Operations Management:

1. Which of the following is not one of the five basic performance objectives in operations management? a) Quality b) Cost c) Innovation d) Flexibility

2. Which inventory management method aims to minimize holding costs by ordering just enough inventory to meet immediate demand? a) Just-In-Time (JIT) b) Economic Order Quantity (EOQ) c) ABC Analysis d) Safety Stock

3. Lean production principles originated from which manufacturing system? a) Toyota Production System b) Six Sigma c) Total Quality Management (TQM) d) Theory of Constraints (TOC)

4. What is the primary goal of capacity planning in operations management? a) Minimizing lead time b) Maximizing inventory levels c) Balancing demand and supply d) Reducing production costs

5. Which tool is commonly used for process mapping and identifying areas of improvement in a process? a) Pareto Chart b) Fishbone Diagram (Ishikawa Diagram) c) Control Chart d) Value Stream Map

6. Which of the following is not a component of the PDCA cycle? a) Plan b) Do c) Check d) Analyze

7. What is the primary purpose of a Gantt chart in project management? a) Cost estimation b) Resource allocation c) Schedule visualization d) Quality control

8. Which of the following is a key principle of Total Quality Management (TQM)? a) Mass production b) Employee empowerment c) High inventory levels d) Cost reduction at all costs

9. What does the acronym MRP stand for in operations management? a) Manufacturing Resource Planning b) Materials Requirement Planning c) Master Resource Planning d) Maximum Resource Production

10. Which type of forecasting method uses historical data to predict future values based on patterns and trends? a) Qualitative forecasting b) Time series forecasting c) Delphi method d) Regression analysis

1. In calculus, what is the derivative of ln(x) with respect to x? 2. Solve the differential equation dy/dx = 2x + 3, where y(0) = 1. 3. Find the limit as x approaches infinity of (e^x) / (x^2). 4. What is the Maclaurin series expansion for sin(x)? 5. Determine the eigenvalues and eigenvectors of the matrix: | 3 1 | | 1 2 | 6. Solve the system of linear equations: 2x + 3y = 8 4x - y = 5 7. Find the volume of the region bounded by the surfaces z = x^2 + y^2 and z = 4 - x^2 - y^2. 8. Evaluate the integral (x^3 + 2x^2 - 5x + 1)dx from 0 to 2. 9. What is the probability of rolling a sum of 7 with two fair six-sided dice? 10. Calculate the Taylor series expansion of e^(2x) centered at x = 1. 11. Find the arc length of the curve y = x^3/2 from x = 0 to x = 4. 12. Determine the magnitude and direction of the gradient of the function f(x, y, z) = x^2 + 2y^2 - 3z^2 at the point (1, 2, -1). 13. What is the determinant of the 3x3 matrix: | 2 1 3 | | 0 -2 1 | | -1 4 2 | 14. Solve the differential equation d^2y/dx^2 + 4y = 0, subject to the initial conditions y(0) = 1 and y'(0) = 0. 15. Determine the Taylor series expansion of ln(1 + x) centered at x = 0. 16. Find the area enclosed by the curves y = x^2 and y = 2x. 17. What is the value of the binomial coefficient C(10, 3)? 18. Solve the equation 2^(x - 1) = 8. 19. Calculate the definite integral (sin^2(x) cos^2(x))dx from 0 to /2. 20. Determine the real solutions of the equation x^3 - 3x^2 + 4x - 12 = 0.