If the $9^{th}$ term of an $A.P.$ is zero,then the ratio of its $29^{th}$ term to its $19^{th}$ term is:

Let the terms of an arithmetic progression be $a_1, a_2, a_3, \dots$. If $\frac{a_1 + a_2 + \dots + a_p}{a_1 + a_2 + \dots + a_q} = \frac{p^2}{q^2}$,where $p \neq q$,then $\frac{a_6}{a_{21}} = \dots$

If $S_n$ denotes the sum of $n$ terms of an arithmetic progression,then the value of $(S_{2n} - S_n)$ is equal to

The sum of all two-digit numbers which,when divided by $4$,yield unity as a remainder is:

The solution of the equation $(x + 1) + (x + 4) + (x + 7) + \dots + (x + 28) = 155$ is

If $S_k$ denotes the sum of the first $k$ terms of an arithmetic progression whose first term and common difference are $a$ and $d$ respectively,then $S_{kn}/S_n$ is independent of $n$ if