The value of the series $x \log _e a + \frac{x^3}{3!} (\log _e a)^3 + \frac{x^5}{5!} (\log _e a)^5 + \dots$ is

The current in the windings of a toroid is $2.0\,A$. There are $400$ turns and the mean circumferential length is $40\,cm$. If the magnetic field inside the toroid is $1.0\,T$,the relative permeability is near to:

Which of the following is a synthetic auxin?

The ratio of the de-Broglie wavelength of an $\alpha$-particle to that of a proton,when both are subjected to the same magnetic field such that the radii of their paths are equal,assuming the magnetic field induction vector $\overrightarrow{B}$ is perpendicular to the velocity vectors of both particles,is:

Suggest a possible explanation why the seeds in a pea pod are arranged in a row,whereas those in tomato are scattered in the juicy pulp.

Calculate the $pOH$ of a solution at $25\,^{\circ}C$ that contains $1 \times 10^{-10} \, M$ of hydronium ions,i.e.,$H_3O^{+}$.