$A$ compound of mercury used in cosmetics,in Ayurvedic and Yunani medicines and known as Vermilion is

If $\int\limits_0^{\frac{\pi }{3}} {\frac{{\tan \theta }}{{\sqrt {2k \sec \theta } }}} \,d\theta = 1 - \frac{1}{\sqrt{2}}, (k > 0),$ then the value of $k$ is

The de-Broglie wavelength of a particle accelerated with $150 \ V$ potential is $10^{-10} \ m$. If it is accelerated by $600 \ V$ potential difference,its wavelength will be ........... $\mathring{A}$.

$300 \, g$ of water at $25^{\circ} C$ is added to $100 \, g$ of ice at $0^{\circ} C$. The final temperature of the mixture is ........... $^{\circ} C$.

Which of the following statements is incorrect for physical adsorption?

Let $C$ be the centroid of the triangle with vertices $(3, -1)$,$(1, 3)$,and $(2, 4)$. Let $P$ be the point of intersection of the lines $x + 3y - 1 = 0$ and $3x - y + 1 = 0$. Then the line passing through the points $C$ and $P$ also passes through the point