If `(4+sqrt(15))^n=I+f,w h r en` is an odd natural number, `I` is an integer and `0

What is the sum of first n odd natural numbers ?

The product of first n odd natural numbers equals:

The sum of first n odd natural numbers is always an odd number.

If (2+sqrt(3))^n=I+f, where I and n are positive integers and 0

If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a rational number other than positive integers

If f(x)=^nsqrtx^m ,n in N , is an even function, then m is (a)even integer (b) odd integer any integer (d) f(x)-e v e n i s not pos s i b l e

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)

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 composite function f_1(f_2(f_3((f_n(x))))n timesis an decreasing function and if r of f_i ' s are decreasing function while rest are increasing, then the maximum value of r(n-r) is (n^2-1)/4 , when n is an even number (n^2)/4, when n is an odd number (n^2-1)/4, when n is an odd number (n^2)/4, when n is an even number