MATH RC FULL

RC 1 — Question 1 (PDF page 1) For the parametric equations x = cos t, y = sin t, as t increases from 0 to 2π, the particle moves: A) Along a straight line B) Clockwise around the unit circle C) Counterclockwise around the unit circle D) Back and forth along a diameter

C) Counterclockwise around the unit circle

RC 1 — Question 2 (PDF page 1) Which differential equation represents a simple harmonic oscillator with no damping? A) m(dx/dt) + kx = 0 B) m(d²x/dt²) + c(dx/dt) = 0 C) m(d²x/dt²) = c(dx/dt) D) m(d²x/dt²) + kx = 0

D) m(d²x/dt²) + kx = 0

RC 1 — Question 3 (PDF page 1) The growth of money in a bank account with continuously compounded interest is modeled by: A) dM/dt = r²M B) dM/dt =r C) dM/dt=M-r D) dM/dt = rM

D) dM/dt = rM

RC 1 — Question 4 (PDF page 1) The concentration of a reactant is modeled by C(x, t) = 3x² + 5t². What does ∂C/∂t represent? A) Total concentration B) Rate of concentration change with time C) Reaction equilibrium constant D) Change of concentration with distance

B) Rate of concentration change with time

RC 1 — Question 5 (PDF page 1) Why is Simpson’s Rule often preferred in engineering applications? A) It uses straight-line approximation B) It fits parabolas, reducing curvature error C) It requires fewer data points D) It is easier to compute

B) It fits parabolas, reducing curvature error

RC 1 — Question 6 (PDF page 2) If f(x) > 0 for all x in an interval, the curve is: A) Decreasing B) Concave downward C) Concave upward D) Increasing

C) Concave upward

RC 1 — Question 7 (PDF page 2) If an object cools according to Newton's law, when will it cool the fastest? A) When object temperature equals room temperature B) After infinite time C) At the beginning of cooling D) At steady state

C) At the beginning of cooling

RC 1 — Question 8 (PDF page 2) If the electric potential is constant along a curve, then the electric field is: A) Parallel to the x-axis B) Tangent to the curve C) Zero everywhere D) Perpendicular to the curve

D) Perpendicular to the curve

RC 1 — Question 9 (PDF page 2) A researcher studies the effect of fertilizer type and irrigation level on crop yield. Which analysis is MOST appropriate? A) One-way ANOVA B) Paired t-test C) Two-way ANOVA D) Regression only

C) Two-way ANOVA

RC 1 — Question 10 (PDF page 2) In a two-way ANOVA, the interaction between machine type and operator is found to be significant. What does this imply? A) Operator has no effect B) Experimental error is large C) Machine type has no effect D) Effect of one factor depends on the other

D) Effect of one factor depends on the other

RC 1 — Question 11 (PDF page 2) The energy stored in an electric field is obtained by integrating: A) Electric field intensity B) Voltage C) Current D) Power density

D) Power density

RC 1 — Question 12 (PDF page 3) A discrete-time system has input x[n] = u[n] (unit step), and its Z-transform is X(z). What is X(z)? A) 1/(z - 1) B) z/(z - 1) C) z-1 D) 1/(1 - z)

B) z/(z - 1)

RC 1 — Question 13 (PDF page 3) [REVIEW: Formula/superscript requires review] A falling object experiences air resistance proportional to velocity. Which differential equation models this? A) m(dv/dt) = kv B) m(dx/dt) = mg C) m(d?x/dt?) = mg D) m(dv/dt) - mg - kv

D) m(dv/dt) - mg - kv

RC 1 — Question 14 (PDF page 3) In motion along a line, the third derivative of position represents: A) Velocity B) Jerk C) Acceleration D) Snap

B) Jerk

RC 1 — Question 15 (PDF page 3) A chemical plant wants to maximize yield while minimizing cost by adjusting pressure, temperature, and catalyst concentration. The main purpose of DOE here is to: A) Optimize process performance B) Inspect finished products C) Reduce sample size D) Monitor process stability

