Number of solutions of the equation 5{x}=x+[x] and x- [x] =`(1)/(2)` (where [.] denotes greatest integer function and {x} denotes fractional part of x ) is

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

The number of solutions of the equation tan^(-1)(4{x})+cot^(-1)(x+[x]))=(pi)/(2) is (where [.] denotes greatest integer function and {.} fractional part of function.

Number of solutions of the equation cos[x]=e^(2x-1),x in [0,2pi] , where[.] denotes the greatest integer function is

The number of solutions of the equation |x - 11+|x-10|=9+[x]( where [.] denotes greatest integer of x ) are

f(x)=1+[cos x]x, in 0<=x<=(x)/(2) (where [.] denotes greatest integer function)

f(x)=1+[cos x]x in 0<=x<=(pi)/(2) (where [.] denotes greatest integer function)

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

Find the number of solution of the equations |cos x |=[x] , (where [.] denotes the greatest integer function ).

The number of values of x such that x,[x] and {x} are in H.P.where [.1 denotes greatest integer function and {.} denotes fractional part