If the period of the function f(x)=sin⁡([n]x), where [n] denotes the greatest integer less than or equal to n, is 2π, then

Sin x is a periodic function with period 2π, therefore sin⁡([n]x) is a periodic function with period 2π[n].But the period of f (x) is 2π (given).∴2π[n]=2π⇒[n]=1⇒[n]=1⇒1≤n<2