12.   In 1900, how were members of the United States Senate chosen? 

A. They were elected by the people.
B. They were appointed by their state legislatures.
C. They were appointed by the governor of their state.
D. They were elected by the House of Representatives.

B?

Yes, you are correct. The constitution was amended in 1913 changing to direct election of senators by the people.

Right.

13.   The New Jersey plan called for 

A. a strong president.
B. abandoning the Articles of Confederation.
C. equal representation for all states in the Congress.
D. the abolition of slavery.

C? Could not find this question in my book or on any useful site's.

C is right.

http://www.u-s-history.com/pages/h369.html

19.   Suppose a bill has passed both the House and the Senate. It goes to the president at the beginning of the annual session of Congress. The president doesn't sign the bill but holds it for more than 10 days. What happens to the bill? 

A. It becomes law only if two-thirds of the House and Senate vote for it.
B. It becomes law.
C. It cannot become law, but it has not been vetoed.
D. It has been vetoed.

B?

Right -- unless the Congress adjourns within that 10-day period.

http://www.google.com/#q=president+doesn%27t+sign+bill

Yes, B is the correct answer. In 1900, members of the United States Senate were chosen by being appointed by their state legislatures.

To arrive at this answer, you could use historical knowledge or conduct a search using keywords like "how were senators chosen in 1900." This would lead you to information about the Seventeenth Amendment, which was ratified in 1913 and established the direct election of senators by the people. However, prior to that amendment, senators were chosen by state legislatures, as indicated by option B.