Modern physics is the cheapest marks in the paper

If you are short on time and want the largest score improvement per hour of study, modern physics is usually the answer. It is a small, closed, formula-light group of topics that contributes reliably to every JEE Main paper.

Why it is cheap

Mechanics rewards years of accumulated problem-solving intuition. Modern physics rewards knowing about fifteen relations and being careful with units. The questions are short, the algebra is light, and the same ideas recur:

• photoelectric effect: $E = h\nu$, stopping potential, work function
• de Broglie wavelength: $\lambda = h/p$
• the Bohr model: energy levels, radii, transitions
• nuclear binding energy and mass defect
• radioactive decay and half-life
• X-ray production, characteristic versus continuous spectra

That is close to the entire topic.

The five things that cause almost all the errors

Electron-volts versus joules. Most of these questions are cleaner in eV. Keep $hc = 1240$ eV·nm in your head and the photon energy for a given wavelength is one division away. Mixing unit systems mid-question is the most common mistake here by a wide margin. Which energy the work function comes off. The maximum kinetic energy is $K_{\max} = h\nu - \phi$. Stopping potential relates to $K_{\max}$, not to $h\nu$. Questions are frequently built so the wrong choice lands on one of the offered options. Bohr scaling. Energy goes as $Z^2/n^2$ and radius as $n^2/Z$. Almost every Bohr question is a scaling question. Knowing that hydrogen's ground state is $-13.6$ eV at a radius of $0.53$ Å, you can produce any level of any hydrogen-like ion without a formula sheet. Transition counting. The number of distinct spectral lines produced as a level $n$ cascades to the ground state is $n(n-1)/2$. Worth memorising: it appears constantly and takes ten seconds to answer. Decay in half-lives, not seconds. When the elapsed time is a whole number of half-lives, use $N = N_0/2^k$ and skip the exponential. Reach for $\lambda$ only when it is not.

A realistic plan

Two focused sessions get you most of the way. Session one: read a cheat sheet for the whole topic, then write the fifteen relations on one page from memory. Session two: thirty previous year questions on it, one sitting, timer running. Thirty questions covers essentially every pattern the examiners use here, because the topic is genuinely that small. Compare that with thirty questions in rotational motion, which barely scratches the surface, and the arithmetic on where to spend a spare weekend is easy.