The set of values of $x$ for which the inequalities $x^2-3x-10 < 0$ and $10x-x^2-16 > 0$ hold simultaneously,is

The solution of $\frac{dy}{dx} = \frac{y^2}{xy - x^2}$ is

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

Which hormone produces an anabolic effect on protein and carbohydrate metabolism?

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane,then the equation of the plane is

$A$ non-conducting body floats in a liquid at $20^{\circ} C$ with $\frac{2}{3}$ of its volume immersed in the liquid. When the liquid temperature is increased to $100^{\circ} C$, $\frac{3}{4}$ of the body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of the container of the liquid):