Acidified potassium permanganate solution is decolourised by

In a $\triangle ABC$,if $3a = b + c$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

The solution set of $(5+4 \cos \theta)(2 \cos \theta+1)=0$ in the interval $[0, 2 \pi]$ is:

Which of the following has the largest population in a food chain?

$A$ wall has two layers $A$ and $B$, each made of a different material. Both the layers have the same thickness. The thermal conductivity of the material of $A$ is twice that of $B$. Under thermal equilibrium, the temperature difference across the wall is $36^{\circ}C$. The temperature difference across the layer $A$ is ......... $^{\circ}C$

The product of the lengths of the perpendiculars from any point on the hyperbola $x^2-y^2=8$ to its asymptotes is