Explanation
The highest possible transformation line, ie the transformation line with the maximum slope, is the transformation line joining the risk free rate on the y-axis and the portfolio with the maximum Sharpe ratio on the efficient frontier. This line is called the 'capital markets line'. Investors can pick any point on this line according to their risk appetite, and doing so would maximize the return they can obtain for their desired level of risk. The capital markets line is tangential to the efficient frontier. The Sharpe ratio stays constant throughout the CML. Therefore statement IV is not true, while the rest are.

Explanation
Choice 'd' represents the mean-variance function to be maximized for selecting between mutually exclusive gambles. The other choices are incorrect.
(The mean-variance criterion is a fairly complex subject, and this question is only intended to make sure that you know, and can identify the function that is being maximized. A complete explanation/derivation of the mean-variance criterion, that links together expected returns, volatility and the risk tolerance of the investor to arrive at the efficient frontier is beyond the scope of the PRM syllabus.)

Explanation
The square root of time rule can be used to convert, say a 1-day volatility to a 10-day volatility, by multiplying the known volatility number by the square root of time to get the volatility over a different time horizon.
However, there are key assumptions that underlie the application of this rule, and statements I to III correctly state those assumptions. If serial correlations (whether negative or positive) exist, then asset returns are not independent as they are affected by the prior day or prior period's returns, and we cannot use the square root of time rule. Therefore Choice 'd' is the correct answer.
In order to use the 'square root of time' rule, asset returns should be iid, volatility should stay constant (ie there should be no volatility clustering), and no serial correlations (ie the returns of one day should not be affected by the returns of the prior periods). Choice 'd' is the correct answer.

Explanation
Eurodollar deposits refer to US dollar denominated deposits outside the US, for example in a banking center such as London, and held by a non-US bank or a foreign branch of a US bank. Choice 'b' is the correct answer.

Explanation
If $x be the spot price of oil, then in order for the forward price to be $75, the following relationship must hold: ($x + $4/(1.06))*(1 + 6%) = $75. Solving, we get x = $66.98