[" If "[x^(2)-2x+a]=0" has no solution then (I.] is "],[" greatest integer functions) "AA x in R]

If x^(2)+x+1-|[x]|=0, then (where [.] is greatest integer function) -

If [x^(2)]+x=a has solution (s), a in N ,then a may be; (where [.] denotes greatest integer function)

Show that the equation , sin x =[1+ sin x]+[1- cos x] has no solution for x in R . ( where [.] represents greatest integers functions ).

Show that the equation , sin x =[1+ sin x]+[1- cos x] has no solution for x in R . ( where [.] represents greatest integers functions ).

Show that the equation , sin x =[1+ sin x]+[1- cos x] has no solution for x in R . ( where [.] represents greatest integers functions ).

If [log_(2)((x)/([x]))]>=0, where [.] denote the greatest integer function,then

Number of solutions of sin x=[x] where [.] denotes the greatest integer function is

If a in R and the equation (a-2) (x-[x])^(2) + 2(x-[x]) + a^(2) = 0 (where [x] denotes the greatest integer function) has no integral solution and has exactly one solution in (2, 3), then a lies in the interval