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AP EAMCET202419 May 2024Evening ShiftMathematicsBinomial TheoremActual

Numerically greatest term in the expansion of (5+3 x)^6 , when x=1 . is

Options

  1. A3^5 5^3
  2. B3^3 5^5
  3. C3^2 5^5
  4. D3^4 5^4

Correct answer

B. 3^3 5^5

Step-by-step solution

Let T_ r +1 be the greatest term so, T_ r+1 T_r 1 aligned & ^6 C_r(5)^ 6-r (3 x)^r ^6 C_ r-1 (5)^ 6-r+1 (3 x)^ r-1 1 & (r-1)!(7-r)! r! (6-r)! 5^6 5^ -r 3^r x^r 5^7 5^ -r 3^ r-1 x^ r-1 1 aligned 7-r r 3 x 5 1 3(7-r) 5 r 1 ( at, x=1) r 21 8 So, r=2 Now, T_ 2+1 = ^6 C₂(5)⁶⁻²(3 x)^2=3^3 5^5 . ( at x=1)

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