Investment Problems

Hi guys, I have several questions and need your help:

1. Under the Index Model, if Well-diversified Portfolio X has a beta of 1, then the standard deviation of X must be the same as the standard deviation of the index. True or false?
2. If the Capital Asset Pricing Model (CAPM) holds and the expected return of Security A is the same as the expected return of Security B, then the standard deviation of A can higher than, equal to, or lower than the standard deviation of B. True or false? 3a. Suppose all the Capital Asset Pricing Model (CAPM) assumptions hold. If you would like to earn a risk premium that is three times the market risk premium, what should you do? 3b. Unlike part (a), suppose we cannot invest more than 200% in any risky assets. Suppose all the other CAPM assumptions still hold. If you would like to earn a risk premium that is the same as part (a), what should you do now?
3. When choosing the optimal complete portfolio C* along the Capital Allocation Line (CAL), investors are trying to maximize the Sharpe ratio. True or false?
4. There are two risky securities, C and D. The standard deviation of C is lower than the standard deviation of D. If a risk-averse investor prefers holding C to holding D, then C must have a higher expected return than D. True or false?

(Note: to have more views, I put this into IB forum instead of others. Much help is appreciated. Thanks!!