Q. 215.0( 2 Votes )
Find the sixth term in the expansion 
if the binomial coefficient of the third term from the end is 45.
Answer :
In the binomial expansion of 
, there are (n + 1) terms.
The third term from the end in the expansion of 
, is the third term from the beginning in the n expansion of 
.
The binomial coefficient of the third term from the end = nC2
It is given that the binomial coefficient of the third tern from the end is 45.
Since, nC2 = 45
n2 - n - 90 = 0
(n – 10) (n + 9) = 0
Therefore, n = 10 (n cannot be negative)
Let T6 be the 6th term in the binomial expansion of 
.Then
T6 = nC5
Now, Put n = 10
T6 = T5 + 1 = 10C5
T5 + 1 = 
T5 + 1 = 
T5 + 1 = 
Hence, the 6th Term is 
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