Operations Management:

$2.$ 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 $=2$x $+3,$ 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:

$|31|$

$|12|$

$6.$ Solve the system of linear equations:

$2$x $+3$y $=8$

$4$x $-$ 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$^3+2$x$^2-5$x $+1)$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$^(2$x$)$ 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$^2+2$y$^2-3$z$^2$ at the point $(1,2,-1).$

$13.$ What is the determinant of the $3$x$3$ matrix:

$|213|$

$|0-21|$

$|-142|$

$14.$ Solve the differential equation d$^2$y$/$dx$^2+4$y $=0,$ subject to the initial conditions y$(0)=1$ and y$\text{'}(0)=0.$

$15.$ 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 $=2$x$.$

$17.$ 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 $\backslash$pi $/2.$

$20.$ Determine the real solutions of the equation x$^3-3$x$^2+4$x $-12=0.$