Odisha Board Solutions for Chapter: Relation and Function, Exercise 1: Exercise- 1(a)

Find the least positive integer $r$ such that $-375\in {\left[r\right]}_{11}$

Find the least positive integer $r$ such that $-12\in {\left[r\right]}_{13}$

Find the least non negative integer $r$ such that $7\times 13\times 23\times 413=r\left(\mathrm{mod}11\right)$

Find the least non negative integer $r$ such that $6\times 18\times 27\times (-225)\equiv \mathrm{r}\left(\mathrm{mod}8\right)$

Find the least non negative integer $r$ such that $1237\left(\mathrm{mod}4\right)+985\left(\mathrm{mod}4\right)\equiv r\left(\mathrm{mod}4\right)$

Find the least non negative integer $r$ such that $1936\times 8789\equiv r\left(\mathrm{mod}4\right)$

Find the least positive integer $x$ such that $276x+128\equiv 4\left(\mathrm{mod}7\right)$

Find three positive integers $x_i, i=1,2,3$ satisfying $3x\equiv 2\left(mod7\right)$