{"question": "Let V be the set of all real polynomials p(x). Let transformations T, S be defined on V by T:p(x) -> xp(x) and S:p(x) -> p'(x) = d/dx p(x), and interpret (ST)(p(x)) as S(T(p(x))). Which of the following is true?", "options": ["ST = 0", "ST = T", "ST = TS", "ST - TS is the identity map of V onto itself."], "answer": "D"}
{"question": "A tank initially contains a salt solution of 3 grams of salt dissolved in 100 liters of water. A salt solution containing 0.02 grams of salt per liter of water is sprayed into the tank at a rate of 4 liters per minute. The sprayed solution is continually mixed with the salt solution in the tank, and the mixture flows out of the tank at a rate of 4 liters per minute. If the mixing is instantaneous, how many grams of salt are in the tank after 100 minutes have elapsed?", "options": ["2", "2 - e^-2", "2 + e^-2", "2 + e^-4"], "answer": "D"}
{"question": "Let A be a real 2x2 matrix. Which of the following statements must be true?\r\nI. All of the entries of A^2 are nonnegative.\r\nII. The determinant of A^2 is nonnegative.\r\nIII. If A has two distinct eigenvalues, then A^2 has two distinct eigenvalues.", "options": ["I only", "II only", "III only", "II and III only"], "answer": "B"}
{"question": "Suppose that f(1 + x) = f(x) for all real x. If f is a polynomial and f(5) = 11, then f(15/2)", "options": ["-11", "0", "11", "33/2"], "answer": "C"}
{"question": "Let A be the set of all ordered pairs of integers (m, n) such that 7m + 12n = 22. What is the greatest negative number in the set B = {m + n : (m, n) \\in A}?", "options": ["-5", "-4", "-3", "-2"], "answer": "B"}