Let $2^{\text {nd }}, 8^{\text {th }}$ and $44^{\text {th }}$, terms of a non-constant $A.P.$ be respectively the $1^{\text {st }}, 2^{\text {nd }}$ and $3^{\text {rd }}$ terms of $G.P.$ If the first term of $A.P.$ is $1$ then the sum of first $20$ terms is equal to-
$980$
$960$
$960$
$970$
If $a, b$ are positive real numbers such that the lines $a x+9 y=5$ and $4 x+b y=3$ are parallel, then the least possible value of $a +b$ is
${2^{\sin \theta }} + {2^{\cos \theta }}$ is greater than
If $p,q,r$ are in $G.P$ and ${\tan ^{ - 1}}p$, ${\tan ^{ - 1}}q,{\tan ^{ - 1}}r$ are in $A.P.$ then $p, q, r$ are satisfies the relation
If $a_1, a_2...,a_n$ an are positive real numbers whose product is a fixed number $c$ , then the minimum value of $a_1 + a_2 +.... + a_{n - 1} + 2a_n$ is
The sum of three numbers in $G.P.$ is $56.$ If we subtract $1,7,21$ from these numbers in that order, we obtain an arithmetic progression. Find the numbers.