Home
Class 12
MATHS
If in the expansion of 2x+5^(10) , the n...

If in the expansion of `2x+5^(10)` , the numerically greatest tem in equal to the middle term, then find the values of `xdot`

Text Solution

Verified by Experts

The correct Answer is:
`x in (-3,-25/12) uu (25/12,3)`
In the expansion of `(2x+5)^(10)`, the middle term is `T_(6)` .
Consider the expansion of `(1+2x//5)^(10)` .Now
`|(T_(6))/(T_(5))|gt1` and `|(T_(7))/(T_(6))|lt 1`
`rArr |(10-5+1)/(5)(2x)/(5)|gt1` nd `|(10-6+1)/(6)(2x)/(5)|lt1`
`rArr |(12)/(25)x|gt1` and `|(x)/(3)|lt1`
`rArr (25)/(12)lt|x|lt3`
`rArrx in (-3,-25/12)uu(25/1,3)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.6|10 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.7|9 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.4|13 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

Find the numerically greatest term in (3 + 2x)^15 when x = 5/2

Given that the 4th term in the expansion of [2+(3x//8)]^(10) has the maximum numerical value. Then find the range of value of xdot

Find the middle terms are in the expansion of (2x+3y)^7

Write the middle term in the expansion of (x+1/x)^(10)dot

Find the middle term in the expansion of (x/y-y/x)^7

If the middle term in the expansion of (1+x)^(2n) is the greatest term, then x lies in the interval

Find the numerically greatest term in the expansion of (2+5x)^(21) when x = 2/5 .

The numerically greatest term in the expansion of (1 + x)^(10) when x = 2//3 , is

Find the middle term in the expansion of (2x^2-1/x)^7

Find the middle term in the expansion of (2x^2-1/x)^7