If a gas contains only three molecules that move with velocities of $100, 200, 500 \ ms^{-1}$. What is the $rms$ velocity of that gas in $ms^{-1}$?

If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

Two identical parallel plate air capacitors are connected in series to a battery of emf $V$. If one of the capacitors is inserted in a liquid of dielectric constant $K$,then the potential difference of the other capacitor will become:

What is the molar solubility of $Ag_{2}CO_{3}$ $(K_{sp} = 4 \times 10^{-13})$ in $0.1 \ M \ Na_{2}CO_{3}$ solution?

Which one of the following statements is not correct?

Identify $A$ and $B$ in the following reactions: