What theorem is used to solve for centroid?
APappus
BVarignon's
CCastiglliano's
DPascals's
Mathematics · Question Bank
Advanced Engineering Mathematics
28 of 84 questions match · page 1 of 2. Answer in your head first, then check the solution.
The ff Fourier series equation represents a periodic _______ wave i(x)=i+icosx+i²cos2x+i³cos3x +...... + i sinx+i²sin2x
Acosine
Btangent
Ccotangent
Dsine
The scalar product of A and B is equal to the product of the magnitudes of A and B and the __________ of the angle between them
Asine
Bvalue in radians
Ctangent
Dcosine
In complex algebra, we use a diagram to represent a complex plane commonly called:
ADe Moivre's diagram
BArgand diagram
CVenn diagram
DFunicular diagram
When the corresponding elements of two rows of a determinant are proportional, then the value of the determinant is:
Aunknown
Bone
Czero
Dmultiplied by the ratio
A sequence of number where the succeeding term is greater than the preceding term
Aisometric series
Bdivergent series
Cconvergent series
Ddissonant series
In any square matrix, when the elements of any two rows are exactly the same, the determinant is:
Aunity
Bpositive integer
Czero
Dnegative integer
Which of the ff cannot be an operation of matrices?
Asubtraction
Bmultiplication
Caddition
Ddivision
Convergent series is a sequence of decreasing numbers or when the succeeding term is ________ than the preceding term
Aten times more
Bequal
Cgreater
Dlesser
The triangle with the minimum perimeter which may be inscribed in another triangle is called a
AEuclid's triangle
BRihley's triangle
CPedal triangle
Dnone of these
What is the Laplace Transform of a unit step function?
A1
Bs
C1 / s
Du(t)
It is an equation that contains one or several derivatives of an unknown function called y(x) and which we want to determine from the equation.
Ahomogeneous differential equation
Bordinary differential equation
Cpartial differential equation
Dlinear constant coefficient differential equation
These variables are dimensionless combinations of the physical variable and parameters of the original.
ACanonical Variables
BDependent Variables
CX and Y Variables
DControlled Variables
Determine the general solution of xdy + ydx=0.
Axy = c
Bln xy = c
Cln x + ln y = c
Dx + y = c
Given the following series:
\(\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots\)
\(\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \dots\)
\(e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots\)
What relation can you draw from these series?
\(\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots\)
\(\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \dots\)
\(e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots\)
What relation can you draw from these series?
A\(e^x = \cos x + \sin x\)
B\(e^{ix} = \cos x + i \sin x\)
C\(e^{ix} = i \cos x + \sin x\)
D\(i e^x = i \cos x + i \sin x\)
If \(A = \begin{vmatrix} 2 & 3 & 1 \\ -1 & 2 & 4 \\ 0 & 5 & 7 \end{vmatrix}\), what is the cofactor of the second row, third column element?
A\(\begin{vmatrix} 2 & 3 \\ 0 & 5 \end{vmatrix}\)
B-\(\begin{vmatrix} 2 & 3 \\ 0 & 5 \end{vmatrix}\)
C-\(\begin{vmatrix} 1 & 7 \\ 2 & 0 \end{vmatrix}\)
D\(\begin{vmatrix} 3 & 1 \\ 5 & 7 \end{vmatrix}\)
If \(A = \begin{vmatrix} 3 & 1 & 2 \\ -2 & -1 & 0 \\ 0 & 2 & -1 \end{vmatrix}\), what is the cofactor of the first row, second column element?
A-\(\begin{vmatrix} 3 & 2 \\ 0 & -1 \end{vmatrix}\)
B\(\begin{vmatrix} -2 & -1 \\ 0 & 2 \end{vmatrix}\)
C\(\begin{vmatrix} 3 & 2 \\ 0 & -1 \end{vmatrix}\)
D-\(\begin{vmatrix} -2 & 0 \\ 0 & -1 \end{vmatrix}\)
If a \(3 \times 3\) matrix and its inverse are multiplied together, write the product.
A\(\begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{vmatrix}\)
B\(\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\)
C\(\begin{vmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{vmatrix}\)
D\(\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}\)
If \(A = \begin{bmatrix} 4 & 5 & 0 \\ 6 & 7 & 3 \\ 1 & 2 & 5 \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\), what is A times B equal to?
A\(\begin{bmatrix} 4 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 5 \end{bmatrix}\)
B\(\begin{bmatrix} 0 & 0 & 0 \\ 0 & 7 & 0 \\ 1 & 0 & 0 \end{bmatrix}\)
C\(\begin{bmatrix} 6 & 7 & 0 \\ 8 & 9 & 4 \\ 2 & 3 & 5 \end{bmatrix}\)
D\(\begin{bmatrix} 4 & 5 & 0 \\ 6 & 7 & 3 \\ 1 & 2 & 5 \end{bmatrix}\)
Transpose the matrix \(\begin{bmatrix} 3 & 1 & 2 \\ -2 & -1 & 0 \\ 0 & 2 & -1 \end{bmatrix}\)
A\(\begin{bmatrix} -1 & 2 & 0 \\ 0 & -1 & -2 \\ 2 & 1 & 3 \end{bmatrix}\)
B\(\begin{bmatrix} 3 & -2 & 0 \\ 1 & -1 & 2 \\ 2 & 0 & -1 \end{bmatrix}\)
C\(\begin{bmatrix} 3 & 1 & 2 \\ 1 & 2 & -1 \\ -2 & -1 & 0 \end{bmatrix}\)
D\(\begin{bmatrix} 1 & 3 & 2 \\ -1 & -2 & 0 \\ 2 & 2 & -1 \end{bmatrix}\)