The least positive integer $n$ such that $1 - \frac{2}{3} - \frac{2}{3^2} - \dots - \frac{2}{3^{n-1}} < \frac{1}{100}$ is:

$A$ 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 $m$)

If $A = 1 + r^z + r^{2z} + r^{3z} + .......\infty$,then the value of $r$ will be

If $S_1, S_2, S_3, \dots, S_m$ are the sums of $n$ terms of $m$ arithmetic progressions $(A.P.)$ whose first terms are $1, 2, 3, \dots, m$ and common differences are $1, 3, 5, \dots, 2m - 1$ respectively,then $S_1 + S_2 + S_3 + \dots + S_m = $

If $x, y, z$ are in $H.P.$,then the value of the expression $\log(x + z) + \log(x - 2y + z)$ is

If $a, b, c$ are the $p^{th}, q^{th}$ and $r^{th}$ terms of a $G.P.$,then $\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q$ is equal to