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NDA 1 2024 Maths, question 31

Topic: Algebra

Q31

If the 4th term in the expansion of (mx+1x)n(mx+\frac{1}{x})^{n} is 52\frac{5}{2}, then what is the value of mnmn ?

  1. (a) −3-3
  2. (b) 33Correct answer
  3. (c) 66
  4. (d) 1212

Solution.

Answer: (b) 33

  1. The fourth term is C(n,3)(mx)ⁿ⁻³x⁻³=C(n,3)mⁿ⁻³xⁿ⁻⁶.
  2. For this term to be the constant 5/2, n=6 and 20m³=5/2.
  3. Thus m=1/2 and mn=3.