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NDA 2 2024 Maths, question 6

Topic: Algebra

Q6

In the expansion of (1+x)p(1+x)q(1+x)^{p}(1+x)^{q}, if the coefficient of x3x^{3} is 3535, then what is the value of (p+q)(p+q)?

  1. (a) 55
  2. (b) 66
  3. (c) 77Correct answer
  4. (d) 88

Solution.

Answer: (c) 77

  1. Combine the powers to get (1+x)ⁿ with n=p+q.
  2. The coefficient is n(n−1)(n−2)/6=35.
  3. Since 7×6×5=210, n=7.
  4. The cubic factors as (n−7)(n²+4n+30)=0, and the quadratic has negative discriminant, confirming the only real value.