How many bacteria are produced in four hours if a bacterium divides once in half an hour?

$A$ flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in the figure. The graph of induced emf in the coil is represented by

If $f: R \rightarrow R$ is defined by $f(x) = x - [x]$,where $[x]$ is the greatest integer not exceeding $x$,then the set of points of discontinuity of $f$ is

Which of the following is a correctly matched pair?

In the sequence of sets $(1,2,3), (4,5,6), (7,8,9,10), \ldots$,the sum of elements in the $50^{th}$ set is

$CH_3MgBr + CO_2$ $\xrightarrow{\text{Dry ether}} Y$ $\xrightarrow{H_3O^{\oplus}} Z$. Identify $Z$ from the following.