Let $a, b, c$ and $d$ be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^5 b^3 c^2 d$ is $3750 \beta$,then the value of $\beta$ is

If the four angles of a quadrilateral are in an arithmetic progression and their common difference is $10^{\circ}$,what are the measures of the angles of the quadrilateral?

The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is

Suppose that the number of terms in an $A.P.$ is $2k$,where $k \in N$. If the sum of all odd-positioned terms of the $A.P.$ is $40$,the sum of all even-positioned terms is $55$,and the last term of the $A.P.$ exceeds the first term by $27$,then $k$ is equal to:

If the sum of $n$ terms of an arithmetic progression is given by $Pn + Qn^2$,where $P$ and $Q$ are constants,what is the common difference?

$A$ man deposited $Rs. 10000$ in a bank at the rate of $5\%$ simple interest annually. Find the amount in the $15^{\text{th}}$ year since he deposited the amount and also calculate the total amount after $20$ years.