30 Questions
What does the correlation measure?
The strength and direction of the relationship between two variables
What is the value of g(6) if g(x) = |5x^2 – x^3|?
216
If a unit integrator is cascaded to a control system and a unit ramp input is applied, what is the value of the steady-state error?
0.25
What is the union of C and the intersection of A and B?
{1, 2, 4, 5, 9}
What is the Laplace transform of F(t) = 3 + t?
3/s + 1/s^2
What is the value of cos 2z if cos z = 2?
7
What is the simplified form of i29 + i21 + i?
i51
How many even numbers are present in the union of sets A and B?
6
What is the range of f(z) = arg 1/(1 – z) for |z| = 1, z ≠ 1?
(-π/2, π/2)
What is the function used for determining the similarity between a signal and its delayed version?
Cross-correlation function
What is the centroid's location in the root locus diagram of the transfer function K(s+6)/(s+3)(s+5)?
-2
What is the inverse transform of the Laplace transform function L(s) = 20s/(s2 + 20s + 75)?
Ae-5tcos15t
What is the probability of the homebuilder completing a house within a certain number of days?
At least 95%
What is the Taylor series generated by the function f(x) = eˣ at x = 0?
A series with terms involving xⁿ/n!
What is the directional derivative of U = 2x³y - 3y²z at P(1, 2, −1) in a direction toward Q(3, −1, 5)?
The dot product of the gradient of U at P and the unit vector in the direction of Q
What is the value of the determinant of the matrix A = [(1,0,2),(2,-3,4),(-3,1,9)]?
-40
What is the value of (A + B)∙(B + C) for vectors A = 8i + 2j + 2k, B = 4i + 2j + 4k, and C = 6i + 8j + 10k?
264
What is the Maclaurin series for f(x) = 1/(1 – 2x)?
1 – 2x + 4x² - 8x³
What is the simplified expression for the square root of 8 – 15i?
± (3/sqrt 2 – 5i/sqrt 2) and ± (3/sqrt 2 + 5i/sqrt 2)
What is the probability that at least one doctor is available when needed?
0.98
What is the rejection probability of a Null Hypothesis when it is true?
Level of Significance
Under which condition does an initially relaxed system become unstable?
only if bounded input generates unbounded output
What is the Laplace transform of the function f(t) = u(t – 1) + u(t – 2)?
(e^-s - e^-2s)/s
What is the transfer function of a system with impulse response g (t) = e(-t)?
1/(s+1)
What is not a possible combination of mean and standard deviation for a given population?
The mean is positive and the standard deviation is negative
What is the coefficient of (x – 1)5 in the Taylor series for x ln(x) about x = 1?
-1/20
What must be true if every element from list M is larger than the corresponding element from list N?
The median of the elements in M is greater than the median of the elements in N
What is the range of the temperatures in the first week of July in southern Iceland?
12°C
What is the z-transform of the finite duration signal x(n) = {2,3,4,5,7,0,1}?
2 + 4z-1 + 5z-2 + 7z-3 + z-5
What is the relationship between the elements of list M and list N?
Every element from list M is larger than the corresponding element from list N
Assessment of math concepts including correlation, functions, and control systems. Test your understanding of mathematical relationships and problem-solving skills.
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