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Nope. For new visas, you only ever need your active, current passport - specifically (if you have two or more citizenships), the passport you intend to travel to the country (in this case Japan) on.
You may be asked for other documentation - e.g. proof of funds, accommodation and so on, but you won't need the past passports. They're considered invalid documents for the purpose of acquiring a visa.
Edit: Included visahq link for Indian citizens living in Taiwan applying for a visa to Japan.