Can we do day trading in equities, futures, currencies with the same trading account?

Yeah, if you got the money.

Yes why not…u can surely do this as long as u have margin money.

Yes Ashish you can,

Zerodha has 3 types of account's, Trading, Demat and Commodity.

Trading: Equity & Derivatives Trading Account, An Equity & Derivatives Trading account is what you open with a Trading Member (Stock Broker) of a recognized Stock Exchange (presently NSE,BSE and MCX-SX in India). A Trading account is the account to which you transfer funds and then buy/sell stocks, Futures & Options.This can be done, either online or offline.

Equity Demat Account: Dematerialized Account popularly known as Demat Account, is the account where you keep stocks in electronic format. Similar to how a Savings Account allows you to keep money in electronic format, a Demat account allows you to keep stocks in electronic format. In essence a Demat Account is a safe storage for your stocks and this is the only use of a Demat Account. Whilst opening a Demat Account you’d be required to sign the Demat Form and the Power of Attorney. Click here to read as to why you’d have to sign the PoA.​

Commodity Trading Account: A Commodity Trading account is what you open with a Trading Member (Commodity Broker as you call him) of recognized Commodity Exchange (MCX, NCDEX etc. in India).​