A) Optimize process performance

RC 1 — Question 16 (PDF page 3) A point where f'(x) = 0 is called a: A) Asymptote B) Point of inflection only C) Turning point only D) Stationary point

D) Stationary point

RC 1 — Question 17 (PDF page 4) [REVIEW: Formula/superscript requires review] Which system is modeled by m(d?x/dt?) + c(dx/dt) + kx = 0? A) Undamped vibration B) Forced vibration C) Damped vibration D) Simple harmonic motion

C) Damped vibration

RC 1 — Question 18 (PDF page 4) If f(x) < 0 for all x in an interval, the function is: A) Constant B) Decreasing C) Increasing D) Periodic

B) Decreasing

RC 1 — Question 19 (PDF page 4) In a construction study, ANOVA shows no significant difference in compressive strength among three concrete mixes. What is the BEST interpretation? A) Differences are due to random variation B) Experimental error is zero C) All mixes are identical D) Sample size is infinite

A) Differences are due to random variation

RC 1 — Question 20 (PDF page 4) Years of experience X and annual salary Y satisfy: cor(X, Y) = 1. Which of the following is true? A) Salary is unrelated to experience B) Salary increases linearly with experience C) Salary increases exponentially with experience D) Experience causes salary increase

B) Salary increases linearly with experience

RC 1 — Question 21 (PDF page 4) Third derivative of voltage w.r.t. time corresponds to: A) Curvature B) Rate of change of curvature C) Energy D) Slope

B) Rate of change of curvature

RC 1 — Question 22 (PDF page 4) Which setup is INVALID for volume about the y-axis? A) Washer using dx B) Shell using dx C) Disk method using dy D) Washer using dy

A) Washer using dx

RC 1 — Question 23 (PDF page 5) In kinematics, the second derivative of displacement with respect to time represents: A) Momentum B) Jerk C) Velocity D) Acceleration

D) Acceleration

RC 1 — Question 24 (PDF page 5) [REVIEW: Formula/superscript requires review] The function f(x) = 2x? - 3x + 1 is defined for all real x. Which statement is correct? A) The absolute maximum occurs at x =- 1. B) The absolute maximum occurs at x = 1. C) The function has a local maximum but no absolute maximum. D) The function has an absolute maximum and minimum.

C) The function has a local maximum but no absolute maximum.

RC 1 — Question 25 (PDF page 5) Fuel consumption rate f(t)(L/hr) is measured at equal intervals. Which statement is most accurate? A) Simpson's Rule can be applied with unequal intervals B) Simpson's Rule requires an even number of subintervals C) Trapezoidal Rule requires an odd number of subintervals D) Trapezoidal Rule is always more accurate than Simpson's Rule

B) Simpson's Rule requires an even number of subintervals

RC 2 — Question 1 (PDF page 6) To measure the correlation between X and Y while removing the effect of Z, which method is used? A) Partial correlation B) Multiple regression C) Simple correlation D) Spearman correlation

Partial correlation

RC 2 — Question 2 (PDF page 6) Which statement best describes the difference between control elements and designed elements? A) Control elements are intentional variations, designed elements are standard features B) Both are the same C) Designed elements increase defects D) Designed elements are standard features, control elements maintain process stability

Designed elements are standard features, control elements maintain process stability

RC 2 — Question 3 (PDF page 6) Near a discontinuity, the Fourier series approximation exhibits: A) Infinite oscillations B) Exponential decay C) Complete cancellation D) Finite overshoot that does not vanish

Finite overshoot that does not vanish

RC 2 — Question 4 (PDF page 6) The primary purpose of a screening experiment in DOE is to: A) Measure the cost of the process B) Identify non-influential variables C) Increase process variability D) Randomly select variables

