The area bounded by the curves $y = x(x - 3)^2$ and $y = x$ is (in sq. units) :

The major product of the following reaction is

$A$ ball moving with velocity $2 \, m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$,then their velocities (in $m/s$) after collision will be

Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R$. At time $t = 0$,the number of $P$ species is $4N_0$ and that of $Q$ is $N_0$. The half-life of $P$ is $1$ minute,while that of $Q$ is $2$ minutes. Initially,there are no nuclei of $R$ present in the sample. When the number of nuclei of $P$ and $Q$ are equal,the number of nuclei of $R$ present in the sample would be:

$A$ long straight wire carrying a current of $30 ~A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} ~T$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 ~cm$ away from the wire is
$\left(\mu_0=4 \pi \times 10^{-7} ~H/m\right)$

Read the following five statements ($a$ to $e$) and select the option with all correct statements:
$(a)$ Mosses and Lichens are the first organisms to colonise a bare rock.
$(b)$ $Selaginella$ is a homosporous pteridophyte.
$(c)$ Coralloid roots in $Cycas$ have $VAM$ mycorrhizae.
$(d)$ Main plant body in bryophytes is gametophytic,whereas in pteridophytes it is sporophytic.
$(e)$ In gymnosperms,male and female gametophytes are present within sporangia located on sporophyte.