The number of solutions of `4{x}=x+ [x]` where `[.]` denotes G.I.F and `{.}` represents fractional part function is equal to

The number of solutions of 4{x}=x+[x] is p and the number of solutions of {x+1}+2x=4[x+1]-6 is q, where [.] denotes G.I.F and {.} denotes fractional part. Then

The number of solution of the equation sgn({x})=|1-x| is/are (where {*} represent fractional part function and sgn represent signum function)

The number of solution of the equation sgn({x})=|1-x| is/are (where {*} represent fractional part function and sgn represent signum function)

If f(x)={x}+{2x} and g(x)=[x]. The number of solutions of f(x)=g(x), where {.} and [x] are respectively the fractional part and greatest functions, is

If f(x)={x}+{2x} and g(x)=[x]. The number of solutions of f(x)=g(x), where {.} and [x] are respectively the fractional part and greatest functions, is

The total number of solutions of [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions,respectively,is equal to: 2 (b) 4 (c) 6 (d) none of these

The total number of solution of sin {x}= cos {x} (where {.} denotes the fractional part) in [0, 2pi] is equal to

If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C, where f ((pi)/(4))=1, then the number of solution of the equation (f(x))/(g (x))={x} in [0,2pi] is/are: (where {.} represents fractional part function)

If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C, where f ((pi)/(4))=1, then the number of solution of the equation (f(x))/(g (x))={x} in [0,2pi] is/are: (where {.} represents fractional part function)