If one root is square of the other root of the equation $${x^2} + px + q = 0$$, then the realation between $$p$$ and $$q$$ is

For all $$'x',{x^2} + 2ax + 10 - 3a > 0,$$ then the interval in which '$$a$$' lies is

If $${}^{n - 1}{C_r} = \left( {{k^2} - 3} \right)\,{}^n{C_{r + 1,}}$$ then $$k \in $$

An infinite G.P. has first term '$$x$$' and sum '$$5$$', then $$x$$ belongs to