If x - 11, then the value of x⁵ - 12x⁴ + 12x³ - 12x² + 12x - 1 is?

Solution (By Examveda Team)

$${x^5} - 12{x^4} + 12{x^3} - 12{x^2} + 12x - 1$$
$$ = {x^5} - 11{x^4} - {x^4} + 11{x^3} + {x^3} - 11{x^2} - $$       $$\,{x^2} + $$ $$11x \,+\, $$ $$x - $$ $$1$$
$${\text{Put }}x = 11$$
$$ = {11^5} - {11.11^4} - {11^4} + {11.11^3} + {11^3} - $$       $${11.11^2} -\, $$ $$\,{11^2} \,+\, $$ $$11.11 +\, $$ $$11 - $$ $$1$$
$$\eqalign{ & = 11 - 1 \cr & = 10 \cr} $$