Recent questions in Engineering Mathematics

A fifth-degree polynomial in $x$ is defined for $x>0$. All coefficients of the polynomial are positive. The first derivative of the polynomial is obtained numerically at ...

A partial differential equation is given below.\[\frac{\partial^{2} u}{\partial x^{2}}-\frac{\partial^{2} u}{\partial y^{2}}=0\]Possible solution(s) is/are:$(x+y)^{5}$$(x...

The probability (in $\%$) that a storm having return period of $15$ years may occur in the next $10$ years is $\_\_\_\_$ (rounded off to two decimal places).

Let $f(x)=\left|\begin{array}{ccc}x^{3} & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^{2} & p^{3}\end{array}\right|$ where $p$ is a constant.The value of $\dfrac{d^{3}}{d x^{3...

Consider differential equation $\dfrac{d y}{d x}+x y=x$ with the condition as $y=0$ at $x=0$. The value of $y$ at $x=1.0$ is $\_\_\_\_$ (rounded off to two decimal places...

The age (in years) of a population is normally distributed with a mean of $36$ and standard deviation of $12$. The height (in cm) of the same population is also normally ...

Matrix $P$ is given as\[P=\left[\begin{array}{lll}1 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 1\end{array}\right]\]The TRUE option isTrace of $P$ is equal to the sum of the Eigen val...

Given:\[\left[\begin{array}{lll}1 & 1 & 1 \\1 & 0 & 2\end{array}\right]\left\{\begin{array}{l}x_{1} \\x_{2} \\x_{3}\end{array}\right\}=\left\{\begin{array}{l}0 \\0\end{ar...

Bag $\text{I}$ contains $4$ white and $6$ black balls.Bag $\text{II}$ contains $4$ white and $3$ black balls.One ball is drawn at random from any one of the two bags and ...

A matrix is given as:\[\left[\begin{array}{cc}9 & 15 \\15 & 50\end{array}\right]\]By performing Cholesky decomposition, $\left|l_{22}\right|$ of the lower triangular matr...

Let $f(x)$ be a continuous function defined in $[0,2] \rightarrow \mathbb{R}$ and satisfying the equation $\int_{0}^{2} f(x)[x-f(x)] d x=\dfrac{2}{3}.$The value of $f(1)$...

An ordinary differential equation is given below.\[x^{2} \frac{d^{2} y}{d x^{2}}=6 y\]Considering $a$ and $b$ as arbitrary constants, the general solution of the equation...

Starting with the first approximation as $x=0.5$, the second approximation for the root of the following function by the Newton-Raphson method is $\_\_\_\_$ (rounded off ...

Values of $y$ for different values of $x$ are tabulated below.\[\begin{array}{|c|c|c|c|}\hlinex & -2 & 1 & 2 \\\hliney & 28 & 4 & 16 \\\hline\end{array}\]If a second-degr...

Given that $A$ and $B$ are not null sets, which of the following statements regarding probability is/are CORRECT?$\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathr...

Consider a discrete random variable $X$ whose probabilities are given below. The standard deviation of the random variable is $\_\_\_\_\_\_\_\_\_$ (round off to one decim...

​​​​The sum of the following infinite series is:$$ \frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\frac{1}{5!}+\cdots $$$\pi$$1+e$$e-1$$e$

​​​​Which one of the following options is the correct Fourier series of the periodic function $f(x)$ described below:$$ f(x)=\begin{cases}0 & \text { if }-2 < x <-1 \\ 2...

​​​​​$X$ is a random variable that can take any one of the values $0,1,7,11$, and $12$ . The probability mass function for $X$ is$$\begin{array}{l}P(X=0)=0.4 ; \quad P(X=...

Let $y$ be the solution of the initial value problem $y^{\prime \prime}+0.8 y^{\prime}+0.16 y=0$, where $y(0)=3$ and $y^{\prime}(0)=4.5$. Then, $y(1)$ is equal to $\_\_\_...

Consider the differential equation given below. Using the Euler method with the step size $(h)$ of $0.5$, the value of $y$ at $x=1.0$ is equal to $\_\_\_\_\_$ (rounded of...

A one-way, single lane road has traffic that consists of $30 \%$ trucks and $70 \%$ cars. The speed of trucks (in $\mathrm{km} / \mathrm{h}$ ) is a uniform random variabl...

​​​​A partial differential equation\[\frac{\partial^{2} T}{\partial x^{2}}+\frac{\partial^{2} T}{\partial y^{2}}=0\]is defined for the two-dimensional field $T: T(x, y)$,...

​​​​The statements $\mathrm{P}$ and $\mathrm{Q}$ are related to matrices $\mathbf{A}$ and $\mathbf{B}$, which are conformable for both addition and multiplication.$\text{...

​​​​​The second derivative of a function $f$ is computed using the fourth-order Central Divided Difference method with a step length $h$.The CORRECT expression for the se...

​​​​​​The function $f(x)=x^{3}-27 x+4,1 \leq x \leq 6$ hasMaxima pointMinima pointSaddle pointInflection point