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AP EAMCET201823 Apr 2018Morning ShiftMathematicsBinomial TheoremActual

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

In the expansion of (3^ 1 / 4 +7^ 1 / 6 )¹⁴⁴ General term is aligned T_ r+1 & = ¹⁴⁴ C_r (3^ 1 / 4 )^ 144-r (7^ 1 / 6 )^r & = ¹⁴⁴ C_r(3)^ 144-r 4 7^ r 6 aligned For rational terms 144-r is divisible of 4 . r=0,4,8, and r is divisible by 6 r=0,6,12, . So, common value of r will be multiple of 12 . aligned & i=0,12,24, 144 & total values of r=13 & Number of rational terms =13 aligned

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