If [.] denotes greatest integer function and `x in (0,20),` then the number of points of discontinuities of `f(x)=[2x+[x]]` is 19 (b) 20 (c) 39 (d) 40

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

If [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)]

If function y=f(x) has only two points of discontinuity say x_1,x_2, where x_1,x_2<0, then the number of points of discontinuity of y=f(-|x+1|) is (a) 0 (b) 2 (c) 6 (d) 4

If f(x)=[4x]+{3x} where [.] denotes GIF and {.} denotes FPF then for x in [0,5] number of points of discontinuity of f(x) are

Let f(x)=[x^3 - 3] , where [.] is the greatest integer function, then the number of points in the interval (1,2) where function is discontinuous is (A) 4 (B) 5 (C) 6 (D) 7

If f(x)=x+{-x}+[x] , where [x] and {x} denotes greatest integer function and fractional part function respectively, then find the number of points at which f(x) is both discontinuous and non-differentiable in [-2,2] .

If f(x)=([x])/(|x|),x ne 0 where [.] denotes the greatest integer function, then f'(1) is

Let f(x)={8^(1/x),x<0a[x],a in R-{0},xgeq0, (where [.] denotes the greatest integer function). Then (a) f(x) is Continuous only at a finite number of points (b)Discontinuous at a finite number of points. (c)Discontinuous at an infinite number of points. (d)Discontinuous at x=0

Draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

Statement 1: Minimum number of points of discontinuity of the function f(x)=(g(x)[2x-1]AAx in (-3,-1) , where [.] denotes the greatest integer function and g(x)=a x^3+x^2+1 is zero. Statement 2: f(x) can be continuous at a point of discontinuity, say x=c_1 of [2x-1] if g(c_1)=0.