Found three challenging questions on exotic options (which I'm not sure of my answers):

Question 1: Calculate the price of a European-style exotic option with terminal payoff min(max(S2-20,0),30) using the BSM formula, where S2 denotes stock price at the end of year 2.

Question 2: In the Black-Scholes world, price a European option with a payoff of max(ST^2-K,0) at time T.

Question 3: Develop a formula for the price of a derivative paying max(ST(ST-K),0) in the Black-Scholes model.

I need your solutions guys. You're free to post your ideas (or whataver you think about these problems). Discussions are welcomed, while uploading your approach in a Word file is highly appreciated. Let's start working on it!