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
$90$
$110$
$55$
$108$
The common difference of an $A.P.$ whose first term is unity and whose second, tenth and thirty fourth terms are in $G.P.$, is
The minimum value of the sum of real numbers $a^{-5}, a^{-4}, 3 a^{-3}, 1, a^8$ and $a^{10}$ with $a>0$ is
Let $x, y, z$ be three non-negative integers such that $x+y+z=10$. The maximum possible value of $x y z+x y+y z+z x$ is
If $A.M.$ of two terms is $9$ and $H.M.$ is $36$, then $G.M.$ will be
Let the range of the function
$f(x)=\frac{1}{2+\sin 3 x+\cos 3 x}, x \in \operatorname{IR} \text { be }[a, b] .$ If $\alpha$ and $\beta$ are respectively the $A.M.$ and the $G.M.$ of a and $b$, then $\frac{\alpha}{\beta}$ is equal to :