Class 11

Math

Algebra

Binomial Theorem

The numerically greatest term in the expansion of $(3−2x)_{9}$ when $x=1$ is

- 4th term
- 5th term
- 6th term
- 7th term

$=(3−2x)_{9}$

$=3_{9}(1−32x )_{9}$

$=3_{9}(1−32 )_{9}$

let Trt, be the greatest term this exp.

Tr+1 $≥Tr$

$_{9}C_{r}(3−2 )_{r}≥_{9}C_{r−1}(3−2 )_{r−1}$

$⇒r!∣9−r∣!9! (3−2 )_{r−r+1}≥(r−1)!∣9−r+1∣!9! $

$⇒r∣r−1∣!∣9−r∣!1 ∣∣ 3−2 ∣∣ ≥(r−1)!(10−r)(9−r)!1 $

$=(−2(10−r))≥(3r)$

$=20−2r≥3r$

$=20≥5r$

$=r≤4$

$T_{5}$ is the greatest term