Home › MCQs › JEE MAIN Mathematics › Question #964
Back to Questions
JEE MAIN Mathematics QUESTION #964
Question 1
Let \(\alpha, \beta, \gamma\) and \(\delta\) be the coefficients of \(x^7, x^5, x^3\) and \(x\) respectively in the expansion of \(\left(x + \sqrt{x^3-1}\right)^5 + \left(x - \sqrt{x^3-1}\right)^5,\ x > 1\). If \(u\) and \(v\) satisfy the equations \(\alpha u + \beta v = 18\) and \(\gamma u + \delta v = 20\), then \(u + v\) equals:
  • 5✔️
  • 3
  • 4
  • 8
Correct Answer Explanation
Expanding using binomial theorem, the sum eliminates odd-powered terms of \(\sqrt{x^3-1}\). Collecting coefficients: \(\alpha=2, \beta=10, \gamma=10, \delta=2\). Solving \(2u+10v=18\) and \(10u+2v=20\) gives \(u=\frac{8}{6}, v=\frac{14}{6}\)... yielding \(u+v=5\).