Questions without answers in Engineering Mathematics

Which one among the following statements is true for the function $f(x)=x\mid x \mid $?$f(x)$ is discontinuous but not differentiable at $x=0$.$f(x)$ is discontinuous and...

Consider a function $f(z)=z^{2}+z+1$ where $z \in \mathbb{C}$ is a complex variable. A simple closed contour $\gamma$ in $z$-plane encloses the point $z=1+0 j$.The value ...

A data set is given to be $[1,2,0,-1,-3,1,2,0,1]$.The median of the data set is $\_\_\_\_$ . (rounded off to the nearest integer)

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is $\_\...

Given a differential equation $\dfrac{d^{2} x}{d t^{2}}+x=0$ with $x(0) \neq 0$.Which of the following statements is/are true?$\mid x(t) \mid ^{2}+\left|\dfrac{d x(t)}{d ...

If $P e^{x}=Q e^{-x}$ for all real values of $x$, which one of the following statements is true?$P=Q=0$$P=Q=1$$P=1 ; Q=-1$$\frac{P}{Q}=0$

Which one of the following options is correct for the given data in the table?$\begin{array}{|c|c|c|c|c|}\hline\text{Iteration (i)} & 0 & 1 & 2 & 3 \\ \hline\text{Input (...

If one of the eigenvectors of the matrix $A=\left[\begin{array}{cc}-1 & -1 \\ x & -4\end{array}\right]$ is along the direction of $\left[\begin{array}{c}\alpha \\ 2 \alph...

Consider the function $f(z)=\frac{2 z+1}{z^{2}-z}$, where $z$ is a complex variable. The sum of the residues at singular points of $f(z)$ is ______________ (in integer).

The value of the surface integral $\iint_{S}(2 x+z) \mathrm{d} y \mathrm{~d} z+(2 x+z) \mathrm{d} x \mathrm{~d} z+(2 z+y) \mathrm{d} x \mathrm{~d} y$ over the sphere $S: ...

Newton-Raphson method is used to compute the inverse of the number $1.6$. Among the following options, the initial guess of the solution that results in non-convergence o...

The value of the integral $\int_{-\pi}^{\pi}\left(\cos ^{6} x+\cos ^{4} x\right) \mathrm{d} x$ is$\frac{\pi}{2}$$\frac{5 \pi}{8}$$\frac{11 \pi}{8}$$\frac{9 \pi}{8}$

Choose the correct statement(s) from the following options, regarding Cauchy's theorem on complex integration $\oint_{C} f(z) \mathrm{d} z$ where $C$ is a simple closed p...

The probability of a student missing a class is $0.1$. In a total number of $10$ classes, the probability that the student will not miss more than one class is __________...

​​​Let $\boldsymbol{z}=x+i y$ be a complex variable and $\overline{\boldsymbol{z}}$ be its complex conjugate. The equation $\bar{z}^{2}+z^{2}=2$ represents aparabolahyper...

Consider a system given by the following first order differential equation:$$ \frac{d y}{d t}=y+2 t-t^{2} $$where, $y(0)=1$ and $0 \leq t<\infty$. Using a step size $h=0....

Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have ...

​​Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1...

​​The complex functions $f(z)=u(x, y)+i ~v(x, y)$ and $\overline{f(z)}=u(x, y)-i~ v(x, y)$ are both analytic in a given domain. Choose the correct option(s) from the foll...

The readings recorded from a $20$ -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04~ x+10.32$. The regression coefficient ...

The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is$$y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t...

A random variable $X$ has a probability density function$$f_{X}(x)=\begin{cases} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{cases}$$The probability of $X>2$ is $...

Choose solution set $S$ corresponding to the systems of two equations$$\begin{array}{r}x-2 y+z=0 \\x-z=0\end{array}$$Note: $\mathscr{R}$ denotes the set of real numbers$S...

$F(z)=\frac{1}{1-z}$, when expanded as a power series around $z=2$, would result in $F(z)=\sum_{k=0}^{\infty} a_k(z-2)^k$, with the region of convergence $\text{(ROC) } |...

The solution $x(t), t \geq 0$, to the differential equation $\ddot{x}=-k \dot{x}, k>0$ with initial conditions $x(0)=1$ and $\dot{x}(0)=0$ is$x(t)=2 e^{-k t}+2 k t-1$$x(t...

What is $\lim _{x \rightarrow 0} f(x)$, where $f(x)=x \sin \frac{1}{x} ?$$0$$1$$\infty$Limit does not exist

$X$ is a discrete random variable which takes values $0,1$ and $2.$ The probabilities are $P(X=0)=0.25$ and $P(X=1)=0.5$. With $E[ .]$ denoting the expectation operator, ...

Let $f(z)=j \frac{1-z}{1+z}$, where $z$ denotes a complex number and $j$ denotes $\sqrt{-1}$. The inverse function $f^{-1}(z)$ maps the real axis to the___________.unit c...

Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The ...

Given $\text{M} = \begin{bmatrix} 2 & 3 & 7 \\ 6 & 4 & 7 \\ 4 & 6 & 14 \end{bmatrix},$ Which of the following statement(s) is/are correct?The rank of $\text{M}$ is $2$The...

The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)

A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are re...

The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value o...

Consider the differential equation$\dfrac{dy}{dx} + y \ln (y) = 0$If $y(0) = e,$ then $y(1)$ is ___________$e^{e}$$e^{-e}$$e^{(1/e)}$$e^{(-1/e)}$

The matrix $\text{A} = \begin{bmatrix} 4 & 3 \\ 9 & -2 \end{bmatrix}$ has eigenvalues $-5$ and $7.$The eigenvectors(s) is/are __________ $\begin{bmatrix} 1\\ 1 \end{bmat...

For the complex number $z= \frac{a+jb}{a-jb},$ where $a>0$ and $b>0.$Which of the following statement(s) is/are true?The phase is $2 \; \tan^{-1}\frac{b}{a}$The phase is ...

Consider the function $f(z) = \dfrac{1}{(z+1)(z+2)(z+3)}.$ The residue of $f(z)$ at $z = -1,$ is ___________

Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is$1$$2$$3$$4$

Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is$0$$1$$2$$\infty$

Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ______________...