Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Binomial Theorem

BITSAT 2023 · Paper 1 · Mathematics · Binomial Theorem

The middle term in the expansion of ((10)/(x)+(x)/(10))^ 10 is

The middle term in the expansion of (10x+x10)10\left(\frac{10}{x}+\frac{x}{10}\right)^{10} is

Options

  1. A10C5{ }^{10} \mathrm{C}_5
  2. B10C6{ }^{10} \mathrm{C}_6
  3. C10C51x10{ }^{10} \mathrm{C}_5 \frac{1}{x^{10}}
  4. D10C5\mathrmx10{ }^{10} \mathrm{C}_5 \mathrmx^{10}

Correct answer

A. 10C5{ }^{10} \mathrm{C}_5

Step-by-step solution

General term =Tr+1=T_{r+1}
=10Cr(10x)10−r(x10)r={ }^{10} \mathrm{C}_r\left(\frac{10}{x}\right)^{10-r}\left(\frac{x}{10}\right)^r
Here n=10n=10, which is an even number.
Now, \left[\frac{10}{2}+1\right]^{\text{th }}termi.e.term i.e.6^{\text{th }}termisthemiddleterm.<br/>Hence,middletermterm is the middle term.<br />Hence, middle term=T_6<br/><br />\mathrm{T}_{5+1}={ }^{10} \mathrm{C}_5\left(\frac{10}{x}\right)^{10-5}\left(\frac{x}{10}\right)^5<br/><br />={ }^{10} \mathrm{C}_5\left(\frac{10}{x}\right)^5\left(\frac{x}{10}\right)^5={ }^{10} \mathrm{C}_5.
Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

The coefficient of x^2 term in the binomial expansion of ((1)/(3) x^ (1)/(2) +x^ (-1)/(4)… BITSAT 2024The coefficient of x^n in the expansion of e^ 7 x +e^x e^ 3 x is BITSAT 2024The coefficient of the highest power of x in the expansion of (x+ x^2-1 )^8+(x- x^2-1 )^8 BITSAT 2024If the 17^ th and the 18^ th terms in the expansion of (2+a)^ 50 are equal, then the… BITSAT 2024If x^ 18 occurs in the rth term in the expansion of (x^4+(1)/(x^3))^ 15 , then what is… BITSAT 2023The number of terms in the expansion of (1+5 2 x)^9+(1-5 2 x)^9 , is BITSAT 2022If the sum of the coefficients in the expansion of (x+y)^n is 1024 , then the value of… BITSAT 2022The coefficient of the term independent of x in the expansion of ( (x)/(3) + 3 2 x^ 2 )^… BITSAT 2021Coefficient of x^ 13 in the expansion of (1-x)^ 5 (1+x+x^ 2 +x^ 3 )^ 4 is BITSAT 2021If a, b, c are three natural numbers in AP and a + b+c=21 then the possible number of… BITSAT 2020Let (2x^ 2 + 3x + 4)10 = ∑ _ r = 0 ^ 20 a _ r x^ r , then the value of a_ 8 a_ 12 , is BITSAT 2019If (1 + x + x^ 2 )20 = ∑ _ r = 0 ^ 40 a _ r · x^ r , then ∑ _ r = 0 ^ 39 (- 1)r · a _ r ·… BITSAT 2019If the coefficient of x^ 3 and x^ 4 in the expansion of (1 + ax + bx^ 2 ) (1 - 2x)18 in… BITSAT 2019In the expansion of (1 + x + x^ 3 + x^ 4 )10 , the coefficient of x^ 4 is BITSAT 2019The coefficient of x^ - n in (1 + x)n(1 + (1)/(x))n is BITSAT 2018The greatest term in the expansion of 3 (1 + (1)/(3))20 is BITSAT 2018 Full Binomial Theorem list Binomial Theorem JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs