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AP EAMCET201823 Apr 2018Evening ShiftMathematicsBinomial TheoremActual

If = 5 2 ! 3 + 5 7 3 ! 3^2 + 5 7 9 4 ! 3^3 + . , then ^2+4 =

Options

  1. A21
  2. B23
  3. C25
  4. D27

Correct answer

B. 23

Step-by-step solution

Since, aligned (1+x)^n=1+n x+ & n(n-1) 2 ! x^2+ n(n-1)(n-2) 3 ! x^3 & + n(n-1)(n-2)(n-3) 4 ! x^4+ aligned On comparing n(n-1) 2 ! x^2= 5 2 ! 3 and n(n-1)(n-2) 3 ! x^3= 5 7 3 ! 3^2 So, x=- 2 3 and n=-3 / 2 array ll (1-2 / 3)^ -3 / 2 =1+1+ & 3^ 3 / 2 =2+ ^2+4 +4=27 & ^2+4 =23 array

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