If the number of $5$-element subsets of the set $A = \{a_1, a_2, \ldots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

$X$ being a higher category is the assemblage of families which exhibit a few $Y$ characters. The $Z$ characters are less in number as compared to different genera included in a family. Identify $X$,$Y$,and $Z$.

In the following combinations of logic gates,the outputs $A, B$ and $C$ are respectively

Who discovered $TMV$ (Tobacco Mosaic Virus)?

An inductance $L$ having a resistance $R$ is connected to an alternating source of angular frequency $\omega$. The Quality factor $Q$ of the inductance is

Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity $v$. If the wire $AB$ is replaced by a semicircular wire of the same chord length,the magnitude of the induced current will