Exchange rate of national currency like US dollar or INR don't fluctuate much during a month or year, but the exchange rate of cryptocurrency like bitcoin is highly volatile even in a single day. What are the variables that impact the volatility of a currency? How does the government maintain the stability of its currency? Can one have a stable coin mathematically for example by changing the count of currency? How exchange rates of cryptocurrency and other currencies are calculated, who calculates it, what is math behind it?
The value of currencies (including most popular cryptocurrencies) is set by a market. If more people want to sell the currency (i.e., exchange it for a different currency) than to buy it then some of the sellers will be unable to find a buyer. Their only option will be to lower the price they demand until someone is willing to buy.
Likewise, if more people want to buy, say, euros than are willing to sell them then they will have to be willing to pay a bit more for the euros in order to persuade someone to sell.
In this way, price rises or falls until the supply and demand of the currency are equalised. So when the price fluctuates a lot, it is because either the supply or demand (or both) are changing a lot.
At the moment, cryptocurrencies have very little practical use. It's quite difficult to use them for many kinds of transaction. Thus, most of the trading of those currencies is driven by speculation: people buying and selling them in the hope of making money through changes in the price. This means the price can fall very rapidly when people think there is about the be a crash because everyone wants to sell to protect the value of their money. This is called a speculative bubble.
While euros (and dollars, and pounds,...) are sometimes used for speculation too, the main reason most people want euros is to buy stuff from/in Europe—whether that's German cars, or Bordeaux wine, or just stock in an Italian company. Likewise, the main reason people want to sell Euros is because they are Europeans who are trying to buy stuff made in America or China or elsewhere. They sell their Euros for dollars so that they can buy Ford cars or Coca Cola. In normal times the value of euros tends to be quite stable because the amount of stuff people buy from Europe and the amount of foreign-made stuff that Europeans buy doesn't change very quickly.