Compute $(98)^{5}$.

Let $R = (5\sqrt{5} + 11)^{2n + 1}$ and $f = R - [R]$,where $[.]$ denotes the greatest integer function. The value of $R \cdot f$ is

The expression $[x + (x^3 - 1)^{1/2}]^5 + [x - (x^3 - 1)^{1/2}]^5$ is a polynomial of degree

Evaluate $(\sqrt{3}+\sqrt{2})^{6}-(\sqrt{3}-\sqrt{2})^{6}$ (in $\sqrt{6}$)

Let $x \in \mathbb{R}$ be so small that the powers of $x$ beyond two are insignificant and negligibly small. For such $x$,if $(1-x)^3(2+x)^6$ is approximated by $a+bx+cx^2$,then $a+b+c=$

The coefficient of $x^{48}$ in $(1+x)+2(1+x)^2+3(1+x)^3+ . . . +100(1+x)^{100}$ is equal to: