This question makes it sound as though you are expected to know ten particular duties that a citizen has in a democracy, a list perhaps from a textbook. Since we have no way of knowing what that textbook and list might be, I will list the duties that I think should be expected of a citizen in a democracy. I am basing my response on a presumption that we are speaking of a constitutional democracy.
First, a citizen in a democracy should have the duty to vote. If it were up to me, voting would be a requirement. What is wonderful about a democracy is that we choose who will represent us. There is no point to a democracy in which we do not participate.
Second, a citizen in a democracy should have an obligation to understand the powers and duties of the government, generally set forth in a constitution. If we do not know this, the government that does not act properly has no checks upon it and can avoid carrying out its duties.
Third, a citizen in a democracy should have the responsibility of knowing his or her rights, which are also generally set forth in a constitution. If we do not know what our rights are, they are meaningless.
Fourth, a citizen in a democracy should always know who his or her representatives are. If we do not know who is representing us, we do not know whether or not that person is representing us properly, to whom we should complain if that is the case, or to whom we should state our own opinions and preferences.
Fifth, a citizen in a democracy should assume the responsibility of being informed about the issues that affect the country as a whole, for example, the economy, immigration policy, environmental policy, and foreign policy.
Sixth, a citizen in a democracy is also a citizen of the world and as such, should be informed about the major issues that affect other countries. These inevitably have an impact on the citizen. A drought in one country might mean providing foreign aid or might mean a rise in prices of a commodity that the citizen needs.
Seventh, a citizen should be concerned and informed about local conditions, those that affect him or her most directly, what a city is doing about urban blight or homeless people. This is one of the most important aspects of living in a democracy when a citizen is informed, since the information closest to home is usually the best information, and this provides one's greatest opportunity to participate in the democratic process.
Eighth, a citizen should be willing to pay taxes, since without taxes to provide a democratic government, there would be no democracy. A democracy must provide for all of its citizens.
Ninth, a citizen must have a duty to obey the law. A democracy cannot exist in a lawless society, and without the willingness of citizens to obey the law, which is really a social contract, no government has the wherewithal to police a nation of lawbreakers, and anarchy results.
Tenth, a citizen must support public education in every way possible, through the payment of taxes, through local volunteer efforts, through affording this system the respect to which it should be entitled. Public education is the foundation of democracy, meant to educate children to be responsible and knowledgeable participants in the democratic process. Education is our power to perpetuate the democracy.