Identify non-influential variables

RC 2 — Question 5 (PDF page 6) Which statement is TRUE regarding designed elements and randomization? A) Designed elements and randomization are unrelated B) Randomization increases process variability C) Designed elements eliminate the need for randomization D) Randomization is used within designed elements to reduce bias

Randomization is used within designed elements to reduce bias 𝑥↑⇒ln(𝑥) 𝑔𝑟𝑜𝑤𝑠 𝑚𝑜𝑟𝑒 𝑠𝑙𝑜𝑤𝑙𝑦 In systematic sampling, items are selected at regular intervals after choosing a random starting point. energy stored by a capacitor 𝐸= 1 2 𝐶𝑣 2(𝑡) Inductor: 𝐸= 1 2 𝐿𝐼 2 Trapezoidal → exact through degree 1 Simpson → exact through degree 3 Both exact → linear functions Simpson uses parabolic interpolation. Trapezoidal – linear Good process design → variability ↓ Variability → consistency ↓ ↑ Robust design → less sensitivity to noise

RC 2 — Question 6 (PDF page 7) If T(x) is the temperature distribution along a rod, what does dT/dx physically represent? A) Heat flow rate B) Temperature C) Temperature gradient D) Thermal energy

Temperature gradient

RC 2 — Question 7 (PDF page 7) If a periodic signal x(t) is even, which Fourier series coefficients are nonzero? A) Neither sine nor cosine terms B) Both sine and cosine terms C) Only cosine terms D) Only sine terms

Only cosine terms

RC 2 — Question 8 (PDF page 7) Which distribution property best captures rare but impactful events? A) Heavy-tailed B) Binomial C) Uniform D) Thin-tailed (Gaussian)

Heavy-tailed

RC 2 — Question 9 (PDF page 7) Which statement about IVP (Initial Value Problem) and BVP (Boundary Value Problem) is TRUE? A) IVPs always have multiple solutions B) BVPs always have unique solutions C) IVPs may fail to have a solution D) BVPs may have no solution or multiple solutions

BVPs may have no solution or multiple solutions

RC 2 — Question 10 (PDF page 7) A voltage across the capacitor in a series RLC circuit is observed to oscillate and gradually decrease in amplitude after the circuit is energized. Which damping condition is present? A) Critically damped B) Overdamped C) Underdamped D) No damping

Underdamped

RC 2 — Question 11 (PDF page 8) For a convex upward function (f”(x) > 0), which statement is TRUE? A) Both overestimate equally B) Trapezoidal overestimates; Simpson's is closer C) Trapezoidal underestimates; Simpson's overestimates D) Both underestimate equally

Trapezoidal overestimates; Simpson's is closer

RC 2 — Question 12 (PDF page 8) Which of the following is best modeled by a first-order differential equation? A) Charging of a capacitor B) Pendulum motion C) LC oscillations D) Mechanical resonance

Charging of a capacitor

RC 2 — Question 13 (PDF page 8) In an experiment testing two machining speeds on surface roughness, the operator is treated as a blocking factor. ANOVA results: A. Operator: not significant B. Machining speed: significant What does this indicate? A) Operator differences dominate surface roughness. B) Blocking failed because the block effect was not significant. C) Both speed and operator are equally important. D) Machining speed affects surface roughness, operator differences are minor.

Machining speed affects surface roughness, operator differences are minor.

RC 2 — Question 14 (PDF page 8) [REVIEW: Formula/superscript requires review] A series RLC circuit with R? > 4L/C shows: A) Non-oscillatory exponential decay B) Constant current C) Oscillatory current D) Sudden jump in current

Non-oscillatory exponential decay

RC 2 — Question 15 (PDF page 8) Which engineering problem is most commonly modeled as a BVP (Boundary Value Problem)? A) Deflection of a beam with fixed ends B) Speed of a vehicle from rest C) Transient current in an RL circuit D) Charging of a capacitor

