Evaluate \(\cosh(j\frac{\pi}{4})\)
A0.707
B1.41 + j0.866
C0.5 + j0.707
Dj0.707
Mathematics · Question Bank
Advanced Engineering Mathematics
56 of 84 questions match · page 2 of 3. Answer in your head first, then check the solution.
Evaluate \(\tanh(j\frac{\pi}{3})\)
A0.5 + j1.732
Bj0.866
Cj1.732
D0.5 + j0.866
Evaluate \(\ln(2+j3)\)
A1.34 + j0.32
B2.54 + j0.866
C2.23 + j0.21
D1.28 + j0.98
Evaluate the terms of a Fourier series \(2 e^{j10\pi t} + 2 e^{-j10\pi t}\) at \(t = 1\)
A2+j
B2
C4
D2+j2
One term of a Fourier series in cosine form is \(10 \cos 40\pi t\). Write it in exponential form.
A\(5 e^{j40\pi t}\)
B\(5 e^{j40\pi t} + 5 e^{-j40\pi t}\)
C\(10 e^{-j40\pi t}\)
D\(10 e^{j40\pi t}\)
Evaluate the determinant: \(\begin{vmatrix} 1 & 2 & 3 \\ -2 & -1 & -2 \\ 3 & 1 & 4 \end{vmatrix}\)
A4
B2
C5
D0
Evaluate the determinant: \(\begin{vmatrix} 1 & 6 & 0 \\ 4 & 2 & 7 \\ 0 & 5 & 3 \end{vmatrix}\)
A110
B-101
C101
D-110
Evaluate the determinant: \(\begin{vmatrix} 2 & 14 & 3 & 1 \\ 1 & 5 & -1 & 3 \\ 1 & -2 & 2 & -3 \\ 3 & -4 & -3 & -4 \end{vmatrix}\)
A489
B389
C326
D452
Compute the value of x by determinant: \(x = \begin{vmatrix} 4 & -1 & 2 & 3 \\ 2 & 0 & 2 & 1 \\ 10 & 3 & 0 & 1 \\ 14 & 2 & 4 & 5 \end{vmatrix}\)
A-32
B-28
C16
D52
Given the equations:
\(x+y+z=2\)
\(3x-y-2z=4\)
\(5x-2y+3z=-7\)
Solve for y by determinants.
\(x+y+z=2\)
\(3x-y-2z=4\)
\(5x-2y+3z=-7\)
Solve for y by determinants.
A1
B-2
C3
D0
Solve the equations by Cramer's Rule:
\(2x-y+3z=-3\)
\(3x+3y-z=10\)
\(-x-y+z=-4\)
\(2x-y+3z=-3\)
\(3x+3y-z=10\)
\(-x-y+z=-4\)
A(2, 1, -1)
B(2, -1, -1)
C(1, 2, -1)
D(-1, -2, 1)
If matrix \(\begin{bmatrix} 1 & -1 & 2 \\ 2 & 1 & 3 \\ 0 & -1 & 1 \end{bmatrix}\) is multiplied by \(\begin{bmatrix} x \\ y \\ z \end{bmatrix}\) is equal to zero, then matrix \(\begin{bmatrix} x \\ y \\ z \end{bmatrix}\) is
A3
B1
C0
D-2
Given the matrix equation, solve for x and y:
\(\begin{bmatrix} 1 & 1 \\ 3 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 0 \end{bmatrix}\)
\(\begin{bmatrix} 1 & 1 \\ 3 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 0 \end{bmatrix}\)
A-4, 6
B-4, 2
C-4, -2
D-4, -6
If matrix \(\begin{bmatrix} 1 & 4 \\ -4 & 1 \end{bmatrix}\) is multiplied by \(\begin{bmatrix} x \\ y \end{bmatrix}\) is equal to zero, then matrix \(\begin{bmatrix} x \\ y \end{bmatrix}\) is
A8
B1
C4
D0
Evaluate: \(\begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix} + 2 \begin{bmatrix} -1 & 2 \\ 1 & 1 \end{bmatrix}\)
A\(\begin{bmatrix} -1 & 2 \\ 1 & 1 \end{bmatrix}\)
B\(\begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix}\)
C\(\begin{bmatrix} -2 & 4 \\ 2 & 2 \end{bmatrix}\)
D\(\begin{bmatrix} 0 & 5 \\ 1 & 5 \end{bmatrix}\)
Elements of matrix \(B = \begin{bmatrix} 1 & 2 \\ 0 & -5 \end{bmatrix}\) and elements of matrix \(C = \begin{bmatrix} 3 & 6 \\ 4 & 1 \end{bmatrix}\). Find the elements of the product matrix BC.
A\(\begin{bmatrix} 11 & 8 \\ -20 & -5 \end{bmatrix}\)
B\(\begin{bmatrix} -11 & 8 \\ 19 & 5 \end{bmatrix}\)
C\(\begin{bmatrix} -10 & 9 \\ -19 & 6 \end{bmatrix}\)
D\(\begin{bmatrix} -11 & 9 \\ -20 & -4 \end{bmatrix}\)
Determine the inverse matrix of \(\begin{bmatrix} 1 & 2 \\ 5 & 9 \end{bmatrix}\)
A\(\begin{bmatrix} -9 & 5 \\ 2 & -1 \end{bmatrix}\)
B\(\begin{bmatrix} 9 & 5 \\ 2 & 1 \end{bmatrix}\)
C\(\begin{bmatrix} 2 & 5 \\ 9 & 1 \end{bmatrix}\)
D\(\begin{bmatrix} -9 & -5 \\ 2 & 1 \end{bmatrix}\)
Find the inverse Laplace transform of \(\frac{2}{s+1} - \frac{4}{s+3}\)
A\(2e^{-t} - 4e^{-3t}\)
B\(e^{-2t} + e^{-3t}\)
C\(e^{-2t} - e^{-3t}\)
D\(2e^{-t}(1 - 2e^{-3t})\)
Determine the inverse Laplace transform of \(I(s) = \frac{200}{s^2 - 50s + 10625}\)
A\(I(t) = 2e^{25t} \sin 100t\)
B\(I(t) = 2t e^{25t} \sin 100t\)
C\(I(t) = 2e^{25t} \cos 100t\)
D\(I(t) = 2t e^{25t} \cos 100t\)
Find the inverse Laplace transform of \(\frac{2s-18}{s^2+9}\) as a function of x.
A\(2 \cos x - \sin 3x\)
B\(2 \cos 3x - 6 \sin 3x\)
C\(3 \cos 2x - 2 \sin 6x\)
D\(6 \cos x - 3 \sin 2x\)