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📐 Mathematics  ·  Binomial Theorem  ·  JEE

The value of C(10,0) + C(10,2) + C(10,4) + ... + C(10,10) is:

Answer: 512.

  • A 256
  • B 512
  • C 1024
  • D 511

Correct answer: B. 512

Explanation: The sum of even-indexed binomial coefficients equals 2<sup>n−1</sup> = 2⁹ = 512.

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 →