The approximate value of $(1.0002)^{3000}$ is

$\binom{n}{0} + 2\binom{n}{1} + 2^2\binom{n}{2} + \dots + 2^n\binom{n}{n}$ is equal to

Using the Binomial Theorem,evaluate $(99)^{5}$.

If $f(x) = x^n$,then the value of $f(1) - \frac{f'(1)}{1!} + \frac{f''(1)}{2!} - \frac{f'''(1)}{3!} + ...... + \frac{(-1)^n f^n(1)}{n!}$ is

If the sum of the coefficients in the expansion of $(1 - 3x + 10x^2)^n$ is $a$ and if the sum of the coefficients in the expansion of $(1 + x^2)^n$ is $b$,then:

When $|x| < 2$, the coefficient of $x^2$ in the power series expansion of $\frac{x}{(x-2)(x-3)}$ is