Explanation
Tailing the hedge refers to adjusting the number of futures contracts required to hedge a position given that futures contracts result in daily cash flows from daily P&L. In the case of forward contracts, P&L is not settled daily but at the end of the contract. Because margin payments (ie the daily P&L) for futures contracts create interest cost or income (depending upon the direction of the flows), the number of contracts required to hedge a given position can fluctuate. This effect is generally small for small positions, or where the time period under consideration is not very long. But it can get large for larger positions that are open for longer time periods, therefore requiring an adjustment to 'tail the hedge'. The adjustment is straightforward - the number of contracts required needs to be divided by (1+r)t, where r is the interest and t the time period (or by ert if continuously compounded rates are being used. Therefore statement I is true and statement II is false.
Statement III is not correct as counterparty risk is certainly an issue for forward contracts, while futures contracts are guaranteed by the exchange, besides having margin requirements and daily P&L movement in place.
Statement IV is not correct as futures come in standardized contracts with standard amounts and a few standard expiry dates to pick, whereas forward contracts are customized and dates, amounts and other details of the contract can be negotiated.

In an American option, early exercise of the option is permitted. In a European option, early exercise is not permitted. Therefore Choice 'b' is the correct answer.

Explanation
Short calls and short puts have negative gamma, ie their delta increases at a decreasing rate as the price of the underlying change. Likewise, remember that long calls and long puts have positive gamma.

Explanation
Treasury bond futures do not specify which bond can be used to effect delivery, but allow the seller to pick from a number of available bonds. As a result, one of these eligible bonds emerges as being the 'cheapest' to deliver, and this CTD bond is determined by the basis between the cash price of the bond and the futures spot price as adjusted by the conversion factor for this specific bond. (ie, basis = Cash Price of the Bond - Futures Price x Conversion Factor) The bond with the lowest basis is generally the CTD - therefore Choice 'c' is the correct answer.

Explanation
This is a trick question, no great science to it. Remember that the 'present value of a basis point' refers to PV01, which is the same as BPV (basis point value) referred to in the PRMIA handbook. In other textbooks, the same term is also variously called 'DV01' (dollar value of a basis point). Remember these other terms too.
PV01, or the present value of a basis point, is the change in the value of a bond (or other fixed income security) from a 1 basis point change in the yield. PV01 is calculated as (Price * Modified Duration/10,000).