In the questions, `[x]a n d{x}` represent the greatest integer function and the fractional part function, respectively. Solve: `[x]^2-5[x]+6=0.`

In the questions, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. If y=3[x]+1=4[x-1]-10 , then find the value of [x+2y]dot

Solve 2[x]=x+{x},where [.] and {} denote the greatest integer function and the fractional part function, respectively.

If f(x) = [x] , 0<= {x} < 0.5 and f(x) = [x]+1 , 0.5<{x}<1 then prove that f (x) = -f(-x) (where[.] and{.} represent the greatest integer function and the fractional part function, respectively).

Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 , h(x)={x}, k(x)=5^((log)_2(x+3)). Then in [0,1], lagranges mean value theorem is not applicable to (a) f (b) g (c) k (d) h (where [.] and {.} represents the greatest integer functions and fractional part functions, respectively).

The greatest integer function f(x)=[x] is -

Solve (x-2)[x]={x}-1, (where [x]a n d{x} denote the greatest integer function less than or equal to x and the fractional part function, respectively).

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

Draw the graph of |y|=[x] , where [.] represents the greatest integer function.

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

Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).