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NDA 2 2025 Maths, question 20

Topic: Algebra

Q20

Which one of the following is the greatest coefficient in the expansion of (1+x)100(1+x)^{100}?

  1. (a) The coefficient of x100x^{100}
  2. (b) The coefficient of x99x^{99}
  3. (c) The coefficient of x51x^{51}
  4. (d) The coefficient of x50x^{50}Correct answer

Solution.

Answer: (d) The coefficient of x50x^{50}

  1. Successive binomial coefficients satisfy C(100,r+1)/C(100,r)=(100−r)/(r+1).
  2. They increase until r=50 and then decrease.
  3. Therefore C(100,50), the coefficient of x⁵⁰, is the largest.