Explanation
There are two ways to think about this question: First, because the asset manager thinks that interest rates are going to decline, his profit will be maximized if he buys the bond with the greatest duration. The zero coupon bond has the greatest duration among the alternatives listed. Therefore Choice 'c' is the correct answer.
The second way to look at this question is to consider what is called 'reinvestment risk'. Yields to maturity calculations have an implicit assumption that any cash flows received prior to maturity are investible at the ytm rate. Thus, an yield to maturity calculation for a coupon bearing bond assumes that coupon payments get invested at the same rate as the calculated ytm from the time they are received till the time the bond matures.
In an environment where interest rates fall, this assumption will not hold true. Reinvestment risk is the risk that coupons will not be able to earn the ytm that the bond was brought at - and the investor will be at a loss to the extent the money does not earn the ytm rate till the end of the investment. One way to reduce reinvestment risk is to minimize coupon receipts so the money stays invested as part of the bond, and the zero coupon bond helps to do exactly that.

Explanation
The zero coupon spot rate for 4 years can be calculated as = (1.02*1.03*1.04*1.05)^(1/4) - 1 = 3.49%, which is the correct answer. (3.50% is just the mathematical average of the rates for the four years and is not correct, even though close.)

Explanation
Statement I is not correct because the 4% bond with the same modified duration as the zero coupon bond will have a maturity much later in the future than the zero coupon, and the final repayment coming much later will cause its convexity to be greater than the equivalent duration zero coupon bond.
Statement II is not correct as the convexity of a bond increases not in a linear fashion but in proportion to the square root of time as the maturity of the bond is increased.
Statement III is not correct as mortgage based bonds bring negative convexity even in the case of long positions, Statement IV is not correct as the duration of a zero coupon bond maturing in 10 years has a modified duration greater than that of a coupon bearing bond of the same maturity, which means its convexity is higher and not lower (note this is different from statement I where the modified durations were identical. Here, the maturity is identical which has different implications.) Therefore none of the statements is correct and Choice 'd' is the correct answer.

Notional principals are not exchanged at the start and the end of an FRA. In fact, if the notional principals were to be exchanged, it would increase credit risk and not decrease it by introducing settlement risk.
Therefore Choice 'd' is incorrect.
All other choices correctly describe various aspects of an FRA.