Binomial TheoremHard
Question
In the expansion of (x + y + z)25
Options
A.every term is of the form 25Cr. rCk. x25 - r. yr - k. zk
B.the coefficient of x8 y9 z9 is 0
C.the number of terms is 325
D.none of these
Solution
(x + y + z)25
General term
xr1 yr2 xr3
Putting r3 = k, r2 = r - k and r1 = 25 - r
=
× x25-r yr-k zk = 25Cr . rCk . x25-r yr-k zk
r1 + r2 + r3 = 25
∴ coefficient of x8 y9 z9 is 0
General term
xr1 yr2 xr3Putting r3 = k, r2 = r - k and r1 = 25 - r
=
× x25-r yr-k zk = 25Cr . rCk . x25-r yr-k zk r1 + r2 + r3 = 25
∴ coefficient of x8 y9 z9 is 0
Create a free account to view solution
View Solution FreeMore Binomial Theorem Questions
The coefficient of x52 in the expansion(x - 3)100-m. 2m is :...If the third term in the binomial expansion of (1 + x)m is −x2 , then the rational value of m is-...The sum of the series (12 + 1). 1! + (22 + 1). 2! + (32 + 1). 3! + ....... + (n2 + 1). n! is -......Given that the term of the expansion (x1/3 - x-1/2 )15 which does not contain x is 5 m where m ∈ N, then m is equa...