If the $5^{th}$ term of a geometric progression is $2$,what is the product of its first $9$ terms?

If the first term of a $G.P.$ $a_1, a_2, a_3, \dots$ is unity such that $4a_2 + 5a_3$ is least,then the common ratio of the $G.P.$ is

The quotient when $1+x^2+x^4+x^6+\ldots+x^{34}$ is divided by $1+x+x^2+x^3+\ldots+x^{17}$ is

If the arithmetic mean and geometric mean of the $p^{\text{th}}$ and $q^{\text{th}}$ terms of the sequence $-16, 8, -4, 2, \ldots$ satisfy the equation $4x^{2}-9x+5=0$,then $p+q$ is equal to ..... .

The numbers $(\sqrt{2} + 1), 1, (\sqrt{2} - 1)$ will be in

If $a, b, c, d$ are in a geometric progression,then $(a^3 + b^3)^{-1}, (b^3 + c^3)^{-1}, (c^3 + d^3)^{-1}$ are in which progression?