Explain the answers in details...

$1-$Suppose that f$(0,1,2)=2\%$ and r$(0,2)=3\%$ Which of the following is$/$are true?

Select one or more alternatives:

A$-$ r$(0,1)=3\%$

B$-$The yield curve is upward$-$sloping between t$=1$ and t$=2.$

C$-$ The yield curve is downward$-$sloping between t$=1$ and t$=2.$

D$-$ r$(0,1)=4\%.$

$2-$ Which of the following statement about a semi$-$annual $5-$year Treasury bond with a coupon rate of $4\%$ is$/$are true?

Select one or more alternatives:

A$-$ It has a duration less than $5.$

B$-$ It has a duration of at least $5.$

C$-$ If its price is less than USD $100,$ its YTM is greater than $4\%$

D$-$ If its price is less than USD $100,$ its YTM is lower than $4\%$

$3-$ Suppose you are told that:The price of a semi$-$annual $2-$year fixed$-$rate bond A with a $2\%$ coupon is USD$103.$The price of a $2-$year zero$-$coupon bond B is USD$98.$What is true for the arbitrage$-$free price of a $2-$year fixed$-$rate bond C with a $4\%$ coupon?

Select one or more alternatives:

A$-$ The price of C is USD$108.$

B$-$ The price of C is USD$106.$

C$-$ The price of C is USD$105.$

D$-$ There is not enough information in the question to determine the price of C$.$