Let `R=(8+3sqrt7)^20` and `[R]`= the greatest integer less than or equal to `R`. then

The greatest integer less than or equal to (sqrt2+1)^6 is

The greatest integer less than or equal to (sqrt2+1)^6 is

If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the greatest integer less than or equal to x, then f'"("sqrt(pi//3)")" is equal to

If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the greatest integer less than or equal to x, then f'"("sqrt(pi//3)")" is equal to

If (6 sqrt6+14)^(2n+1)=R and F=[R] , where [R] denotes the greatest integer less than or equal to R thwn RF=

If the function f: R->R be such that f(x) = x-[x], where [x] denotes the greatest integer less than or equal to x, then f^-1(x) is

For each x in R , let [x]be the greatest integer less than or equal to x. Then lim_(xto1^+) (x([x]+absx)sin[x])/absx is equal to

Let f(x) be defined by f(x) = x- [x], 0!=x in R , where [x] is the greatest integer less than or equal to x then the number of solutions of f(x) +f(1/x) =1

Let f(x) be defined by f(x) = x- [x], 0!=x in R , where [x] is the greatest integer less than or equal to x then the number of solutions of f(x) +f(1/x) =1

The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the greatest integer less than or equal to x , is R (b) [0,+oo] (-oo,0) (d) none of these