With a resistance of ' $X$ ' in the left gap and resistance of $9 \Omega$ in the right gap of a meter bridge, the balance point is obtained at 40 cm from the left end. In what way and to which resistance $3 \Omega$ resistance be connected to obtain the balance at 50 cm from the left end?

The excess of pressure, due to surface tension, on a spherical liquid drop of radius ' $R$ ' is proportional to

$\mathbf{P}$ and $\mathbf{Q}$ are two non-zero vectors inclined to each other at an angle ' $\theta$ '. ' $p$ ' and ' $q$ ' are unit vectors along $\mathbf{P}$ and $\mathbf{Q}$ respectively. The component of $\mathbf{Q}$ in the direction of $\mathbf{Q}$ will be