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Earn 100

Mark Shekhar Garg goes to a school to demonstrate how the kids can use the Facebook harmlessly and take the optimum advantage of socialization with fellow kids online at the early age of their social being. He tells the kids, after demonstrating the usage and safety features, that to make someone your facebook friend you have to send her/him a request and the other person has to accept it; as in out of two classmates A and B if first A sends request to B then B will accept it or if first B sends request to A then A will accept it and thus both A and B will become facebook friends.

As every kid responds to his instructions, within a minute Mark finds that every student in the class is now facebook friend of the other. In that class the number of female students is twice that of male students. He also notices that the number of friend-requests sent by the female kids is equal to the number of friend-requests sent by the male kids. Which of the following can be the number of friend-requests sent by female students to male students of that class?

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Important Questions on Permutations & Combinations

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A king calls 11 masseurs for his queen, as she wants the body massage from Monday to Friday, while on weekends she wants to go on the long trips with the king. She wants everyday a new masseur, so basically 5 masseurs are required. But a confidant of the king tells him that out of 11 masseurs 5 are familiar with the queen before her marriage and she used to get very close to them. But the king has no idea of these 5 people who are familiar with the queen. In spite of knowing this very odd fact he takes the risk of telling the masseurs that they can start giving massage to his lovely queen, as he doesn't want to make any fuss over it. However, he wants to identify the 5 masseurs who are close to the queen. Based on the queen's personal behaviour with him the wise king gets an idea that if in any week out of the 5 familiar masseurs any 3 masseurs give the massage to the beautiful queen he will certainly identify who all these 5 people familiar with the queen are. Minimum how many weeks are required to identify these 5 masseurs familiar with the queen?
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There is a set of 10 integers {0,1,2,3,.,9}. In how many ways can you permute this set of integers such that either 3 and 6 or 5 and 4 or 6 and 5 appear consecutively?
(For example, we do not count (4,5,0,6,9,2,3,7,8,9), as we want 5 and 4 to appear consecutively in that order. But we count (7,2,0,1,4,3,6,5,8,9), both 3 and 6, and 6 and 5 appear consecutively in it.)
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How many integer solutions are there to the equation x1+x2+x3+x4=30, such that 3x1,x2,x3,x410.
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If Crn-1=k2-3Cr+1n, then kR
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A shopping mall in Kashipur, a meditative and idyllic town near Nainital, has three food courts - Chinese, Thai and Italian, situated on its rooftop. Each food court is designed in such a way that all the restaurants are situated in a circle. Chinese, Thai and Italian food courts have 20,15 and 10 restaurants, respectively. Having the. change (coins and paper currency in smaller denomination) is usually a terrible job due to digital payments and rush in the food courts, so restaurants try to avoid giving the change to each other. Still it is found that each restaurant gives the change to any other restaurant at most three times a day and if the restaurants belong to the same food court then each restaurant gives the change to other restaurant at most two times a day. However, any two adjoining restaurants do not give change to each other at all. On a certain day at most how many times the change can be given to each other among all the restaurants on the roof top?
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Find the total number of quadratic polynomial ax2+bx+c, if a, b, c are some three positive distinct integers less than 2000, such that (x+1) is the factor of the quadratic polynomial ax2+bx+c.
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Find the number of isosceles triangles with inṭeger sides, if no side exceeds 2014 unit.
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A five-digit number is called a mountain number if the first three digits increase and the last three digits decrease. For example, 35763 is a mountain number, but 35663 is not. How many five-digit numbers greater than 70,000 are mountain numbers?