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Questions:

1. If matrix A = [[5, 6, 7], [8, 9, 10]] and A + B = 0, then find matrix B.
2. If [[2, 3, -3], [7, 4, -1]] * [[3], [6]] = [[13]], then find x and y.
3. The ages of Ram and Mohan are in the ratio 5:7 and the difference between their ages is 12 years. Find their ages.
4. What capital is to be invested at a rate of 6% per annum to earn Rs. 600 per month?
5. Write the 6th term of the series: 8, 40/5, 8/3, 9.
6. If A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}, find A U B.
7. Find the value of 9P2.
8. If y = 35 - 2x - x^2, find dy/dx at x = 1.
9. Prove that A(B + C) = AB + AC, given matrices A, B, and C.
10. Using mathematical induction, prove: [[1, 0], [na, 1]] for matrix A.
11. Find the rank of the matrix: [[3, -1, -2], [2, 4, 1], [-6, -3, 2]].
12. A student obtained 30% marks and failed by 45 marks, while another obtained 42% marks, which was 45 marks more than the minimum marks to pass. Find the maximum marks and minimum marks to pass.
13. Verify that A (B C) = (A B) (A C), given sets A, B, and C.
14. In how many ways can 52 cards be distributed to four players with 13 cards each?
15. The total cost function for producing x units of a product is TC = 60 - 12x + 2x^2. Find the average cost function and the level of output at which it is minimized.
16. Evaluate the integral: (1 / (x^3 - x + 3)) dx.