The true solution set of the inequality,$\sqrt{5x - 6 - x^2} + \frac{\pi}{2} \int_{0}^{x} dz > x \int_{0}^{\pi} \sin^2 x \, dx$ is :

If $z=\log (\tan x+\tan y)$,then $(\sin 2x) \frac{\partial z}{\partial x}+(\sin 2y) \frac{\partial z}{\partial y}$ is equal to

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by:

Hot water cools from $60\,^{\circ}C$ to $50\,^{\circ}C$ in the first $10\,min$ and to $42\,^{\circ}C$ in the next $10\,min$. The temperature of the surrounding is ......... $^{\circ}C$.

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $\frac{-2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

Which of the following is the most stable?