If the sum of $n$ terms of an arithmetic progression is $3n^2 + 5n$ and $T_m = 164$,then $m = \dots$

If $\frac{3 + 5 + 7 + \dots \text{ to } n \text{ terms}}{5 + 8 + 11 + \dots \text{ to } 10 \text{ terms}} = 7$,then the value of $n$ is

If the roots of the equation $32x^3 - 48x^2 + 22x - 3 = 0$ are in arithmetic progression,then the square of the common difference of the roots is

$A$ software company sets up $m$ number of computer systems to finish an assignment in $17$ days. If $4$ computer systems crashed on the start of the second day,$4$ more computer systems crashed on the start of the third day and so on,then it took $8$ more days to finish the assignment. The value of $m$ is equal to :

What is the sum of all numbers between $100$ and $300$ that are divisible by $7$?

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an arithmetic sequence are $a$,$b$,and $c$ respectively,then the value of $[a(q - r) + b(r - p) + c(p - q)]$ is: