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📐 Mathematics  ·  Binomial Theorem  ·  JEE

The 4th term in the expansion of (x - 1/x)⁷ is:

Answer: -35x.

  • A -35x
  • B 35/x
  • C 35x
  • D -35/x

Correct answer: A. -35x

Explanation: T<sub>4</sub> = 7C3 x<sup>7-3</sup> x (-1/x)<sup>3</sup> = 7C3 x<sup>4</sup> x (-1/x<sup>3</sup>) = -7C3 x = -35x.

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 →