Deflection of a beam with fixed ends

RC 2 — Question 16 (PDF page 9) A planar loop of wire encloses a region R in the xy-plane. To compute the total circulation of a 2D vector field F = Pi + Qj along the loop, which theorem allows converting a line integral around the loop to an area integral over R? A) None of the choices B) Gauss’s Divergence Theorem C) Stokes’ Theorem D) Greens Theorem

Green's Theorem

RC 2 — Question 17 (PDF page 9) A second-order ODE requires how many boundary/initial conditions? A) 3 B) 1 C) Depends on linearity D) 2

2

RC 2 — Question 18 (PDF page 9) [REVIEW: Formula/superscript requires review] A falling object experiences drag proportional to velocity squared: m(dv/dt) = mg - kv?. Which of the following statement is true? A) Terminal velocity exists and is finite. B) Terminal velocity does not exist. C) Velocity grows without bound. D) Motion is oscillatory.

Terminal velocity exists and is finite.

RC 2 — Question 19 (PDF page 9) A quality engineer wants to ensure every resistor in a batch has an equal chance of being selected. Which method should they use? A) Snowball sampling B) Random sampling C) Judgment sampling D) Convenience sampling

Random sampling

RC 2 — Question 20 (PDF page 9) A chemical engineer measures the concentration of a solution produced in a batch process. The standard concentration should be 0.5 M. If the sample mean differs from 0.5 M, the engineer wants to determine if this difference is statistically significant or due to random variation. Which method applies? A) Hypothesis testing B) Descriptive statistics C) Confidence interval estimation D) Histogram plotting

Hypothesis testing

RC 2 — Question 21 (PDF page 10) Which transformation is commonly applied to positive, right-skewed data to reduce skewness? A) Logarithmic B) Multiplying by a constant C) Cubing D) Subtracting standard deviation

Logarithmic

RC 2 — Question 22 (PDF page 10) A manufacturer wants to test the tensile strength of steel rods from a large production lot. Which sampling method will give the most unbiased representation of the batch? A) Convenience sampling B) Judgment sampling C) Snowball sampling D) Systematic sampling

Systematic sampling

RC 2 — Question 23 (PDF page 10) [REVIEW: Formula/superscript requires review] Energy stored in capacitor C with voltage v(t) is: A) E=(1/2)Cv?t B) E =Cv(t) C) E = (1/2)Li?(t) D) E = Ri2(t)

E = (1/2)Cv^2(t)

RC 2 — Question 24 (PDF page 10) For which type of function are both Trapezoidal and Simpson's Rules exact? A) Trigonometric functions B) Quadratic polynomials C) Linear polynomials D) Cubic polynomials

Linear polynomials

RC 2 — Question 25 (PDF page 10) The primary purpose of incorporating designed elements in a manufacturing process is to: A) Increase development costs B) Eliminate the need for process control C) Reduce process variability and improve quality D) Increase product variability

Reduce process variability and improve quality

RC 3 — Question 1 (PDF page 12) A transfer function has complex conjugate poles. The system's time response will: A) Be unstable always B) Be sinusoidal with constant amplitude C) Show damped oscillations D) Be purely exponential

C) Show damped oscillations

RC 3 — Question 2 (PDF page 12) If all poles are moved farther left in the s-plane: A) Stability is lost B) Gain increases but speed is same C) system becomes faster D) system becomes slower

C) system becomes faster

RC 3 — Question 3 (PDF page 12) The pole-zero plot of a transfer function is usually plotted in: A) Time domain B) Frequency domain only C) Z-domain D) Laplace s-plane

D) Laplace s-plane

RC 3 — Question 4 (PDF page 12) The curl of a constant vector field is: A) Equal to magnitude of vector B) Maximum C) Zero D) Undefined

C) Zero

RC 3 — Question 5 (PDF page 12) Which of the following is a vector quantity? A) Temperature B) Displacement C) Mass D) Speed

