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📐 Mathematics  ·  Binomial Theorem  ·  JEE

Find the term independent of x in (x + 1/x)⁶.

Answer: 20.

  • A 10
  • B 15
  • C 20
  • D 6

Correct answer: C. 20

Explanation: T(r+1) = 6Cr x<sup>6-r</sup> x<sup>-r</sup> = 6Cr x<sup>6-2r</sup>. For independent term: 6-2r=0, r=3. T<sub>4</sub> = 6C3 = 20.

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

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