Q$1)$ In project management, the Critical Path Method $($CPM$)$ is used to:

A$)$ Estimate the shortest possible time to complete the project

B$)$ Manage the project budget

C$)$ Evaluate team performance

D$)$ Identify project risks

Q$2)$ Which of the following is not a primary objective of operations management?

a$)$ Cost reduction

b$)$ Quality improvement

c$)$ Market expansion

d$)$ Efficiency enhancement

Q$3)$ In the context of supply chain management, which inventory strategy aims to maintain a safety stock to meet unexpected demand fluctuations?

a$)$ Just$-$in$-$time $($JIT$)$

b$)$ Economic Order Quantity $($EOQ$)$

c$)$ Reorder Point $($ROP$)$

d$)$ Lean manufacturing

Q$4)$ Which of the following is a key performance indicator $($KPI$)$ commonly used to measure manufacturing efficiency?

a$)$ Customer satisfaction

b$)$ Return on investment $($ROI$)$

c$)$ Overall equipment effectiveness $($OEE$)$

d$)$ Employee turnover rate

Q$5)$ Lean production principles emphasize the elimination of:

a$)$ Product variety

b$)$ Customer demand

c$)$ Waste $($Muda$)$

d$)$ Inventory turnover

Q$6)$ What is the primary purpose of a Gantt chart in project management?

a$)$ Resource allocation

b$)$ Risk analysis

c$)$ Time scheduling

d$)$ Cost estimation

Q$7)$ Which quality management technique focuses on improving processes by using statistical methods to reduce variation?

a$)$ Six Sigma

b$)$ Total Quality Management $($TQM$)$

c$)$ Kaizen

d$)$ Just$-$in$-$time $($JIT$)$

Q$8)$ Which type of layout arranges workstations and machines in a sequence to produce a specific product?

a$)$ Process layout

b$)$ Cellular layout

c$)$ Product layout

d$)$ Functional layout

Q$9)$ When using the ABC analysis method for inventory management, which category typically includes high$-$value items with the highest priority for control?

a$)$ A items

b$)$ B items

c$)$ C items

d$)$ D items

Q$10)$ Which production scheduling method aims to balance production lines and optimize resource utilization?

a$)$ First$-$Come$-$First$-$Served $($FCFS$)$

b$)$ Shortest Job First $($SJF$)$

c$)$ Theory of Constraints $($TOC$)$

d$)$ Critical Path Method $($CPM$)$

Q$11)$ Which of the following is the correct formula for calculating the volume of a sphere?

A$)$ V $=\backslash$pi r$^2$

B$)$ V $=4/3\backslash$pi r$^3$

C$)$ V $=2\backslash$pi rh

D$)$ V $=1/2\backslash$pi r$^2$

Q$12)$ In calculus, which of the following is the derivative of the function f$($x$)=$ e$^$x$?$

A$)$ f$\text{'}($x$)=$ ln$($x$)$

B$)$ f$\text{'}($x$)=$ x

C$)$ f$\text{'}($x$)=$ e$^$x

D$)$ f$\text{'}($x$)=1$

Q$13)$ When solving a quadratic equation of the form ax$^2+$ bx $+$ c $=0,$ which formula should be used to find the roots?

A$)$ Discriminant formula: x $=(-$b $\backslash$pm $($b$^2-4$ac$))/(2$a$)$

B$)$ Vertex formula: x $=-$b $/(2$a$)$

C$)$ Factoring

D$)$ Completing the square

Q$14)$ Which trigonometric function represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle?

A$)$ Sine $($sin$)$

B$)$ Cosine $($cos$)$

C$)$ Tangent $($tan$)$

D$)$ Secant $($sec$)$

Q$15)$ In linear algebra, which matrix operation results in a scalar $($single value$)$ rather than a matrix?

A$)$ Matrix addition

B$)$ Matrix multiplication

C$)$ Determinant

D$)$ Inverse

Q$16)$ Which theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides?

A$)$ Pythagorean theorem

B$)$ Law of Sines

C$)$ Law of Cosines

D$)$ Heron's Formula

Q$17)$ Which branch of mathematics focuses on the study of sets and their properties, including operations like union and intersection?

A$)$ Calculus

B$)$ Number theory

C$)$ Set theory

D$)$ Topology

Q$18)$ Which of the following is NOT a type of conic section?

A$)$ Parabola

B$)$ Hyperbola

C$)$ Ellipse

D$)$ Spiral

Q$19)$ Which mathematical constant is approximately equal to $3\mathrm{.}14159$ and represents the ratio of a circle's circumference to its diameter?

A$)$ e

B$)\backslash$pi $($pi$)$

C$)2($square root of $2)$

D$)\backslash$phi $($phi$)$

Q$20)$ Which famous conjecture, named after a $19$th$-$century mathematician, deals with the distribution of prime numbers and remains unsolved to this day?

A$)$ Goldbach's conjecture

B$)$ Poincar$$ conjecture

C$)$ Fermat's Last Theorem

D$)$ Riemann hypothesis

$21$ Which statistical test is most appropriate for comparing the means of three or more independent groups: a$)$ t$-$test, b$)$ ANOVA, c$)$ chi$-$squared test, or d$)$ Mann$-$Whitney U test?

$22$ In a binomial distribution, if the probability of success $($p$)$ decreases while the number of trials $($n$)$ remains constant, what happens to the shape of the distribution? a$)$ It becomes more skewed, b$)$ It becomes more symmetric, c$)$ It remains unchanged, or d$)$ It becomes normal.

$23$ When performing a hypothesis test, if you decrease the significance level $($alpha$)$ from $0\mathrm{.}05$ to $0\mathrm{.}01,$ what is the impact on the likelihood of making a Type I error? a$)$ Increases, b$)$ Decreases, c$)$ Stays the same, or d$)$ Depends on the sample size.