$A$ man standing on a road has to hold his umbrella at $30^{\circ}$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 ~km/h$. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is:

Five masses,each of $2 \, kg$,are placed on a horizontal circular disc that can rotate about a vertical axis passing through its centre. All the masses are equidistant from the axis at a distance of $10 \, cm$. The moment of inertia of the whole system (in $g \cdot cm^2$) is (Assume the disc has negligible mass).

The variation of radiant energy emitted by the sun, the filament of a tungsten lamp, and a welding arc as a function of its wavelength is shown in the figure. Which of the following options is the correct match?

Which of the following factors does $NOT$ favor the formation of an electrovalent (ionic) bond?

$A$ pulley of radius $2\, m$ is rotated about its axis by a force $F = (20t - 5t^2)\, N$ (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10\, kg\, m^2$,the number of rotations made by the pulley before its direction of motion is reversed,is

$A$ bryophyte,which harbours a nitrogen-fixing blue-green alga in its thallus,is