If $x\in (0,\frac{\pi}{4})$ then the expression $ \frac{cos x}{sin^2 x(cos x-sin x)}$ can not take the value

If the arithmetic mean and geometric mean of the $p ^{\text {th }}$ and $q ^{\text {th }}$ terms of the sequence $-16,8,-4,2, \ldots$ satisfy the equation $4 x^{2}-9 x+5=0,$ then $p+q$ is equal to ..... .

The reciprocal of the mean of the reciprocals of $n$ observations is their

If the $A.M.$ and $H.M.$ of two numbers is $27$ and $12$ respectively, then $G.M.$ of the two numbers will be

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 $A.M.$ and $G.M.$ of roots of a quadratic equations are $8$ and $5$ respectively, then the quadratic equation will be