The formula of azurite is

If $\frac{x^2}{a} + \frac{2xy}{h} + \frac{y^2}{b} = 0$ represents a pair of straight lines such that the slope of one of the lines is twice the other,then $\frac{ab}{h^2} =$

The solution of $x dx + y dy = x^2 y dy - x y^2 dx$ is

For the reaction $C_{(s)} + CO_{2_{(g)}} \rightleftharpoons 2CO_{(g)}$,the partial pressures of $CO_2$ and $CO$ are $2.0 \ atm$ and $4.0 \ atm$ respectively at equilibrium. The $K_p$ for the reaction is

The average kinetic energy of a gas molecule at $27\,^{\circ}C$ is $6.21 \times 10^{-21}\,J$. Its average kinetic energy at $227\,^{\circ}C$ will be

If the equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines,then the square of the distance of their point of intersection from the origin is