If $\frac{x^3}{(2x-1)(x+2)(x-3)} = A + \frac{B}{2x-1} + \frac{C}{x+2} + \frac{D}{x-3}$,then $A$ is equal to

$A$ centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers $140^{\circ}F$. What is the fall in temperature as registered by the centigrade thermometer in $^{\circ}C$?

An oxide of an element is a gas and dissolves in water to give an acidic solution. The element belongs to

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials with refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses,then the focal length of the combination is:

At $298 \ K$,the molar conductivities at infinite dilution $(\Lambda_m^{\circ})$ of $NH_4Cl$,$KOH$,and $KCl$ are $152.8$,$272.6$,and $149.8 \ S \ cm^2 \ mol^{-1}$ respectively. The $\Lambda_m^{\circ}$ of $NH_4OH$ in $S \ cm^2 \ mol^{-1}$ and $\%$ dissociation of $0.01 \ M \ NH_4OH$ with $\Lambda_m = 25.1 \ S \ cm^2 \ mol^{-1}$ at the same temperature are:

At a certain temperature and at infinite dilution,the equivalent conductances of sodium benzoate,hydrochloric acid,and sodium chloride are $240$,$349$,and $229 \ \Omega^{-1} \ cm^2 \ \text{equiv}^{-1}$ respectively. The equivalent conductance of benzoic acid in $\Omega^{-1} \ cm^2 \ \text{equiv}^{-1}$ at the same conditions is: