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 
Rate this question :
Quiz on Greatest term in binomial expansion | Revising Binomial theorem38 mins
Binomial theorem for any index | Interactive Quiz48 mins
Greatest term in binomial expansion | Revising Binomial theorem43 mins
Finding remainder using binomial theorem43 mins
Finding coefficient of x^n in binomial expansion59 mins
Interactive Quiz on Binomial Theorem40 mins
Lecture on properties of Binomial Coefficients58 mins
Interactive Quiz on properties of Binomial Coefficients51 mins
Master on Binomial Theorem for any index41 mins
Interactive Quiz | general & middle terms53 mins
Show that the coefficient of x4 in the expansion of 
is 
.
Show that the middle term in the expansion of 
is 252.
Show that the coefficient of x-3 in the expansion of 
is -330.
Show that the term independent of x in the expansion of 
is -252.
Find the middle term in the expansion of 
If the 17th and 18th terms in the expansion of (2 + a)50 are equal, find the value of a.
RS Aggarwal - MathematicsIf the coefficients of x2 and x3 in the expansion of (3 + px)9 are the same then prove that 
.
