. What will be the remainder when sum of cube of that number and square of that number is divided by 5 ?

Solution (By Examveda Team)

Let us assume any such number which when divided by 5 leaves remainder as 3.
Let it be 8
So, now
$$\eqalign{ & = \frac{{{{\left( 8 \right)}^2} + {{\left( 8 \right)}^3}}}{5} \cr & = \frac{{64 + 512}}{5} \cr & = \frac{{576}}{5} = 1\,\,\left[ {{\text{Remainder}}} \right] \cr} $$