How much cash can I carry while travelling from India to Poland?

There is a limit, though I am surprised by Mumbai Custom website wordings. In the same website if you scroll down you will see limits on hard currency you can carry.

Reserve Bank of India

Travellers are allowed to purchase foreign currency notes/coins only up to US$ 2000. Balance amount can be taken in the form of traveller’s cheque or banker’s draft. Exceptions to this are (a) travellers proceeding to Iraq and Libya can draw foreign exchange in the form of foreign currency notes and coins not exceeding US$ 5000 or its equivalent; (b) travellers proceeding to the Islamic Republic of Iran, Russian Federation and other Republics of Commonwealth of Independent States can draw entire foreign exchange released in form of foreign currency notes or coins.

As a Tourist, this is a total limit

In connection with private visits abroad, viz., for tourism purposes, etc., foreign exchange up to US$10,000, in any one calendar year may be obtained from an authorised dealer. The ceiling of US$10,000 is applicable in aggregate and foreign exchange may be obtained for one or more than one visits provided the aggregate foreign exchange availed of in one calendar year does not exceed the prescribed ceiling of US$10,000 {The facility was earlier called B.T.Q or F.T.S.}. This US$10,000 (BTQ) can be availed of by a person alongwith foreign exchange for travel abroad for any purpose, including for employment or immigration or studies. However, no foreign exchange is available for visit to Nepal and/or Bhutan for any purpose.

For Business Travel

Authorised dealers can release foreign exchange up to US$25,000 for a business trip to any country other than Nepal and Bhutan. Release of foreign exchange exceeding US$25,000 for a travel abroad (other than Nepal and Bhutan) for business purposes, irrespective of period of stay, requires prior permission from Reserve Bank. Visits in connection with attending of an international conference, seminar, specialised training, study tour, apprentice training, etc., are treated as business visits. Visit abroad for medical treatment and/or check up also falls within this category.

In fact both, the Custom Department and RBI are correct. Passengers visits for different purposes. So they are entitled to different amount of foreign exchange. Foreign exchange can only be purchased from authorised persons. So there may be any amount. However specifically for tourism only US$ 10000 can be taken in a calendar year.