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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2022 · Mathematics · Binomial Theorem

Consider the following statements in respect of the expansion of...

Consider the following statements in respect of the expansion of (x+y)10(x+y)^{10} : 1. Among all the coefficients of the terms, the coefficient of the 6th term has the highest value 2. The coefficient of the 3 rd term is equal to coefficient of the 9th term Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

Middle term of (x+y)10is(10+22)th (x+y)^{10} is \left(\frac{10+2}{2}\right)^{\text{th }} term =6th =6^{\text{th }} term We know that coefficient of middle term is highest value. So, statement 1 is correct Since total number of term =10+1=11=10+1=11 Coefficient of 3rd term = coefficient of (11−3+1)th (11-3+1)^{\text{th }} term = Coefficient of 9th 9^{\text{th }} term So, statement 2 is correct
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