The ratio of angular speeds of the minute hand and the hour hand of a watch is:

$A$ solid sphere of radius $r$ made of a soft material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. $A$ massless piston of area $a$ floats on the surface of the liquid,covering the entire cross-section of the cylindrical container. When a mass $m$ is placed on the surface of the piston to compress the liquid,the fractional decrement in the radius of the sphere $\left( \frac{dr}{r} \right)$ is

If $\overrightarrow{a}=-\hat{i}+\hat{j}+2 \hat{k}$,$\overrightarrow{b}=2 \hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{c}=-2 \hat{i}+\hat{j}+3 \hat{k}$,then the angle between $2 \overrightarrow{a}-\overrightarrow{c}$ and $\overrightarrow{a}+\overrightarrow{b}$ is

The de-Broglie wavelength of a particle moving with a velocity $2.25 \times 10^8 \ m/s$ is equal to the wavelength of a photon. The ratio of the kinetic energy of the particle to the energy of the photon is (velocity of light is $3 \times 10^8 \ m/s$). (in $/8$)

Consider the following statements:
$(I)$ The radius of an anion is larger than that of the parent atom.
$(II)$ The ionization energy generally increases with increasing atomic number in a period.
$(III)$ The electronegativity of an element is the tendency of an isolated atom to attract an electron.
Which of the above statements is/are correct?

The electric field component of an electromagnetic wave in vacuum is given as $\vec E = 3\cos(1.8y + 5.4 \times 10^8 t)\hat i$. Its direction of propagation and wavelength are: