If `x^2 + 3x + 5` is the greatest common divisor of `(x^3 + ax^2 +bx+1) and (2x^3 +7x^2 + 13x + 5)` then find the value of `[a+b].`[Note :[k] denotes greatest integer less than or equal to k.]

int_(0)^(15/2)[x-1]dx= where [x] denotes the greatest integer less than or equal to x

Solve the equation x^(3)-[x]=3 , where [x] denotes the greatest integer less than or equal to x .

Let f(x)=x-x^(2) and g(x)=ax . If the area bounded by f(x) and g(x) is equal to the area bounded by the curves x=3y-y^(2) and x+y=3 , then find the value of |[a]| : [Note: denotes the greatest integer less than or equal to k.]

Let [x] denotes the greatest integer less than or equal to x and f(x)= [tan^(2)x] .Then

The solutions of the equation 2x-2[x]=1, where [x]= the greatest integer less than or equal to x, are

Find [2.75], if [x] denotes greatest integer not greater than x ?

Let f(x)=(x^(2)-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x), then

If x=(2+sqrt(3))^n ,then the value of x-x^(2)+x[x] where [.] denotes the greatest integer function, is equal to