Let `R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[]` denotes the greatest integer function, prove that `Rf=4^(2n+1)`

If p=(8+3sqrt(7))^n a n df=p-[p],w h e r e[dot] denotes the greatest integer function, then the value of p(1-f) is equal to a. 1 b. 2 c. 2^n d. 2^(2n)

Statement-1: The integeral part of (8+3sqrt(7))^(20) is even. Statement-2: The sum of the last eight coefficients in the expansion of (1+x)^(16) is 2^(15) . Statement-3: if R(5sqrt(5)+11)^(2n+1)=[R]+F , where [R] denotes the greatest integer in R, then RF=2^(2n+1) .

If R = (sqrt(2) + 1)^(2n+1) and f = R - [R] , where [ ] denote the greatest integer function, then [R] equal (a) f+1/f (b) f-1/f (c) 1/f-f (d) None of these

Evaluate: int_0^(2pi)[sinx]dx ,w h e r e[dot] denotes the greatest integer function.

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

Evaluate: int_1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest integer function.

Evaluate:- int_0^(pi)[cot x]dx ,w h e r e[dot] denotes the greatest integer function.

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

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