If `[x]` stands for the greatest integer function, then `[1/2+1/1000]+[1/2+2/1000]+...+[1/2+999/1000]`=

If [.] stands for the greatest integer function, then int_(1)^(2) [3x]dx is equal to

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

The number of roots of x^(2)-2=[sin x], where [.] stands for the greatest integer function is 0(b)1(c)2(d)3 .

If [x] denotes the greatest integer less than or equal to* then [(1+0.0001)^(1000)] equals

The value of sum_(n=1)^1000 int_(n-1)^n e^(x-[x])dx , where [x] is the greatest integer function, is (A) (e^1000-1)/1000 (B) (e-1)/1000 (C) (e^1000-1)/(e-1) (D) 1000(e-1)

If x^(2)+x+1-|[x]|=0, then (where [.] is 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

If [.] denotes the greatest integer function then the domain of the real-valued function log[x+(1)/(2)]|x^(2)-x-2| is