Q. There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices?

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Q. There are 2 twin sisters among a group of 15 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two sisters?

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Q. The number of words of 4 consonants and 3 vowels can be made from 15 consonants and 5 vowels, if all the letters are different is ________

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Q. How many ways are there to arrange 7 chocolate biscuits and 12 cheesecake biscuits into a row of 19 biscuits?

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Q. If a, b, c, d and e are five natural numbers, then find the number of ordered sets(a, b, c, d, e) possible such that a+b+c+d+e=75.

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Q. There are 15 people in a committee. How many ways are there to group these 15 people into 3, 5, and 4?

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Q. There are six movie parts numbered from 1 to 6. Find the number of ways in which they be arranged so that part-1 and part-3 are never together.

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Q. How many ways are there to divide 4 Indian countries and 4 China countries into 4 groups of 2 each such that at least one group must have only Indian countries?

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Q. Find the number of factors of the product 5⁸ * 7⁵ * 2³ which are perfect squares.

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Q. From a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done?

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Q. Calculate sum of divisors of n = 1900.

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Q. Given the factorization of a number n, then the sum of divisors can be computed in _______

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Q. Calculate the sum of divisors of N = 9600.

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Q. Find the number of odd positive integers of the number 456.

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Q. The number of even positive integers of 3200 is _______

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Q. What is the sum of divisors of the number 1872?

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Q. Find the odd positive integer of the number 6500.

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Q. How many even positive integers are there in the number 7362?

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Q. Calculate sum of divisors of n = 8620.

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Q. Find the odd positive integer of the number 4380.

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