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📐 Mathematics  ·  Binomial Theorem  ·  JEE

The binomial coefficient nCr satisfies nCr = nC___.

Answer: n-r.

  • A n+r
  • B r-1
  • C n-r
  • D r

Correct answer: C. n-r

Explanation: Symmetry property: nCr = nC(n-r). For example, 5C2 = 5C3 = 10.

Pascal's Triangle: Binomial Coefficients11112113311464115101051n=0n=1n=2n=3n=4n=5Each entry = sum of the two entries diagonally above it (Pascal's identity); row n gives nC0...nCn

Row n of Pascal's triangle gives the coefficients nC0, nC1, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.

Concept context

Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term

Read the full Binomial Theorem notes →