If a hydrogen electrode is dipped in a solution of $pH = 3$ and $pH = 6$ and a salt bridge is connected,then the $emf$ of the resulting cell is ........... $V$.

The number of tetrahedral voids present in $0.5 \text{ mole}$ of an $hcp$ crystal structure is:

$100$ cells each of e.m.f. $5 \ V$ and internal resistance $1 \ \Omega$ are to be arranged so as to produce maximum current in a $25 \ \Omega$ resistance. Each row is to contain equal number of cells. The number of rows should be

Two identical blocks $A$ and $B$,each of mass $m$,are placed on a smooth horizontal surface and are connected by a light spring of length $L$ and force constant $k$. $A$ third identical block $C$ of mass $m$ moves along the line joining $A$ and $B$ with velocity $v$ and collides with block $A$. The maximum compression in the spring is:

If the plane $7x + 11y + 13z = 3003$ meets the coordinate axes at $A, B, C$,then the centroid of the $\triangle ABC$ is

If the pairs of straight lines $x^2-2 p x y-y^2=0$ and $x^2-2 q x y-y^2=0$ are such that each pair bisects the angle between the other pair,then