Which of the following has the highest solubility product?

In the Compton scattering process,the incident $X$-radiation is scattered at an angle of $60^{\circ}$. The wavelength of the scattered radiation is $0.22 \ \mathring{A}$. The wavelength of the incident $X$-radiation in $\mathring{A}$ units is:

Select the correct option on the basis of the following sentences regarding a gland's function:
$(I)$ Hormones increase alertness.
$(II)$ Hormones increase the heart beat.
$(III)$ Stimulate the breakdown of glycogen.
$(IV)$ Stimulate the breakdown of lipids and proteins.

When a vibrating tuning fork is placed on a sound box of a sonometer, $8$ beats per second are heard when the length of the sonometer wire is kept at $101 \, cm$ or $100 \, cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $ \, Hz$)

$A$ pressure $P-$ absolute temperature $T$ diagram was obtained when a given mass of gas was heated. During the heating process from state $1$ to state $2$,the volume:

Evaluate $\int_{-2}^1 f(x) dx$,where $f(x)= \begin{cases} 1-2x, & x \leq 0 \\ 1+2x, & x > 0 \end{cases}$