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**Illustration 1: In the binomial expansion of (a-b)n, n â‰¥ 5 the sum of the 5 ^{th} and 6^{th} terms is zero. Then what is the value of a/b? (2001)**

So, it is given that T

This gives

Hence,

In order to obtain the value of a/b, we shift the terms obtained above on one side.

This gives the value of a/b as =

**Illustration 2: ****Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If T _{n+1- }T_{n} = 21, then what is the value of n? (2001)**

T

Hence,

So, (n+1)(n-1)n/6 â€“ n(n-1)(n-2)/6 = 21

So, n(n-1)3/6 = 21

Hence, n(n-1) = 42

This gives, n =7.

**Illustration 3: Coefficient of t24 in (1 + t ^{2})^{12}(1 + t^{12})(1 + t^{24}) isâ€¦.? (2003)**

This is same as the coefficient of t

Or the coefficient of t

Hence,the coefficient of t

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