Find the value of `[1/2]+[1/2+1/1000]+ *[1/2+2946/1000]` where [.] denote greatest integer function ?

The sum of [1/2]+[1/2+1/(2000)]+[1/2+2/(2000)]+[1/2+3/(2000)]++[1/2+(1999)/(2000)] where [.] denote the greatest integer function, is equal to: 1000 (b) 999 (c) 1001 (d) none of these

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

[(4)/(5)] + [(4)/(5)+(1)/(1000)] + [(4)/(5)+(2)/(1000)] + ...+[(4)/(5) + (999)/(1000)] = where [.] denotes greatest integer function

The value of int_(-g)^(1)[x[1+cos((pi x)/(2))]+1]dx where [.] denotes greatest integer function is

Domain of cos^(-1)[2x^(2)-3] where [ ] denotes greatest integer function, is

The value of B=int_1^100 [sec^-1x]dx, (where [ . ] denotes greatest integer function), is equal to

The value of I = int_(-1)^(1)[x sin(pix)]dx is (where [.] denotes the greatest integer function)

The value of int_(-pi//2)^(pi//2)[ cot^(-1)x] dx (where ,[.] denotes greatest integer function) is equal to

Find the number of integral values of x in the domain of f(x) = cos^(-1) [2 - 4x^2] . (where [.] denotes greatest integer function)