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📐 Mathematics  ·  Binomial Theorem  ·  JEE

If the coefficients of 2nd and 3rd terms in (1+x)ⁿ are in ratio 1:2, find n.

Answer: 5.

  • A 3
  • B 6
  • C 4
  • D 5

Correct answer: D. 5

Explanation: nC<sub>1</sub> : nC<sub>2</sub> = 1:2. n/(n(n-1)/2) = 1/2. 2/(n-1) = 1/2. n-1 = 4, n = 5.

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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