Zaymiey

📐 Mathematics  ·  Binomial Theorem  ·  JEE

The greatest binomial coefficient in (1+x)¹⁰ is:

Answer: 10C5.

  • A 10C4
  • B 10C3
  • C 10C6
  • D 10C5

Correct answer: D. 10C5

Explanation: For even n, greatest coefficient is nC(n/2). Here n=10, greatest coefficient = 10C5 = 252.

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 →