CAIE P1 2020 November — Question 5

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionNovember
TopicBinomial Theorem (positive integer n)
TypeRatio of coefficients condition

5 In the expansion of \(\left( 2 x ^ { 2 } + \frac { a } { x } \right) ^ { 6 }\), the coefficients of \(x ^ { 6 }\) and \(x ^ { 3 }\) are equal.
  1. Find the value of the non-zero constant \(a\).
  2. Find the coefficient of \(x ^ { 6 }\) in the expansion of \(\left( 1 - x ^ { 3 } \right) \left( 2 x ^ { 2 } + \frac { a } { x } \right) ^ { 6 }\).