Binomial Theorem · Mathematics · VITEEE

Last three digits in $$(9)^{50}$$ be

If $$x^n=a_0+a_1(1+x)+a_2(1+x)^2+\ldots \ldots \ldots+ a_n(1+x)^n=b_0+b_1(1-x)+b_2(1-x)^2+\ldots . .+ b_n(1-x)^n$$, then for $$n=201,\left(a_{101}, b_{101}\right)$$ is equal to

If the 2nd, 3rd and 4th terms in the expansion of $$(a+b)^n$$ be $$240,720$$ and 1080 respectively, then the value of $$(n, b, a)$$ is

The coefficient of the term independent of $$x$$ in the expansion $$\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}$$ is

Which of the following is the correct principle of Mathematical induction?