List of top Engineering Mathematics Questions

If the system of equations: \[ 3x + 2y + z = 0, \quad x + 4y + z = 0, \quad 2x + y + 4z = 0 \] is given, then:
If \( A \) is a \( 3 \times 3 \) matrix and the determinant of \( A \) is 6, then find the value of the determinant of the matrix \( (2A)^{-1} \):
For a Binomial distribution with mean 4 and variance 2, the value of \( n \) 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:
The value of the integral \[ \iiint\limits_{0}^{a, b, c} e^{x+y+z} \, dz \, dy \, dx \] is:
The value of \( m \) so that \( 2x - x^2 + m y^2 \) may be harmonic 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:
The value of \( \oint_C \frac{1}{z} dz \), where \( C \) is the circle \( z = e^{i\theta}, 0 \leq \theta \leq \pi \), is:
The complete integral of the partial differential equation \( pz^2 \sin^2 x + qz^2 \cos^2 y = 1 \) is: