Q162 / 270 · NDA 2022 (Phase 1) · Mathematics

Consider the following statements in respect of the expansion of $(x+y)^{10}$ : 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?

  • A
    1 only
  • B
    2 only
  • Correct answer
    C
    Both 1 and 2
  • D
    Neither 1 nor 2

Solution

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

Hence, the correct answer is option: 'C'.

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