Đề Thi FE MAI391 - SU26 - FE - RE

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SU2026

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5/8/26

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FE

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MAI391_SU26_RE_607216

MAI391_SU26_RE_607216

MAI391 Multiple Choice Questions​

This document contains a series of multiple choice questions related to mathematics, including calculus, chain rule, Gaussian mixture models, quadratic programming, and vector spaces. Each question presents a mathematical problem followed by several distinct answer options. It serves as a practice or examination assessment for mathematics students.

MAI391 Multiple Choice Questions​

Question 1
(Choose 1 answer)
Given the computation graph. Find the partial derivative at x1 = 1, x2 = 0, x3 = -1.
A. cos(1)
B. 1+cos(1)
C. 1-cos(1)
D. 0

Question 2
(Choose 1 answer)
Given R(u,v) = ln(u^3 + v^3), u = x + 2y, v = 2xy.
Use the Chain Rule to find when x=y=1.
A. 51/35
B. 35/78
C. 35/51
D. None of the other choices is correct
E. 39/35
F. 78/35

Question 3
(Choose 1 answer)
Consider the mixture of two independent Gaussians X and Y
Find the variance of Y.
A. 4.5
B. None of the other choices is correct
C. 3.5
D. 5.5
E. 2.5

Question 4
(Choose 1 answer)
Consider the quadratic program
Find the derivative of the Lagrangian L(x, lambda) with respect to x.
(i) matrix expression
(ii) matrix expression
(iii) matrix expression
(iv) matrix expression
A. (i)
B. (iv)
C. (ii)
D. (iii)

Question 5
(Choose 1 answer)
Let U = span{[1 1 -2]^T, [1 0 1]^T}.
Which of the following vectors are in U^∕?
x = [1 -1 1]^T y = [0 1 0]^T
A. Both x and y
B. None of x or y
C. y only
D. x only