B) Displacement

RC 3 — Question 6 (PDF page 12) Which of the following is a major advantage of using a signal-flow graph over a block diagram? A) Always simpler B) Easier to draw C) Can only be used for single-loop systems D) Mason's Gain Formula can be directly applied for overall transfer function

D) Mason's Gain Formula can be directly applied for overall transfer function

RC 3 — Question 7 (PDF page 13) The directional derivative of temperature along a pipe in the direction of the flow gives: A) Divergence of temperature field B) Curl of the temperature field C) Rate of temperature change along the flow D) Maximum temperature in the system

C) Rate of temperature change along the flow

RC 3 — Question 8 (PDF page 13) In pole-zero plots, stability of a continuous-time system is ensured when: A) All poles lie on the imaginary axis B) All poles lie in the right half-plane C) All poles lie in the left half-plane D) All zeros lie in the left half-plane

C) All poles lie in the left half-plane

RC 3 — Question 9 (PDF page 13) The system is stable when: A) At least one root of the characteristic equation has positive real part B) Both roots have negative real parts C) R=0 D) Roots are imaginary

B) Both roots have negative real parts

RC 3 — Question 10 (PDF page 13) The number of poles of a transfer function determines: A) system bandwidth B) System order C) System stability margin D) system gain

B) System order

RC 3 — Question 11 (PDF page 13) Partial fraction decomposition is used when integrating: A) Rational functions with numerator degree < denominator degree B) Rational functions with numerator degree = denominator degree C) Exponential integrals D) Trigonometric integrals

A) Rational functions with numerator degree < denominator degree

RC 3 — Question 12 (PDF page 13) For a critically damped system, which of the following is TRUE? A) Fastest response without overshoot B) Slowest response with overshoot C) Undamped oscillations D) Marginally stable

A) Fastest response without overshoot

RC 3 — Question 13 (PDF page 13) If data are collected by using past records, reports, and published statistics, it is known as: A) Primary data B) Observational data C) Secondary data D) Experimental data

C) Secondary data

RC 3 — Question 14 (PDF page 14) Which of the following is an advantage of using sampling over a census? A) Sampling is always more accurate than a census B) Sampling eliminates the need for randomization C) Sampling avoids sampling error D) Sampling is less expensive and quicker

D) Sampling is less expensive and quicker

RC 3 — Question 15 (PDF page 14) Which of the following converts a double integral over an area into a line integral over its boundary? A) Divergence theorem B) Green's theorem C) None of the above D) Stokes’ theorem

B) Green's theorem

RC 3 — Question 16 (PDF page 14) In electromagnetics, Gauss’s law for electric fields is an application of: A) Green's theorem B) Laplace's theorem C) Divergence theorem D) Stokes’ theorem

C) Divergence theorem

RC 3 — Question 17 (PDF page 14) Transfer functions in electronics come from: A) Fourier transforms of differential equations B) Z-+transforms of differential equations C) Inverse Laplace transforms of differential equations D) Laplace transforms of differential equations

D) Laplace transforms of differential equations

RC 3 — Question 18 (PDF page 14) Which of the following is not true about signal-flow graphs? A) They use branch gains between nodes B) They are unidirectional C) They cannot represent multiple inputs D) They can be used to find transfer functions

C) They cannot represent multiple inputs

RC 3 — Question 19 (PDF page 14) [REVIEW: Formula/superscript requires review] The nonlinear oscillator defined by x” + w?x + ax® = 0 is known as: A) Duffing oscillator B) simple harmonic oscillator C) Linear force system D) Bernoulli system

A) Duffing oscillator

RC 3 — Question 20 (PDF page 14) When two feedback loops are connected in cascade, their overall transfer function is: A) Product of their transfer functions B) Sum of their transfer functions C) Division of their transfer functions D) Requires Mason's Gain Formula

A) Product of their transfer functions

RC 3 — Question 21 (PDF page 15) A step response shows no overshoot but a very long settling time. Which design action is most effective? A) Add derivative control (PD) B) Add integral control (Pl) C) Increase system gain D) Reduce damping ratio

