The sum of roots of the equation `cos^(-1)(cosx)=[x],[dot]` denotes the greatest integer function, is (a) `2pi+3` (b) `pi+3` (c) `pi-3` (d) 2`pi-3`

The period of the function f(x)=[6x+7]+cospix-6x , where [dot] denotes the greatest integer function is: (a)3 (b) 2 pi (c) 2 (d) none of these

Evaluate: int_(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the greatest integer function

The value of int_0^(2pi)[2sinx]dx ,w h e r e[dot] represents the greatest integral function, is (a) (-5pi)/3 (b) -pi (c) (5pi)/3 (d) -2pi

The range of sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2] , where [.] denotes the greatest integer function, is (a) {pi/2,pi} (b) {pi} (c) {pi/2} (d) none of these

If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

If [ ] denotes the greatest integer function, lim_(x to(pi)/2)(5 sin [cos x])/([cos x]+2) is

The number of solutions of [sinx+cosx]=3+[-sinx]+[-cosx](w h e r e[] denotes the greatest integer function), x in [0,2pi] , is 0 (b) 4 (c) infinite (d) 1

if f(x) = tan(pi[(2x-3pi)^3])/(1+[2x-3pi]^2) ([.] denotes the greatest integer function), then

If [x]=[pi] , where [.] denotes greatest integer function, then (a) x in (3,4] (b) x in [3,4) (c) x=3 (d) None of these

The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where [.] denotes the greatest integer function), x in [0, 2pi] , is