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NDA 1 2025 Maths, question 28

Topic: Algebra

Q28

If the number of selections of rr as well as (n+r)(n + r) things from 5n5n different things are equal, then what is the value of rr?

  1. (a) nn
  2. (b) 2n2nCorrect answer
  3. (c) 3n3n
  4. (d) 4n4n

Solution.

Answer: (b) 2n2n

  1. The equality is (5nr)=(5nn+r)\binom{5n}{r} = \binom{5n}{n + r}.
  2. For distinct indices in the same binomial row, equal coefficients occur at complementary indices.
  3. Since n>0n > 0, the indices differ; therefore r+(n+r)=5nr + (n + r) = 5n, giving r=2nr = 2n.