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Question

If the ratio of the 7th term from the beginning to the 7th term from the end in the expansion of
(21/3+131/3)n is 16, find n.

A
5
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B
9
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C
7
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D
2
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Solution

The correct option is B 9
The 7th from begining of the expansion (213+1313)n
T6+1 = nC6.2n63.1363 = nC6.2n63.19
To find 7th term from end we just find 7th term of the expansion (1313+213)n from beginning.
T"6+1 = nC6.13n63.263 = nC6. 13n63.4
T7T"7 = 16
16 = nC6.2n63.19nC6.13n63.4
16 = 6n6336
61 = 6n63
On equating the power, we get
1= n63
So, n=9

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