If $a, b, c$ are in $A.P.$,then $(a + 2b - c)(2b + c - a)(c + a - b)$ equals

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

If $p, q, r$ are in $A.P.$ and are positive,the roots of the quadratic equation $px^2 + qx + r = 0$ are all real for

Sum the series $51 + 50 + 49 + \ldots + 21$.

Let $a_1, a_2, ..., a_{10}$ be a $G.P.$ If $\frac{a_3}{a_1} = 25$,then $\frac{a_9}{a_5}$ is equal to:

$A$ ball rolling up an incline covers $36\, m$ during the first second,$32\, m$ during the second,$28\, m$ during the next and so on. How much distance will it travel during the $8^{th}$ second? (in $m$)