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NDA2024MathematicsBinomial TheoremActual

If the 4th term in the expansion of (m x+ 1 x )^n is 5 2 , then that is the value of m n ?

Options

  1. A-3
  2. B3
  3. C6
  4. D12

Correct answer

B. 3

Step-by-step solution

aligned T ₄ & = T ₃+1 & = ^n C ₃(m x)^ n-3 ( 1 x )^3= 5 2 5 2 x^0 & = ^n C ₃(m)^ n-3 x^ n-6 aligned On comparing the power of x aligned & n-6=0 & n=6 & and ^6 C ₃ m^3= 5 2 & 6.5 .4 3.2 m^3= 5 2 & 20 m^2= 5 2 & m^3= 1 8 & m= 1 2 & m n= 1 2 6=3 . aligned

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