Income tax is paid on income earned by any source unless it is specifically exempted.
If you are earning income then there will be income tax on it.
Adsense income is not an exemption. Adsense is your business, and it does not matter what the business is, if there is income there will be tax on it.
To give you a brief idea about tax system in India or elsewhere, basically we have 2 type of taxes. Direct taxes and indirect taxes. Indirect taxes are one where incident of tax is passed on to ultimate consumer of product/service, example GST.
Direct tax is a tax where income earner has to pay the tax.
In India, Income Tax is the direct tax and is to be charged on all incomes earned whether online or offline.
So yes, you have to pay income tax on Adsense income earned.
If you are an individual then tax will be charged based on income tax slabs. For individuals there is not a single rate of tax but slabs are specified based on which income is charged to tax.