The number of terms of the $A.P. 3, 7, 11, 15, ...$ to be taken so that the sum is $406$ is

If the roots of the equation $6x^3-11x^2+6x-1=0$ are in harmonic progression,then the roots of $x^3-6x^2+11x-6=0$ will be in

Consider two sets $A$ and $B$,each containing three numbers in $A.P.$ Let the sum and the product of the elements of $A$ be $36$ and $p$ respectively,and the sum and the product of the elements of $B$ be $36$ and $q$ respectively. Let $d$ and $D$ be the common differences of the $A.P.s$ in $A$ and $B$ respectively such that $D = d + 3$ and $d > 0$. If $\frac{p + q}{p - q} = \frac{19}{5}$,then $p - q$ is equal to:

In an $A.P.$,the sixth term is $a_6 = 2$. If the product $a_1 a_4 a_5$ is the greatest,then the common difference of the $A.P.$ is equal to

Which of the following sequences is an arithmetic sequence?

The sum of the first four terms of an $A.P.$ is $56$. The sum of the last four terms is $112$. If its first term is $11$,the number of terms is