Let $A B C D$ be a quadrilateral such that there exists a point $E$ inside the quadrilateral satisfying $A E=B E=C E=D E$. Suppose $\angle D A B, \angle A B C, \angle B C D$ is an arithmetic progression. Then the median of the set $\{\angle D A B, \angle A B C, \angle B C D\}$ is
$\frac{\pi}{6}$
$\frac{\pi}{4}$
$\frac{\pi}{3}$
$\frac{\pi}{2}$
The sequence $\frac{5}{{\sqrt 7 }}$, $\frac{6}{{\sqrt 7 }}$, $\sqrt 7 $, ....... is
If $x,y,z$ are in $A.P.$ and ${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$ and ${\tan ^{ - 1}}z$ are also in other $A.P.$ then . . .
If the sum of $n$ terms of an $A.P.$ is $\left(p n+q n^{2}\right),$ where $p$ and $q$ are constants, find the common difference.
If $\log _{3} 2, \log _{3}\left(2^{x}-5\right), \log _{3}\left(2^{x}-\frac{7}{2}\right)$ are in an arithmetic progression, then the value of $x$ is equal to $.....$
If $a_1 , a_2, a_3, . . . . , a_n, ....$ are in $A.P.$ such that $a_4 - a_7 + a_{10}\, = m$, then the sum of first $13$ terms of this $A.P.$, is .............. $\mathrm{m}$