The number of terms in the expansion of $(x^{2}+y^{2})^{25}-(x^{2}-y^{2})^{25}$ after simplification is

If in the expansion of $(1+x)^p(1-x)^q$,the coefficients of $x$ and $x^2$ are $1$ and $-2$ respectively,then $p^2+q^2$ is equal to :

In the expansion of the expression $1 + (1 + x) + (1 + x)^2 + \dots + (1 + x)^n$,the coefficient of $x^k$ $(0 \le k \le n)$ is

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 $f(x) = x^n$,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

Which is larger: $(1.01)^{1000000}$ or $10,000$?