You are taxed on the expected rent, not the low one
The key rule is that the tax on a let-out property is based on its annual value, and under Section 23(1) the annual value is the higher of two figures: the rent you actually receive, and the sum the property might reasonably be expected to let for, its fair or expected rent, often benchmarked to the municipal or standard rent. Where the actual rent is higher, that is used; where it is lower, the expected rent is used.
So letting your house to a relative at a nil or nominal rent does not cap your tax at that low figure. Because the actual rent falls below what the property could fetch, the annual value reverts to the expected market rent, and you are taxed on that, less the 30% deduction. In other words, a below-market family let is taxed roughly as if you had let it at the going rate. A very large deposit taken to justify a low rent does not help either; the officer can still fix a fair rent from comparable properties.
It also costs you the own-use treatment
There is a second cost that catches people. Up to two Indian houses that you keep for your own use, not let out, can be taken at a nil annual value, so there is no tax on them, and an NRI living abroad can claim this for houses they are not occupying because they live elsewhere. But that nil-value treatment applies only to a house that is not let. The moment you let the house to a relative, even at nil rent, it counts as let, so it loses the nil-value treatment and is taxed on its expected rent instead.
So, counter-intuitively, a house genuinely kept for your family's own use, with no letting arrangement and no rent, can be treated better, potentially nil, than the same house formally let to a relative cheaply. The distinction between your family simply occupying a house you keep for your own use and a formal low-rent letting to a relative genuinely changes the tax. And for an NRI, if the relative does pay any rent, they are paying a non-resident, so they must deduct TDS under Section 195 on it. A practising CA works out the annual value correctly, positions a genuinely own-use house for the nil treatment where it qualifies, and handles the TDS where rent is paid.