Zaymiey

📐 Mathematics  ·  Binomial Theorem  ·  JEE

The term independent of x in the expansion of (x² − 1/x)⁶ is:

Answer: 15.

  • A 15
  • B −15
  • C 20
  • D 6

Correct answer: A. 15

Explanation: General term power is 12 − 3r; independent when r = 4, giving C(6,4)(−1)⁴ = 15.

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 →