Home
Class 12
MATHS
The middle term in the expansion of (1-3...

The middle term in the expansion of `(1-3x+3x^2-x^3)^(2n)` is

A

`((6n)!x^(n))/((3n)!(3n)!)`

B

`((6n)!x^(3n))/((3n)!)`

C

`((6n))/((3n)!(3n)!)(-x)^(3n)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(1-3x+3x^(2)-x^(3))^(2n)=(1-x)^(6n)`
middle term is `((6n)/(2)+1)^(th)`
i.e., `(3n+1)^(th)` term is middle term,
`T_(3n+1)=^(6n)C_(3n)(-x)^(3n)=(6n!)/(3n!3n!)(-x)^(3n)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The coefficient of the middle term in the expansion of (1+x)^(2n) is

The coefficient of the middle term of the expansion of (1-2x+x^2)^n is

Show that the middle term in the expansion of (x-1/x)^(2n) is (1.3.5.7....(2n-1))/(n!)(-2)^n

Show that the value of the middle term in the expansion of (x+(1)/(2x))^(2n)" is " (1.3.5.....(2n-1))/(n!)

The middle term in the expansion of (2x-3y)^(12) is -

Prove that the middle term in the expansion of (1+x)^(2n)" is " (1.3.5....(2n-1))/(n!).2^(n)x^(n)

If the coefficient of the middle term in the expansion of (1+x)^(2n+2) is alpha and the coefficients of middle terms in the expansion of (1+x)^(2n+1) are beta and gamma then relate alpha, beta and gammadot

find the middle term in the expansion of (x/2+1/x)^7

Show that the middle term in the expansion of (x+1)^(2n)" is " (1.3.5. ......(2n-1))/(n!).2^(n).x^(n).