A) Add derivative control (PD)

RC 3 — Question 22 (PDF page 15) The gradient of a scalar function points in the direction of: A) Maximum increase of the function B) Perpendicular to the function C) Maximum decrease of the function D) Minimum increase of the function

A) Maximum increase of the function

RC 3 — Question 23 (PDF page 15) The divergence of a magnetic field in free space is: A) Undefined B) Maximum C) Equal to electric charge density D) Zero

D) Zero

RC 3 — Question 24 (PDF page 15) The conservative property of a vector field is guaranteed if: A) Gradient is constant B) Field is discontinuous C) Divergence = 0 D) Curl = 0 in a simply connected region

D) Curl = 0 in a simply connected region

RC 3 — Question 25 (PDF page 15) The divergence theorem is also called: A) stokes’ theorem B) Helmholtz theorem C) Gauss’s theorem D) Green's theorem

C) Gauss’s theorem

RC 4 — Question 1 (PDF page 16) Implicit differentiation is used when: A) function is expressed as y = f(x) B) The derivative of a constant is unknown C) The variable y cannot be isolated easily in terms of D) Both variables are constants

C) The variable y cannot be isolated easily in terms of

RC 4 — Question 2 (PDF page 16) Which of the following is NOT a probability sampling method? A) simple random sampling B) Stratified sampling C) Systematic sampling D) Convenience sampling

D) Convenience sampling

RC 4 — Question 3 (PDF page 16) what is the formula for the integral of sec x tan x? A) fsec x tan x dx = - secx+C B) fsec x tanx dx =cscx+c C) fsec x tan x dx = tanx+C D) fsec x tan x dx = secx+C

D) fsec x tan x dx = secx+C

RC 4 — Question 4 (PDF page 16) A Fourier series represents: A) discrete-time signal B) periodic continuous-time signal C) Only sine waves D) Arandom signal

B) periodic continuous-time signal

RC 4 — Question 5 (PDF page 16) In DOE (Design of Experiments) terminology, the “interaction effect” refers to: A) The uncontrolled variation in the experiment B) The effect of one factor on the response regardless of other factors C) The combined effect of two or more factors on the response D) The replication of a single factor’s effect

C) The combined effect of two or more factors on the response

RC 4 — Question 6 (PDF page 16) A researcher randomly selects 5 schools from a city and collects data from all students in those schools. This is an example of: A) simple random sampling B) Systematic sampling C) Cluster sampling D) Stratified sampling

D) Stratified sampling

RC 4 — Question 7 (PDF page 17) The primary purpose of regression analysis is to: A) Measure the strength of association between variables B) Compare means of two populations C) Predict the value of a dependent variable based on independent variables D) Test for normality of data

C) Predict the value of a dependent variable based on independent variables

RC 4 — Question 8 (PDF page 17) A mathematical function is a relation in which: A) Each input corresponds to multiple outputs B) Only algebraic expressions are allowed C) Every input has exactly one output D) The domain is always the set of real numbers

C) Every input has exactly one output

RC 4 — Question 9 (PDF page 17) Which of the following statements about correlation coefficient (r) is TRUE? A) can take values from -00 to +00 B) ranges between -1 and +1 C) r measures causation D) ris always positive

B) ranges between -1 and +1

RC 4 — Question 10 (PDF page 17) Which of the following formulas correctly represents the antiderivative of cos x? A) fcos x dx =-sinx+C B) fcos x dx=sinx+C C) fcos x dx=-cosx+C D) fcos x dx=cosx+C

B) fcos x dx=sinx+C

RC 4 — Question 11 (PDF page 17) A 99% confidence interval is computed as (24, 36). Which of the following is TRUE if we switch to a 95% confidence level with the same sample? A) Interval will become wider B) Interval will become narrower C) Interval will shift right D) Interval will remain same

