List of top Engineering Mathematics Questions

Solution of the system of equations \( 3x + y + 2z = 3 \), \( 2x - 3y - z = -3 \), \( x + 2y + z = 4 \)
Starting from \( x_0 = 1 \), one step Newton-Raphson method in solving the equation \( x^3 + 3x - 7 = 0 \) gives the next value as
The values of \( \mu \) which satisfy the equation \( A^{100} \vec{x} = \mu \vec{x} \), where \( A = \begin{bmatrix} 2 & -1 \\ 0 & -2 \\ 1 & 1 \end{bmatrix} \) are
The radius of convergence of Taylor's series expansion of \( f(z) = \frac{1}{(z - 1)^2} \) in powers of \( (z - 1) \) is ...
Evaluate \( \int_C \frac{dz}{z^2 + 9} \), where \( C \) is \( |z - 3| = 4 \)
A solution of the ODE \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = 0 \) is such that \( y(0) = 2 \) and \( y'(0) = 3 \). The value of \( y''(0) \) is
A die is thrown at random, find the probability of getting 5 or a number greater than 2 and is even
For any two arbitrary events \( A \) and \( B \), which of the following is true?
Complete integral of the partial differential equation \( 2\frac{\partial^2 f}{\partial q^2} + 3\frac{\partial f}{\partial q} = 6x + 2y \) is
Determine the value of \( p \) such that the rank of matrix \( A \) is 2:
\[ A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 0 & 2 & p \\ 1 & 0 & p & 7 \end{bmatrix} \]
The matrix \( A = \begin{bmatrix} 3 & -1 & 1 \\ 1 & -5 & 1 \\ 1 & -1 & 3 \end{bmatrix} \) has eigenvalues 2, 3, 6 then the eigenvalues of \( A^4 \) are
The Laplace transform of a signal $X(t)$ is $$ X(s) = \frac{4s + 1}{s^2 + 6s + 3}. $$ The initial value $X(0)$ is:
If \( A \) is a \( 3 \times 3 \) matrix and determinant of \( A \) is 6, then find the value of the determinant of the matrix \((2A)^{-1}\):
For applying Simpson's \( \frac{1}{3} \) rule, the given interval must be divided into how many number of sub-intervals?
Which of the following formula is used to fit a polynomial for interpolation with equally spaced data?
The area between the parabolas \( y^2 = 4 - x \) and \( y^2 = x \) is given by:
The value of the integral \[ \iiint\limits_{0}^{a, b, c} e^{x+y+z} \, dz \, dy \, dx \] is:
The Region of Convergence (ROC) of the signal \( x(n) = \delta(n - k), k>0 \) is:
The Laplace transform of a signal \( X(t) \) is \[ X(s) = \frac{4s + 1}{s^2 + 6s + 3}. \] The initial value \( X(0) \) is:
Given the inverse Fourier transform of \(f(s) = \begin{cases} a - |s|, & |s| \leq a \\ 0, & |s|>a \end{cases}\).The value of \[ \int_0^\pi \left( \frac{\sin x}{x} \right)^2 dx \] is:
If \( \nabla \phi = 2xy^2 \hat{i} + x^2z^2 \hat{j} + 3x^2y^2z^2 \hat{k} \), then \( \phi(x,y,z) \) is:
If the system of equations: \[ 3x + 2y + z = 0, \quad x + 4y + z = 0, \quad 2x + y + 4z = 0 \] is given, then:
The shortest and longest distance from the point \( (1,2,-1) \) to the sphere \( x^2 + y^2 + z^2 = 24 \) is:
The only function from the following that is analytic is:
Let \(M = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}\)The maximum number of linearly independent eigenvectors of \( M \) is: