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
If the sum of the coefficients in the expansion of (1 − 3x + 10x2)n is a and if the sum of the coefficients in the...In the binomial expansion of (a - b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then equals...The term containing x in the expansion of is -...If 1 ≤ r n − 1 then n-1Cr + n-2Cr + .....+ rCr equals-...The greatest terms of the expansion (2x + 5y)13 when x = 10, y = 2 is -...