$\frac{1}{e^{3x}}(e^x + e^{5x}) = a_0 + a_1x + a_2x^2 + \ldots$
$\Rightarrow 2a_1 + 2^3a_3 + 2^5a_5 + \ldots$ is equal to

The equation of the normal to the curve $y=x \log x$,which is parallel to the line $2x-2y+3=0$,is

Which one of the following gives a sooty flame on combustion?

The $pK_a$ of a weak acid is $4.8$. What should be the ratio of $\frac{[\text{acid}]}{[\text{salt}]}$,if a buffer of $pH=5.8$ is required?

The intensity of the electric field required to keep a water drop of radius $10^{-5} \, cm$ just suspended in air when charged with one electron is approximately:

The square of the difference of the slopes of the lines represented by the equation $x^2(\sec^2 \theta - \sin^2 \theta) - 2xy \tan \theta + y^2 \sin^2 \theta = 0$ is: