Let $k$ be a non-zero real number. If $f(x) = \begin{cases} \frac{(e^x - 1)^2}{\sin(\frac{x}{k}) \log(1 + \frac{x}{4})} & x \neq 0 \\ 12 & x = 0 \end{cases}$ is a continuous function,then the value of $k$ is:

The major product obtained on treatment of $CH_3CH_2CH(F)CH_3$ with $CH_3O^-/CH_3OH$ is

The random variable $X$ takes the values $1, 2, 3, \ldots, m$. If $P(X=n) = \frac{1}{m}$ for each $n$,then the variance of $X$ is

$A$ small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L$ $(L \gg l)$. The loops are coplanar and their centers coincide. The mutual inductance of the system is proportional to

One turn of insulated wire in the form of a planar square frame with side $l = 0.2\,m$ and resistance $R = 1\,\Omega$ is placed in a uniform magnetic field perpendicular to the plane of the frame. The current passing through the turn when the magnetic field starts to decrease at a constant rate of $0.1\,T/s$ is......$mA$.

The wavelength of a photon is equal to the wavelength of an electron moving with a kinetic energy of $1.5\, eV$. What is the energy of the photon?