The number $(101)^{100}-1$ is divisible by

In $chloroethane$,the carbon bearing halogen is bonded to $...$ hydrogen $(s)$. It is called $......$ alkyl halide.

Consider the following statements about manganate and permanganate ions. Identify the correct statements:
$(A)$ The geometry of both manganate and permanganate ions is tetrahedral.
$(B)$ The oxidation states of $Mn$ in manganate and permanganate are $+7$ and $+6$, respectively.
$(C)$ Oxidation of $Mn(II)$ salt by peroxodisulphate gives manganate ion as the final product.
$(D)$ Manganate ion is paramagnetic and permanganate ion is diamagnetic.
$(E)$ Acidified permanganate ion reduces oxalate, nitrite and iodide ions.
Choose the correct answer from the options given below:

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

The chemical entities present in the thermosphere of the atmosphere are:

If $a>0$,then $\int_{-\pi}^\pi \frac{\sin ^2 x}{1+a^x} d x$ is equal to