Home
Class 12
MATHS
Coefficient of x^(11) in the expansion o...

Coefficient of `x^(11)` in the expansion of `(1+x^2)^4(1+x^3)^7(1+x^4)^(12)` is 1051 b. 1106 c. 1113 d. 1120

A

1051

B

1106

C

1113

D

1120

Text Solution

Verified by Experts

Coefficient of `x^r` in `(1+x)^n` is `.^nC_r`.
In this type of questions, we find different composition of terms where product will give us `x^11`.
Now , consider the following cases for `x^11` in
`(1+x^2)^4(1+x^3)^7(1+x^4)^12`.
Coefficient of `x^0x^3x^8`, Coefficient of `x^2x^9x^0`
Coefficient of `x^4x^3x^4`, Coefficient of `x^8 x^3 x^0`
`=.^4C_0 xx .^7C_1 xx .^12C_2 xx .^4C_1 xx .^7C_3 xx .^12C_0+.^C_0+.^4C_2 xx .^7C_1xx .^12C_1 +.^4C_4 xx .^7C_1 xx .^12C_0`
`=462 +140 +504+7=1113`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The coefficient of x^(4) in the expansion of (1 + x + x^(2))^(3) is

Find the coefficient of x^5 in the expansion of (1+x^2)^5 (1+x)^4

The coefficient of x^(4) in the expansion of (1 + x + x^(2) + x^3)^(11) is

The coefficient of x^(4) in the expansion of (x/2-3/x^(2))^(10) is

The coefficient of x^(n) in expansion of (1 + x)(1 - x)^(n) is

The coefficient of x^9 in the expansion of (1+x)(1+ x^2)(1+x^3)....(1+x^(100)) is

The coefficient of x^(7) in the expansion of (1-x-x^(2) + x^(3))^(6) is :

Find the coefficient of x^(8) in the expansion of (1-2x)^(- 1/2) .

The coefficient of X^24 in the expansion of (1+X^2 )^12(1+X^12)(1+X^24)