## 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 2^{5} × 3^{6} × 5^{2} are perfect squares?

^{5}× 3

^{6}× 5

^{2}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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