$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

The value of $\tan \left[\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right]$ is

Diborane reacts with ammonia under different conditions to give a variety of products. Which one among the following is not formed in these reactions?

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ (where $k > 0$). Then the terminal speed of the ball is:

In $Pteridophytes$,meiosis occurs during which of the following processes?

Let $\vec{V} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{W} = \hat{i} + 3\hat{k}$. If $\vec{U}$ is a unit vector,then the maximum value of the scalar triple product $[\vec{U} \, \vec{V} \, \vec{W}]$ is: