Solve `1/[x]+1/([2x])= {x}+1/3`where [.] denotes the greatest integers function and{.} denotes fractional part function.

The sum of solutions of the equation 2[x] + x =6{x} is (where [.] denotes the greatest integer function and {.} denotes fractional part function)

Solve : 4{x}= x+ [x] (where [*] denotes the greatest integer function and {*} denotes the fractional part function.

The function f(x)=[x]+sqrt({x}), where [.] denotes the greatest Integer function and {.} denotes the fractional part function respectively,is discontinuous at

If f(x)=[2x], where [.] denotes the greatest integer function,then

Find x if 4x,5[x],6{x} are sides of a triangle ( triangle where [..] denotes the greatest integers function and {.} denotes fractional part function)

The function f(x)={x} sin (pi[x]) , where [.] denotes the greatest integer function and {.} is the fractional part function, is discontinuous at

Consider the function f(x) = {x+2} [cos 2x] (where [.] denotes greatest integer function & {.} denotes fractional part function.)

The number of values of x such that x, [x] and {x} are in arithmetic progression is equal to (where [.] denotes the greatest integer function and {.} denotes the fractional part function)

Let f(x)=(-1)^([x]) where [.] denotes the greatest integer function),then