If $f(x)=x e^{x(1-x)}$,then $f(x)$ is

Choose the correct option from the following:
$I$. Dehydration and dormancy of mature seed are crucial for seed storage.
$II$. Seed of $Lupinus \; arcticus$ is the oldest one which germinated after $2,000 \; years$.
$III$. Orchid seed is one of the largest seeds in the plant kingdom.
$IV$. Seeds of parasitic plants $Orobanche$ and $Striga$ are tiny seeds.

If $\log_e \left( \frac{a + b}{2} \right) = \frac{1}{2}(\log_e a + \log_e b)$,then the relation between $a$ and $b$ is:

Magnesium wire is heated in the atmosphere of $CO_2$ because

$A$ circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\,J$. What is its translational kinetic energy in $J$?

$A$ whistle revolves in a circle with an angular speed of $20\, rad/s$ using a string of length $50\, cm$. If the frequency of sound from the whistle is $385\, Hz$,then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? (Speed of sound is $340\, m/s$)