B) Interval will become narrower

RC 4 — Question 12 (PDF page 17) Which of the following is the null hypothesis (H,) in hypothesis testing? A) statement that is never tested B) statement that is always true C) statement you try to prove true D) statement you try to reject

D) statement you try to reject

RC 4 — Question 13 (PDF page 18) Which of the following statements about p-value is TRUE? A) Itis the smallest a at which H, would be rejected B) Itis always greater than a C) ttis the probability that H, is true D) It depends only on sample size

A) Itis the smallest a at which H, would be rejected

RC 4 — Question 14 (PDF page 18) The main difference between correlation and regression is: A) Correlation implies causation, regression does not B) Regression can only be used for one variable C) Regression does not use slope, correlation does D) Correlation measures association, regression predicts y based on x

D) Correlation measures association, regression predicts y based on x

RC 4 — Question 15 (PDF page 18) Which of the following is a one-tailed test? A) Testing whether the mean is greater than 1, B) Testing whether two means are different C) Testing whether the mean is different from py D) Testing whether two proportions are different

A) Testing whether the mean is greater than 1,

RC 4 — Question 16 (PDF page 18) Which of the following best describes an observational study? A) Researcher uses only secondary data B) Researcher records data without manipulating variables C) Researcher controls treatment and compares outcomes D) Researcher randomly assigns subjects to groups

B) Researcher records data without manipulating variables

RC 4 — Question 17 (PDF page 18) [REVIEW: Formula/superscript requires review] Which of the following distributions is used to construct a confidence interval for variance of a normal population? A) F-distribution B) Normal C) rdistribution D) y?-distribution

D) y?-distribution

RC 4 — Question 18 (PDF page 18) When the sample size is small and the population variance is unknown, the sampling distribution of the mean follows: A) Poisson distribution B) Student's t-distribution C) Binomial distribution D) Normal distribution

B) Student's t-distribution

RC 4 — Question 19 (PDF page 18) Which of the following statements about sampling distribution of the mean is TRUE? A) tts shape is always normal, regardless of n B) Its variance equals the population variance C) tts standard deviation is equal to sample mean D) Its mean equals the population mean

D) Its mean equals the population mean

RC 4 — Question 20 (PDF page 19) Which of the following is the primary purpose of Design of Experiments (DOE)? A) To collect random data without a plan B) To find the cause-and-effect relationship between factors and response C) To reduce sample size D) To avoid statistical analysis

B) To find the cause-and-effect relationship between factors and response

RC 4 — Question 21 (PDF page 19) [REVIEW: Formula/superscript requires review] Consider the equation: (d?y/dx?) + (dy/dx)? + y = 0. This equation is: A) Linear, second-order, ODE B) Linear, second-order, PDE C) Nonlinear, second-order, ODE D) Nonlinear, first-order, ODE

C) Nonlinear, second-order, ODE

RC 4 — Question 22 (PDF page 19) Which of the following is NOT a step in hypothesis testing? A) Estimating the population parameter B) Formulating H, and H, C) Computing the test statistic D) Choosing a significance level

A) Estimating the population parameter

RC 4 — Question 23 (PDF page 19) In regression analysis, heteroscedasticity refers to: A) Nonlinear relationship between variables B) Presence of autocorrelation C) Non-constant variance of residuals D) Correlation among predictors

C) Non-constant variance of residuals

RC 4 — Question 24 (PDF page 19) Which condition must be satisfied for uniqueness of the solution of a first-order differential equation dy/dx = f(x,y) with y(X,) = Yo? A) f(x,y) is discontinuous but bounded B) f(xy) has a unique minimum at x, C) df/dy is continuous near (Xp, Yo) D) f(x,y) is continuous at (Xp, Yo)

C) df/dy is continuous near (Xp, Yo)

RC 4 — Question 25 (PDF page 19) [REVIEW: Formula/superscript requires review] Which distribution is used for the X?-test for variance? A) Normal B) Chi-square C) tdistribution D) F-distribution

B) Chi-square