$A$ narrow parallel beam of light is incident paraxially on a solid transparent sphere of radius $r$ kept in air. What should be the refractive index if the beam is to be focused at the farther surface of the sphere?

The chemicals and the reaction conditions required for the preparation of ethane are:

Which of the following statement$(s)$ is/are true?
$A.$ An organism represents/occupies a place or position in the system of classification.
$B.$ One specific epithet may be present in different genus representing different species.
$C.$ Human belongs to $Homo$ species.
$D.$ Animals,mammals,and dogs represent the taxa at the same level.

If $x$ and $y$ are acute angles such that $\cos x + \cos y = \frac{3}{2}$ and $\sin x + \sin y = \frac{3}{4}$,then $\sin(x+y)$ is equal to

At any instant,two elements $X_1$ and $X_2$ have the same number of radioactive atoms. If the decay constants of $X_1$ and $X_2$ are $10 \lambda$ and $\lambda$ respectively,then the time when the ratio of their atoms becomes $\frac{1}{e}$ will be:

In the process of transcription in eukaryotes, the $\text{RNA}$ polymerase $\text{II}$ transcribes