For $|x| < \frac{1}{5}$,the coefficient of $x^3$ in the expansion of $\frac{1}{(1-5 x)(1-4 x)}$ is

The refluxing of $(CH_3)_2NCOCH_3$ with acid gives:

In the visible region,the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega, \omega'$ and $d, d'$ respectively. The condition for getting deviation without dispersion when the two prisms are combined is

If $x > 0$ and $x^y = e^{x-y}$,then $\frac{dy}{dx}$ is equal to

Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact and coaxial. The power of the combination is

The equation of the plane passing through $(1, 1, 1)$ and $(1, -1, -1)$ and perpendicular to $2x - y + z + 5 = 0$ is: