For the following questions answer them individually
A pole subtends angles $$30^\circ, 45^\circ, 60^\circ$$ respectively at points A, B and C all lying on a horizontal line through the foot of the pole. Then $$\frac{AB}{BC} =$$
If x - 7 is a factor of the polynomial f(x), then a factor of $$f(2x^2 - 1)$$ among the following is
The sum of seven consecutive even integers is s. Then, in terms of s, the greatest of these integers is
$$\frac{b}{a} = \frac{c}{b} = \frac{d}{c} \Rightarrow (a - c)^2 + (c - b)^2 + (b - d)^2 - (d - a)^2 =$$
The coefficient of $$x^3$$ in the expansion of $$\left(x^2 - \frac{1}{x^3}\right)^9$$ is