Changes in $GnRH$ pulse frequency in females is controlled by circulating levels of

For a crystal,the angle of diffraction $(2 \theta)$ is $90^{\circ}$ and the second order line has a $d$ value of $2.28 \ \mathring{A}$. The wavelength (in $\mathring{A}$) of $X$-rays used for Bragg's diffraction is

Which of the following is not an example of a natural polymer?

$A$ coil of area $80\, cm^2$ and $50\, turns$ is rotating with $2000$ revolutions per minute about an axis perpendicular to a magnetic field of $0.05\, T$. The maximum value of the $emf$ developed in it is

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:

$A$ 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 $^{\circ}C$?