Mathematics AA: BINOMIAL THEOREM Topical Past Paper Questions

[Maximum mark: 5] In the expansion of $ \left(\sqrt{x} + k\right)^{12} $ where $ k \in \mathbb{Z} $, the coefficient of the term in $ x^{\frac{3}{2}} $ is -112640. Find the value of k.

[Maximum mark: 4] Find the coefficient of $ x^{6} $ in the expansion of $ (2x-5)^{9} $.

[Maximum mark: 6] The binomial expansion of $ (1 + kx)^n $ is given by $ 1 + 12x + 28k^2x^2 + \ldots + k^nx^n $ where $ n \in \mathbb{Z}^+ $ and $ k \in \mathbb{Q} $. Find the value of $n$ and the value of $k$.