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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

The number of rational terms in the expansion of 3 1 4 + 7 1 6 144 is

Options

  1. A33
  2. B23
  3. C12
  4. D13

Correct answer

D. 13

Step-by-step solution

Let, S = 3 1 4 + 7 1 6 144 General term of S is given by T r + 1 = C r 144   3 144 - r 4 7 r 6 Now, for the rational terms 144 - r 4 ∈ W whole number For this r must be the multiple of 4 therefore r = 0 ,   4 ,   8 ,   . . . ,   140 ,   144 And, r 6 ∈ W whole number For this r must be the multiple of 6 therefore r = 0 ,   6 ,   12 ,   18 ,   24 ,     . . . . . ,   138 ,   144 Now, common terms are 0 ,   12 ,   24 ,

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