By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2025 Maths, question 21

Topic: Algebra

Q21

If the sum of binomial coefficients in the expansion of (x+y)n(x + y)^{n} is 256, then the greatest binomial coefficient occurs in which one of the following terms?

  1. (a) Third
  2. (b) Fourth
  3. (c) FifthCorrect answer
  4. (d) Ninth

Solution.

Answer: (c) Fifth

  1. The sum of coefficients is 2n=256=282^{n} = 256 = 2^{8}, so n=8n = 8.
  2. For even nn, the central coefficient (nn/2)\binom{n}{n/2} is greatest.
  3. Here it is (84)=70\binom{8}{4} = 70, occurring in T4+1T_{4 + 1}, the fifth term.