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AP EAMCET202018 Sep 2020Morning ShiftMathematicsBinomial TheoremActual

In the expansion of (( [5] 3 + [3] 2 )¹⁵ )

Options

  1. ANumber of rational terms is 3
  2. BSum of all rational terms is 58
  3. CSum of all rational terms is greater than the sum of all irrational terms
  4. DSum of all irrational terms is greater than the sum of all rational terms

Correct answer

D. Sum of all irrational terms is greater than the sum of all rational terms

Step-by-step solution

Given binomial is (( [5] 3 + [3] 2 )¹⁵ ) ( ) The general term (T_ r+1 = ¹⁵ C_r 3^ 15-r 5 2^ r 3 ) (= ¹⁵ C_r 3^ 3-r / 5 2^ 1 / 3 ) For rational terms (r ) must be multiple of 15 , so possible values of (r=0 ) and (15 ( 0 r 15) ) ( ) Sum of rational terms (= ¹⁵ C₀ 3^3+ 15 15 2^5 ) (=27+32=59. ) ( ) The sum of all irrational terms is greater than the sum of all rational terms.

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