If $y=3x$ is a tangent to a circle with centre $(1,1)$,then the other tangent drawn through $(0,0)$ to the circle is

Chlorination of toluene in the presence of light and heat followed by treatment with aqueous $NaOH$ yields:

On the interval $[0, 1]$,the function $f(x) = x^{25}(1-x)^{75}$ takes its maximum value at the point

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of earth to a height equal to the radius of the earth $R$,is

Xylem tissue is composed of

Let $\overline{a}=\hat{i}+\hat{j}+\hat{k}$,$\overline{b}=\hat{i}-\hat{j}+\hat{k}$ and $\overline{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. $A$ vector $\overline{v}$ in the plane of $\overline{a}$ and $\overline{b}$,whose projection on $\overline{c}$ is $\frac{1}{\sqrt{3}}$,is given by