15. Which of the following is NOT a major component of the Six Sigma methodology? a) Define b) Measure c) Analyze d) Optimize 16. What is the primary objective of demand forecasting in operations management? a) To control production costs b) To meet customer demand c) To maximize inventory levels d) To reduce lead times 17. Which production scheduling technique aims to prioritize jobs based on their due dates and processing times? a) First-come, first-served (FCFS) b) Shortest job first (SJF) c) Earliest due date (EDD) d) Critical path analysis (CPA) 18. What does the acronym "ERP" stand for in the context of operations management? a) Enterprise Resource Planning b) Effective Resource Procurement c) Efficient Resource Production d) Enterprise Risk Planning 19. Which of the following is a key principle of sustainability in operations management? a) Minimizing waste generation b) Maximizing resource consumption c) Ignoring environmental regulations d) Focusing solely on short-term profits a) Agile manufacturing b) Vendor-managed inventory (VMI) c) Service level agreement (SLA) d) Just-in-time (JIT) inventory management 1. Find the derivative of f(x)=3x42x3+5x27x+9 with respect to x. 2. Solve the integral (2x2+3x+1)dx. 3. Determine the limit lim(x0)(sin(3x)/x). 4. Find the eigenvalues and eigenvectors of the matrix A=[12,1],[4,3]. 5. Calculate the volume of the solid formed by rotating the region bounded by y=x2 and the x-axis about the y-axis. 6. Solve the differential equation dy/dx=2x2+3x1. 7. Evaluate the double integral (x2+y2)dA over the region bounded by the circle x2+y2=4. 8. Determine the Taylor series expansion of f(x)=ln(x) centered at x=1. 9. Compute the determinant of the 44 matrix given by the Pascal's triangle pattern. 10. Find the global maximum and minimum of the function f(x)=x36x2+9x+2 on the interval [0, 4]. 11. Solve the recurrence relation a(n)=2a(n1)3a(n2) with initial conditions a(0)=1 and a(1)=4. 12. Determine the radius of convergence for the power series (3nxnl), where n ranges from 0 to infinity. 13. Compute the curl of the vector field F(x,y,z)=(2xy+z2)i+(x2+3yz)j+(xyzy2)k. 14. Find the equation of the plane that is perpendicular to the vector (2,1,3) and passes through the point (1,2,1). 15. Solve the system of linear equations: 2x+3yz=7x2y+2z=43x+y3z=1 16. Determine the nth term of the Fibonacci sequence using the closed-form expression involving the golden ratio. 17. Find the principal value of arctan(3). 18. Calculate the Laplace transform of the function f(t)=e(2t)sin(3t). 19. Evaluate the triple integral (x2+y2+z2)dV over the region bounded by the sphere x2+ y2+z2=9 20. Determine the number of ways to arrange the letters of the word "MATHEMATICS" such that no two vowels are adjacent. 1. In calculus, what is the limit of (sin(x))/x as x approaches 0 ? 2. Solve the differential equation: dy/dx=2x2+3x1. 3. Find the eigenvalues of the 33 matrix: {{2,1,0},{1,3,1},{0,1,4}}. 4. Calculate the derivative of the function f(x)=ln(x2+1). 5. What is the volume of the region bounded by the surfaces z=x2+y2 and z=4x2y2 ? 6. Evaluate the integral (cos3(x)sin(x))dx. 7. Determine the Taylor series expansion of ex centered at x=2. 8. What is the solution to the system of linear equations: 2x+3y=7 and 4x2y=6 ? 9. Find the maximum and minimum values of the function f(x)=x33x2+4x on the interval [1,3]. 10. Calculate the gradient of the scalar field (x,y,z)=x2+2y23z2. 11. Prove the Pythagorean theorem using geometry and algebra. 12. Determine the radius of convergence for the power series (n2xn), where n ranges from 0 to infinity. 13. Solve the recurrence relation: a(n+2)5a(n+1)+6a(n)=0 with initial conditions a(0)=1 and a(1)= 3. 14. Find the inverse Laplace transform of F(s)=(2s+3)/(s2+4s+5). 15. What is the area enclosed by the curve y=ex, the x-axis, and the lines x=0 and x=2 ? 16. Determine the modulus and argument of the complex number z=3+4i. 17. Given a triangle with sides of lengths a=5,b=7, and c=9, find the area of the triangle. 18. Solve the Diophantine equation 6x+9y=15 for integer values of x and y. 19. Calculate the determinant of the 44 matrix: {{1,2,3,4}, {5,6,7,8}, {9,10,11,12}, {13,14,15,16}}. 20. Determine the integral of the function f(x,y,z)=x2+2y2+3z2 over the region bounded by the sphere x2+y2+z2=4