Recent activity in Engineering Mathematics

Consider a disk $D$ of radius $1$ centered at the origin. Let $X$ be a point uniformly distributed on $D$ and let the distance of $X$ from the origin be $R$. Let $A$ be t...

Consider a sequence of non-negative numbers $\left\{x_{n}: n=1,2, \ldots\right\}$. Which of the following statements cannot be true?$\sum_{n=1}^{\infty} x_{n}=\infty$ but...

The differential equation, $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+\sin$ $y=0$, islinearnon-linearhomogeneousof degree two

Define the $\ell_{p}$ ball in two dimensions as the set of points $(x, y)$ such that $|x|^{p}+|y|^{p} \leq 1$. Which of the following is $\text{FALSE:}$The $\ell_{2}$ bal...

In radioactive decay, the disintegration rate of the nuclei isconstant at all timesinversely proportional to half-life of the nucleiinversely proportional to the number o...

Which one of the following functions is strictly bounded?$\frac{1}{x^2}$$e^x$$x^2$$e^{-x^2}$

For $|x| \ll 1$, $\operatorname{coth}(x)$ can be approximated as$x$$x^2$$\frac{1}{x}$$\frac{1}{x^2}$

 The derivative of the symmetric function drawn in given figure will look like          

The value of the integral of the function $g(x, y)=4 x^{3}+10 y^{4}$ along the straight line segment from the point $(0,0)$ to the point $(1,2)$ in the $x\text{-}y$ plane...

The value of the integral$$ \iint_{D} 3(x^{2} + y^{2})dxdy,$$where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest in...

The value of the integral $\text{I}=\frac{1}{\sqrt{2 \pi}} \int_{0}^{\infty} \exp \left(-\frac{x^{2}}{8}\right)$ $d x$ is$1$$\pi$$2$$2 \pi$

The eigen values of the matrix $A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$ are$1,1$$-1,-1$$j,-j$$1,-1$

Let, $\mathrm{A}=\left[\begin{array}{cc}2 & -0.1 \\ 0 & 3\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{ll}\frac{1}{2} & \mathrm{a} \\ 0 & \mathrm{~b}\end{a...

$e^{A t}$ can be expanded as$\sum_{k=0}^{\infty} \frac{\mathrm{A}^{k} t^{k}}{(k+1) !}$$\sum_{k=0}^{\infty} \frac{\mathrm{A}^{k} t^{k}}{k !}$$\sum_{k=0}^{\infty} \frac{\ma...

The rank of the matrix $\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{array}\right]$ is$0$$1$$2$$3$

Consider the square region $R$ in the $X-Y$ plane as shown with the dark shading in the Figure. The value of $\iint_{R}\left(x^{2}+y^{2}-1\right) d x d y$ is $\_\_\_\_$ ....

Let $X, N, Y$ and $Z$ be random variables. The variables $X$ and $N$ are independent of each other. $X$ is uniformly distributed between $-1$ and $1 ; N$ follows Normal d...

Consider the two series, $S_{A}$ and $S_{B}$, where\[\begin{array}{l}S_{A}=\sum_{n=1}^{\infty} \frac{n^{2}}{2^{n}} \\S_{B}=1+\frac{1}{2}+\frac{1}{8}+\frac{1}{16}+\frac{1}...

A surface is given by $z^{2}=2 x^{2}-y^{2}$ and $\vec{n}$ and $-\vec{n}$ are unit normal vectors to the surface at the point $\vec{P}=\hat{\boldsymbol{\imath}}+\sqrt{2} \...