The centre of mass of a system of particles does not depend on:

From the top of a hill $h$ metres high,the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

$100 \ g$ of water is heated from $30^\circ C$ to $50^\circ C$. Ignoring the slight expansion of the water,the change in its internal energy is ...... $kJ$ (specific heat of water is $4184 \ J/kg/K$).

If $10000\, V$ is applied across an $X$-ray tube, what will be the ratio of the de-Broglie wavelength of the incident electrons to the shortest wavelength of the $X$-rays produced? (Given: $\frac{e}{m}$ for an electron is $1.8 \times 10^{11}\, C\, kg^{-1}$)

The values of $a$ and $b$,so that the function $f(x) = \begin{cases} x + a \sqrt{2} \sin x, & 0 \le x \le \frac{\pi}{4} \\ 2x \cot x + b, & \frac{\pi}{4} < x \le \frac{\pi}{2} \\ a \cos 2x - b \sin x, & \frac{\pi}{2} < x \le \pi \end{cases}$ is continuous for $0 \le x \le \pi$,are respectively:

Vegetative propagation in $Pistia$ occurs by: