Recent questions in Engineering Mathematics

Consider the following differential equation:\[t^{2} \frac{d^{2} y}{d t^{2}}+7 t \frac{d y}{d t}+8 t y=10 \sin (t)\]Which one of the following options is correct?It is a ...

$A$ is an $m \times m$ skew-symmetric matrix with real-valued entries, and $\boldsymbol{x}$ is an $m$-dimensional column vector with real-valued entries such that $\bolds...

Which one of the following statements is ALWAYS correct about a collection of $p$ column vectors, each having $n$ real-valued entries?If $p>n$, then the column vectors mu...

Consider the second-order differential equation\[\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+y=0\]with initial conditions\[y(0)=1,\left.\quad \frac{d y}{d x}\right|_{x=0}=1\]...

Consider an $n \times n$ orthogonal matrix $A$ with real entries and each column having unit Euclidean norm.Which of the following statements is/are correct?The value of ...

The magnitude of the contour integral\[\oint_{C}\left(\frac{(z+1)^{2}}{(z-i)(z-2)}\right) d z\]over the contour $C:|z-2-i|=3 / 2$ is $\_\_\_\_$(Round off to two decimal p...

Let $\text{X}$ and $\text{Y}$ be two real-valued random variables with $\mathrm{E}(\mathrm{X})=1, \mathrm{E}(\mathrm{Y})=2, \mathrm{E}\left(\mathrm{X}^{2}\right)=4, \math...

Consider discrete random variables $X$ and $Y$ with probabilities as follows:$$ \begin{array}{l} P(X=0 \text { and } Y=0)=\frac{1}{4} \\ P(X=1 \text { and } Y=0)=\frac{1}...

Let $X$ and $Y$ be continuous random variables with probability density functions $P_{X}(x)$ and $P_{Y}(y)$, respectively. Further, let $Y=X^{2}$ and$$P_{X}(x)=\begin{cas...

Consider ordinary differential equations given by$\begin{array}{l} \dot{x}_{1}(t)=2 x_{2}(t) \\ \dot{x}_{2}(t)=r(t) \end{array}$with initial conditions $x_{1}(0)=1$ and $...

Let $C$ be a clockwise oriented closed curve in the complex plane defined by $\mid z \mid =1$. Further, let $f(z)=j z$ be a complex function, where $j=\sqrt{-1}$. Then, $...

​​​​​If $u(t)$ is the unit step function, then the region of convergence $\text{(ROC)}$ of the Laplace transform of the signal\[x(t)=e^{t^{2}}[u(t-1)-u(t-10)]\]is$-\infty...