Dimensional analysis is a checking tool, not a chapter

Dimensional analysis gets taught as a chapter and then abandoned. That is a waste, because its real value is not the two or three direct questions it generates — it is that it lets you check almost any answer in the paper in about five seconds.

The check

Every physical equation must be dimensionally homogeneous. So after you derive anything, compare the dimensions of both sides. If they disagree you have made an algebra error, and you found it without redoing the algebra. This catches one very common failure: a factor in the wrong place. If your answer for a time comes out as $$t = \sqrt{\frac{g}{2h}}$$ the dimensions are $\mathsf{T}^{-1}$, not $\mathsf{T}$, so the fraction is inverted. You needed no re-derivation to know that.

Eliminating options without solving

Plenty of JEE Main questions can be answered from dimensions alone. Asked for the oscillation period of a liquid drop, given four expressions built from density $\rho$, radius $r$ and surface tension $S$, only one combination has dimensions of time: $$T \propto \sqrt{\frac{\rho r^3}{S}}$$ You cannot recover the dimensionless constant this way, but the options rarely differ by a constant — they differ in which powers appear. Two minutes saved on a question you might otherwise have skipped.

The limits, which are what gets tested

Dimensional analysis cannot:

• find dimensionless constants, so it will never hand you the $2\pi$ in the pendulum period
• distinguish quantities sharing dimensions — work, heat and energy all carry $\mathsf{ML}^2\mathsf{T}^{-2}$, and so does torque
• resolve a relation with more than three unknown powers in mechanics, since you only have $\mathsf{M}$, $\mathsf{L}$ and $\mathsf{T}$ to work with
• handle sums, only products. If the true relation is $y = A + B$, dimensions tell you $A$ and $B$ match and nothing more.

Questions on this chapter are usually built on these limits rather than on the technique, so know them as precisely as you know the method.

Arguments must be dimensionless

Anything inside a sine, cosine, logarithm or exponential is dimensionless. This is the fastest way to read an unfamiliar formula. In $x = A\sin(\omega t + \phi)$, a dimensionless argument forces $\omega$ to be an inverse time and $A$ to carry the dimensions of $x$. In a decay law $N = N_0 e^{-\lambda t}$, the same reasoning makes $\lambda$ an inverse time, which is why its reciprocal is a lifetime.

Make it a habit, not a chapter

The students who benefit from this are not the ones who scored well on the units chapter. They are the ones who spend five seconds checking dimensions on every derived answer in a mock. Added to your checking routine, it will find two or three errors per paper.