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

int_(0)^(pi)[cos x] dx, [ ] denotes the greatest integer function , is equal to

Number of solutions of the equation cos[x]=e^(2x-1),x in [0,2pi] , where[.] denotes the greatest integer function is

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

The value of int_(1)^(10pi)([sec^(-1)x]) dx (where ,[.] denotes the greatest integer function ) is equal to

The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greatest integer function, is discontinuous

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

If [sin x]+[sqrt(2) cos x]=-3 , x in [0,2pi] , (where ,[.] denotes the greatest integer function ), then

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

The number of points where f(x) = [sin x + cosx] (where [.] denotes the greatest integer function) x in (0,2pi) is not continuous is a. 3 b. 4 c. 5 d. 6