Recent questions in Engineering Mathematics

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} \...

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}...

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 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 $\_\_\_\_$ ....

Consider the following series:$\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$$\sum_{n=1}^{\infty} \frac{1}{n(n+1)}$$\sum_{n=1}^{\infty} \frac{1}{n!}$Choose the correct option.On...

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.What is the probability that the two balls drawn have diff...

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$, defined as$$ f(x)=2 x^{3}-3 x^{2}-12 x+1$$Which of the following statements is/are correct?(Here, $\mathbb{R...

The function $y(t)$ satisfies$$t^{2} y^{\prime \prime}(t)-2 t y^{\prime}(t)+2 y(t)=0,$$where $y^{\prime}(t)$ and $y^{\prime \prime}(t)$ denote the first and second deriva...

A source transmits symbol $S$ that takes values uniformly at random from the set $\{-2,0,2\}$. The receiver obtains $Y=S+N$, where $N$ is a zero-mean Gaussian random vari...

Consider a non-negative function $f(x)$ which is continuous and bounded over the interval $[2,8]$. Let $M$ and $m$ denote, respectively, the maximum and the minimum value...

Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle $C$ in the complex plane is/are TRUE?$\oint_{C} e^{z} \: d ...

The random variable $X$ takes values in $\{-1,0,1\}$ with probabilities $P(X=-1)=P(X=1)=\alpha$ and $P(X=0)=1-2 \alpha$, where $0<\alpha<1 / 2$.Let $g(\alpha)$ denote the...

Two fair dice (with faces labeled $1,2,3,4,5$, and $6$) are rolled. Let the random variable $X$ denote the sum of the outcomes obtained.The expectation of $X$ is ________...

Consider the vectors $$ \boldsymbol{a}=\left[\begin{array}{l} 1 \\ 1 \end{array}\right], \quad \boldsymbol{b}=\left[\begin{array}{c} 0 \\ 3 \sqrt{2} \end{array}\right] ...

​​​​​In the context of Bode magnitude plots, $40 \mathrm{~dB} /$ decade is the same as $\_\_\_\_\_\_.$$12 \mathrm{~dB} /$ octave$6 \mathrm{~dB} /$ octave$20 \mathrm{~dB} ...

​​​Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant. Which one of the following statements is true ...