engineering mathematics

Periodic function $f(x)$ is given below. $f(x) = \begin{cases} -1, & \text{when} & -\pi < x < 0 \\ 1, & \text{when} & 0 < x < \pi \end{cases} ; f(x + 2\pi) = f(x)$ The CORRECT opti...

Which one of the following options is the correct Fourier series of the periodic function f(x) described below: f(x) = { 0 if -2 < x < -1 { 2k if -1 < x < 1 ; period = 4 { 0 if 1 <...

Cholesky decomposition is carried out on the following square matrix [A]. $[A] = \begin{bmatrix} 8 & -5 \\ -5 & a_{22} \end{bmatrix}$ Let $l_{ij}$ and $a_{ij}$ be the $(i,j)^{th}$...

A 5 cm long metal rod AB was initially at a uniform temperature of T 0 °C. Thereafter, temperature at both the ends are maintained at 0°C. Neglecting the heat transfer from the lat...

The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is

Laplace transform of $$f\left( t \right) = \cos \left( {pt + q} \right)$$ is

Given matrix $$\left[ A \right] = \left[ {\matrix{ 4 & 2 & 1 & 3 \cr 6 & 3 & 4 & 7 \cr 2 & 1 & 0 & 1 \cr } } \right],$$ the rank of the matrix is

The Laplace Transform of a unit step function $${u_a}\left( t \right),$$ defined as $$\matrix{ {{u_a}\left( t \right) = 0} & {for\,\,\,t < a\,} \cr { = 1} & {for\,\,\,t > a,} \cr }...