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JEE Main20248 Apr 2024Evening ShiftMathematicsBinomial TheoremActual

If the term independent of x in the expansion of ( a x^2+ 1 2 x^3 )¹⁰ is 105 , then a ^2 is equal to :

Options

  1. A2
  2. B4
  3. C6
  4. D9

Correct answer

B. 4

Step-by-step solution

( a x ^2+ 1 2 x ^3 )¹⁰ General term = ¹⁰ C _ r ( a x ^2 )^ 10- r ( 1 2 x ^3 )^ r aligned & 20-2 r-3 r=0 & r =4 & ¹⁰ C ₄ a ^3 1 16 =105 & a ^3=8 & a ^2=4 aligned SECTION - B

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