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JEE Main202529 Jan 2025Morning ShiftMathematicsBinomial TheoremActual

The least value of n for which the number of integral terms in the Binomial expansion of (( [3] 7 + [12] 11 )^ n ) is 183, is :

Options

  1. A2184
  2. B2196
  3. C2148
  4. D2172

Correct answer

A. 2184

Step-by-step solution

aligned & General term = ^ n C _ r 7^ 1 / 3 ^ n - r (11^ 1 / 12 )^ r & = ^ n C _ r 7 ^ n - r 3 (11)^ r / 12 aligned For integral terms, r must be multiple of 12 r =12 k , k ~W Total values of r=183 Hence r=12(182)=2184 Min value of n=2184

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