The work done by a force $\vec F = (-6x^3 \hat i) \text{ N}$,in displacing a particle from $x = 4 \text{ m}$ to $x = -2 \text{ m}$ is .............. $J$.

Given below are two statements:
Statement $I$: $[CoBr_{4}]^{2-}$ ion will absorb light of lower energy than $[CoCl_{4}]^{2-}$ ion.
Statement $II$: In $[CoI_{4}]^{2-}$ ion,the energy separation between the two sets of $d$-orbitals is more than $[CoCl_{4}]^{2-}$ ion.
In the light of the above statements,choose the correct answer from the options given below:

Two photons of energy $2.5 \ eV$ and $3.5 \ eV$ fall on a metal surface of work function $1.5 \ eV$. The ratio of the maximum velocities of the photoelectrons emitted from the metal surface is

Which of the following statements is correct?

The ratio of minimum wavelengths of Lyman and Balmer series will be

If $x \log x \frac{dy}{dx} + y = \log x^2$ and $y(e) = 0$,then $y(e^2) = $