Questions without a selected answer in Engineering Mathematics

Domain $A$ is bounded by curve $x^{2}=4 y$, ordinate $x=2$, and $x$ axis.The value of $\iint_{A} y d x d y$ is$1 / 5$$1 / 3$$5 / 12$$1 / 2$

The order and degree of the following differential equation are $m$ and $n$, respectively.\[\frac{\partial^{3} \varphi}{\partial x^{3}}+\frac{\partial^{2} \varphi}{\parti...

Newton-Raphson method for solving algebraic equations is based onTaylor seriesFourier seriesLaurent seriesPower series

The exact solution of $\int_{0}^{4} \frac{d x}{1+x}$ is represented as $n$.If $m$ represents numerically evaluated value of the above integral using Trapezoidal rule by c...

If $w=\log _{e} z=\log _{e}(x+i y)$, where $i=\sqrt{-1}$, then which one of the following statements is correct?$w$ is analytic everywhere except at $z=0$$w$ is non-analy...

Consider the following differential equation\[\frac{\partial y}{\partial x}=3 \frac{\partial y}{\partial t}+y\]If $y(x, 0)=10 e^{-2 x}$, then the solution of the differen...

Let $f(t)$ be a function of $t$ defined for all positive values of $t$. The Laplace transform of $f(t)$ denoted by $L\{f(t)\}=\int_{0}^{\infty} e^{-s t} f(t) d t$, provid...

For the differential equation given below, which one of the following options is correct?$$ \frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0 ...

If two unbiased coins are tossed, then what is the probability of having at least one head?$0.25$$0.5$$0.675$$0.75$

The values of a function $f$ obtained for different values of $x$ are shown in the table below.$x$00.250.50.751.0$f(x)$0.92.01.51.80.4Using Simpson's one-third rule,$\int...

​​In the closed interval $[0,3]$, the minimum value of the function $f$ given below is$$ f(x)=2 x^{3}-9 x^{2}+12 x$$ $0$$4$$5$$9$

​​​​​​Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, arePer...

If $C$ is the unit circle in the complex plane with its center at the origin, then the value of $n$ in the equation given below is _________ (rounded off to $1$ decimal ...

The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{\imath}+\sqrt{3} \hat{\jmath})$ is __________ (round...

Let $y$ be the solution of the differential equation with the initial conditions given below. If $y(x=2)=A \ln 2$, then the value of $A$ is ________ (rounded off to $2$ d...

Consider the second-order linear ordinary differential equationx ^ 2 * (d ^ 2 * y)/(d * x ^ 2) + x * d/dx (y) - y = 0with the initial conditionsy(x = 1) = 6 ,The value of...

​​​In order to numerically solve the ordinary differential equation $\frac{d y}{d t}=-y$ for $t>0$, with an initial condition $y(0)=1$, the following scheme is employed\[...

​​The value of the surface integralwhere $S$ is the external surface of the sphere $x^{2}+y^{2}+z^{2}=R^{2}$ is$0$$4 \pi R^{3}$$\frac{4 \pi}{3} R^{3}$$\pi R^{3}$

​​​​​Let $f(z)$ be an analytic function, where $z=x+i y$. If the real part of $f(z)$ is $\cosh x \cos y$, and the imaginary part of $f(z)$ is zero for $y=0$, then $f(z)$ ...

​​​​​A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson dist...

If the value of the double integral\[\int_{x=3}^{4} \int_{y=1}^{2} \frac{d y d x}{(x+y)^{2}}\]is $\log _{e}(a / 24)$, then $a$ is __________ (answer in integer).

If $x(t)$ satisfies the differential equation\[t \frac{d x}{d t}+(t-x)=0\]subject to the condition $x(1)=0$, then the value of $x(2)$ is __________ (rounded off to 2 deci...

Let $\text{X}$ be a continuous random variable defined on $[0,1]$ such that its probability density function $f(x)=1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y=\log...

The figure shows the plot of a function over the interval $[-4,4]$. Which one of the options given $\text{CORRECTLY}$$ identifies the function?$|2-x|$$|2-| x||$$|2+| x||$...