If $(1 + ax)^n = 1 + 8x + 24x^2 + ....,$ then the value of $a$ and $n$ is

Using the binomial theorem, the value of $(0.999)^3$ correct to $3$ decimal places 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

Let $n \geq 5$ be an integer. If $9^{n}-8n-1=64\alpha$ and $6^{n}-5n-1=25\beta$,then $\alpha-\beta$ is equal to

Expand $\left(x^{2}+\frac{3}{x}\right)^{4}, x \neq 0$

Let $[x]$ denote the greatest integer less than or equal to $x$. If for $n \in N$,$(1-x+x^3)^n = \sum_{j=0}^{3n} a_j x^j$,then $\sum_{j=0}^{[\frac{3n}{2}]} a_{2j} + 4 \sum_{j=0}^{[\frac{3n-1}{2}]} a_{2j+1}$ is equal to