In the expansion of $(1 + x)^5$,the sum of the coefficients of the terms is

Expand the expression $(1-2x)^{5}$.

If the coefficients of $x^2$ and $x^3$ are both zero in the expansion of the expression $(1 + ax + bx^2)(1 - 3x)^{15}$ in powers of $x$,then the ordered pair $(a, b)$ is equal to

If $\frac{2 x^3+3 x^2+3 x+5}{(x^2+1)(x^2+2)}$ is expanded in terms of the powers of $x$,then the coefficient of $x^5$ is

The expression $\frac{1}{{\sqrt {4x + 1} }}\left[ {{{\left[ {\frac{{1 + \sqrt {4x + 1} }}{2}} \right]}^7} - {{\left[ {\frac{{1 - \sqrt {4x + 1} }}{2}} \right]}^7}} \right]$ is a polynomial in $x$ of degree

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