Amit M Agarwal Solutions for Chapter: Binomial Theorem, Exercise 2: Work Book Exercise 8.2

If $n>1,$ then $(1+x{)}^n-nx-1$ is divisible by

The positive integer just greater than $(1+0.0001{)}^{10000}$ is

If $\left[x\right]$ denotes the greatest integer less than or equal to $x,$ then $\left[(1+0.0001{)}^{10000}\right]$ equals

If $R=(6\sqrt{6}+14{)}^{2n+1}, n\in N$ and $f=R-\left[R\right],$ where $\left[·\right]$ denotes the greatest integer function, then $Rf$ equals

If $R=(\sqrt{2}+1{)}^{2n+1}$ and $f=R-\left[R\right]$, where $\left[·\right]$ denotes the greatest integer function, then $\left[R\right]$ equals

If $(5+2\sqrt{6}{)}^n=I+f,$ where $I\in N, n\in N$ and $0\le f<1,$ then $I$ equals

If $R=(7+4\sqrt{3}{)}^{2n}=1+f,$ where $I\in N$ and $0<f<1,$ then $R\left(1-f\right)$ equals

The digit at unit's place in the number ${17}^{1995}+{11}^{1995}-7^{1995}$ is