Remember how exchange rates are generally quoted. Most exchange rates are quoted in terms of how many foreign currencies does USD 1 buy. Therefore, a rate of 99 for the JPY means that USD 1 is equal to JPY 99.
These are called 'direct rates'. However, there are four major world currencies where the rate quote convention is the other way round - these are EUR, GBP, AUD and NZD. For these currencies, the FX quote implies how many US dollars can one unit of these currencies buy. So a quote of "1.1023" for the Euro means EUR 1 is equal to USD 1.1023 and not the other way round.

Explanation
The effectiveness of the hedge is solely determined by the correlation between the position being hedged, and the position being used as the hedge. A hedge can be perfect when correlation is 1, and will be less than perfect when it is anything other than 1.The effectiveness of the optimal hedge is given by the formula (1-2), where is the correlation between the two. Therefore Choice 'a' is the correct answer. Standard deviations affect the hedge ratio, not the effectiveness of the hedge.
(Note: In other texts, hedge effectiveness is explained to be measured by , which is essentially the same as (1-
2), both expressions being functions of . You can use either, being aware that one measures the variance explained, and the other is a measure of the unexplained variance.)

Explanation
Gamma risk is unique to options. Therefore gamma risk can only be hedged using options, and Choice 'a', ie an option position that offsets any existing gamma in the portfolio, is the only way to hedge gamma.
Positions in stock or bank deposits do not carry gamma and therefore cannot be used to hedge gamma risk.

Explanation
In terms of beta, his exposure is $10m*0.7 = $7m. This exposure is long. In order order to neutralize his long exposure, he needs to have an equal an identical short position with the same beta as this long position (of course, in the short direction). We need to figure out how many contracts will have a beta equal to his held position. (The beta of a futures contract is slightly different from 1 when compared to spot, but in the absence of other information in the question it is always okay to assume that the beta of the futures contract is 1. Such precision does not matter because of other errors such as rounding etc that cannot be anyway done away with.) He needs to short futures contracts on the index with $7m in notional value. The value of each contract is currently 1000*250 =$250,000. He therefore needs to short $7m/$250,000 = 28 contracts to become market or beta neutral.