If $a, b, c, d$ and $p$ are distinct real numbers such that $(a^2 + b^2 + c^2)p^2 - 2p(ab + bc + cd) + (b^2 + c^2 + d^2) \leq 0$,then:

Insert two numbers between $3$ and $81$ so that the resulting sequence is a $G.P.$

If three successive terms of a $G.P.$ with common ratio $r$ $(r > 1)$ are the lengths of the sides of a triangle,and $[r]$ denotes the greatest integer less than or equal to $r$,then $3[r] + [-r]$ is equal to:

If the sum of an infinite geometric series is $\frac{4}{5}$ and its $1^{st}$ term is $\frac{3}{4}$, then its common ratio is

The roots of the equation $x^3-14x^2+56x-64=0$ are in

The sum of the first four terms of a geometric progression $(G.P.)$ is $\frac{65}{12}$ and the sum of their respective reciprocals is $\frac{65}{18}$. If the product of the first three terms of the $G.P.$ is $1$,and the third term is $\alpha$,then $2\alpha$ is ....... .