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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:

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: Correct Answer 10

If n is even, then the number of boys should be equal to number of girls, let each be a.⇒ n = 2aThen the number of arrangements = 2 × a! × a!If one more students is added, then number of arrangements,= a! × (a + 1)!But this is 200% more than the earlier⇒ 3 × (2 × a! × a!) = a! × (a + 1)!⇒ a + 1 = 6 and a = 5⇒ n = 10But if n is odd, then number of arrangements,= a!(a + 1)!Where, n = 2a + 1When one student is included, number of arrangements,
= 2(a + 1)! (a + 1)!By the given condition, 2(a + 1) = 3, which is not possible.

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