Wood charcoal is used in gas masks because ........

$A$ large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water,the quantities of water flowing out per second from the two holes are the same. Then the value of $R$ is

If the function $f$ defined on $\left( \frac{\pi }{6}, \frac{\pi }{3} \right)$ by $f(x) = \begin{cases} \frac{\sqrt{2} \cos x - 1}{\cot x - 1}, & x \neq \frac{\pi}{4} \\ k, & x = \frac{\pi}{4} \end{cases}$ is continuous,then $k$ is equal to

The area (in square units) of the region bounded by the curves $x=y^2$ and $x=3-2y^2$ is

Where is the Central Rice Research Institute located?

If the position vectors of $A, B$ and $C$ are respectively $2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ and $3 \hat{i}-4 \hat{j}-4 \hat{k}$, then $\cos ^2 A$ is equal to