If ${\log _3}2,\;{\log _3}({2^x} - 5)$ and ${\log _3}\left( {{2^x} - \frac{7}{2}} \right)$ are in $A.P.$, then $x$ is equal to
$1,\;\frac{1}{2}$
$1,\;\frac{1}{3}$
$1,\;\frac{3}{2}$
None of these
Let ${\left( {1 - 2x + 3{x^2}} \right)^{10x}} = {a_0} + {a_1}x + {a_2}{x^2} + .....+{a_n}{x^n},{a_n} \ne 0$, then the arithmetic mean of $a_0,a_1,a_2,...a_n$ is
If $p$ times the ${p^{th}}$ term of an $A.P.$ is equal to $q$ times the ${q^{th}}$ term of an $A.P.$, then ${(p + q)^{th}}$ term is
The number of terms of the $A.P. 3,7,11,15...$ to be taken so that the sum is $406$ is
If the sum and product of the first three term in an $A.P$. are $33$ and $1155$, respectively, then a value of its $11^{th}$ tern is
If $^n{C_4},{\,^n}{C_5},$ and ${\,^n}{C_6},$ are in $A.P.,$ then $n$ can be