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For which of the following values of `x ,5t h` term is the numerically greatest term in the expansion of `(1+x//3)^(10)` , a. -2 b. 1.8 c. `2` d. `-1. 9`

A

-2

B

1.8

C

2

D

-19

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Let `T_(5)` is numerically the greatest term in the expansion of`(1+x//3)^(10)`
Then, `|(T_(5))/(T_(4))| ge 1` and `|(T_(6))/(T_(5))| le 1`
Now, `(T_(r+1))/(T_(r)) = (10-r+1)/(r ) x/3`
`rArr |(7)/(4) xx x/3| ge 1` and `|6/5 xx x/3| le 1`
`rArr |x| gt 12/7` and `|x| le 5/2 " "(1)`
`rArr 12/7 le |x| le 5/2`
`rArr x in [-5/7 , - 12/7] uu [12/7,5/2]`
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