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📐 Mathematics  ·  Binomial Theorem  ·  JEE

The sum of all the binomial coefficients in the expansion of (2x + 3y)¹⁰ is:

Answer: 5¹⁰.

  • A 5¹⁰
  • B 6¹⁰
  • C 1
  • D 0

Correct answer: A. 5¹⁰

Explanation: Setting x = y = 1 gives (2 + 3)¹⁰ = 5¹⁰.

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 →