List of top Engineering Mathematics Questions

If \(\mathbf{f} = f_1(y, z) \hat{i + f_2(z, x) \hat{j} + f_3(x, y) \hat{k}}\), then \( \mathbf{f} \) is

What is the correct formula for Runge-Kutta 3rd order method?
One of the two events must occur. The chance of one is \( \frac{2}{3} \) of the other, then odds in favor of the other are
Solution of the differential equation \( xy \frac{dy}{dx} = 1 + x + y + xy \) is
If \( \mathbf{a} \) is a constant vector, then \( \text{div}[\mathbf{a} \times (\mathbf{r} \times \mathbf{a})] \) is
If \( A \) is an orthogonal matrix, then \( A^{-1} \) is
The work done in displacing a particle from \( r = 0 \) to \( r = 1 \) in a curve \( x = t^2 + 1 \) and \( z = t^2 + 1 \) in a force field \( \mathbf{F} = (2xy, 3x, -5z) \) is
If \( \mathbf{F} = ax \hat{i} + by \hat{j} + cz \hat{k} \), where \( a, b, c \) are constants, then
If \( f(x) = (x^2 - 16)^2 \), where \( x \) is real, \( f(x) \) has
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 value of \( \int_0^3 \int_0^0 (x^2 + 3y^2) \, dy \, dx \) is
For any two arbitrary events \( A \) and \( B \), which of the following is true?
A die is thrown at random, find the probability of getting 5 or a number greater than 2 and is even
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
Complete integral of the partial differential equation \( 2\frac{\partial^2 f}{\partial q^2} + 3\frac{\partial f}{\partial q} = 6x + 2y \) is
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 \( |z - 3| = 4 \)
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 \((2A)^{-1}\):
The complete integral of the partial differential equation \( pz^2 \sin^2 x + qz^2 \cos^2 y = 1 \) 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: