general Maths Puzzle

SUPRIYA,is the name of a film theatre in kerala.now a days, there is no much earning for the manager from this theatre. To solve this problem one day at the theater, the manager announces that a free ticket will be given to the first person in line whose birthday is the same as someone in line who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365 day year, what position in line gives you the best chance of being the first duplicate birthday?

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general Other Question

RAM AND SHYAM USED TO PLAY WITH COINS.CONSIDER THE SITUATION:
RAM has one more coin than player SHYAM. Both throw all of their coins simultaneously and observe the number that come up heads. Assuming all the coins are fair, what is the probability that RAM obtains more heads than SHYAM?
Find the first digit before and after the decimal point in (sqrt2 + sqrt3)^3000.