If the three consecutive coefficients in the expansion of $(1 + x)^n$ are $28, 56$ and $70,$ then the value of $n$ is

The coefficients of three consecutive terms in the expansion of $(1+a)^{n}$ are in the ratio $1:7:42$. Find $n$.

If the coefficient of $x^5$ in the expansion of $(ax^2+\frac{1}{bx})^{13}$ is equal to the coefficient of $x^{-5}$ in the expansion of $(ax-\frac{1}{bx^2})^{13}$,then $ab=$

If $n$ is the degree of the polynomial,$\left[ {\frac{1}{{\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8 + \left[ {\frac{1}{{\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8$ and $m$ is the coefficient of $x^{12}$ in it,then the ordered pair $(n, m)$ is equal to

The largest term in the expansion of $(3 + 2x)^{50}$ where $x = \frac{1}{5}$ is

Find the coefficient of $x^{64}$ in the expansion of $P(x) = (x - 1)^2(x - 2)^3(x - 3)^4 \dots (x - 10)^{11}$.