How many terms are there in an $A.P.$ whose first and fifth terms are $-14$ and $2,$ respectively,and the sum of terms is $40$?

$A$ body falls $16\, m$ in the first second of its motion,$48\, m$ in the second,$80\, m$ in the third,$112\, m$ in the fourth and so on. How far does it fall during the $11^{th}$ second of its motion? (in $m$)

If the sum of an infinite $G.P.$ is $9$ and the sum of the first two terms is $5$,then the common ratio is

If $x, y, z$ are in $G.P.$ and $a^x = b^y = c^z$,then

If $\alpha, \beta$ are the roots of the equation $x^2 - 3x + a = 0$ and $\gamma, \delta$ are the roots of the equation $x^2 - 12x + b = 0$,and $\alpha, \beta, \gamma, \delta$ form an increasing $G.P.$,then $(a, b) = $

Given that $n$ $A$.$M$.'s are inserted between two sets of numbers $a, 2b$ and $2a, b$,where $a, b \in R$. Suppose further that the $m^{th}$ mean between these sets of numbers is the same,then the ratio $a:b$ equals