1. The number of ways of arranging n students in a row such that no two boys sit together and no two girls sit together is m(m > 100). If one more student is added, then number of ways of arranging as above increases by 200%. The value of n is:
2. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4 if repetition of digits is allowed?
3. How many five digit positive integers that are divisible by 3 can be formed using the digits 0, 1, 2, 3, 4 and 5, without any of the digits getting repeated.
4. There are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man. If P and Q denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then P : Q equals
5. How many factors of 25 × 36 × 52 are perfect squares?
6. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
7. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
8. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
9. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
10. In how many ways can the letters of the word 'LEADER' be arranged?
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