Many countries will allow you a second or even third passport, so you can still travel while visa are being processed.
> 13. Issue of additional passport or travel document in special circumstances. A person holding a passport or travel document shall not be entitled to another passport or travel 'document unless he surrenders to the passport authority the passport or travel document already held by him.
https://passportindia.gov.in/AppOnlineProject/pdf/Passport_R...