Recent questions and answers in Engineering Mathematics

Let $G$ be an undirected graph, which is a path on $8$ vertices. The number of matchings in $G$ is $\_\_\_\_$. (answer in integer)

The value of the triple integral$$\int_{1}^{2} \int_{0}^{1} \int_{-3}^{3} 2 x y-z^{3} dx \: dy \: dz$$$9$$18$$0$None of the above

What is the matrix transformation which takes the independent vectors $\begin{pmatrix}1& \\2& \end{pmatrix}$ $\text{and}$ $\begin{pmatrix}2& \\5& \end{pmatrix}$ $\text{an...

Suppose an unbiased coin is tossed $6$ times. Each coin toss is independent of all previous coin tosses. Let $E_{1}$ be the event that among the second, fourth, and sixth...

​​​​​Let $X=a Z+b$, where $Z$ is a standard normal random variable, and $a, b$ are two unknown constants. It is given that\[E[X]=1, \quad E[(X-E[X]) Z]=-2, \quad E\left[(...

Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as\[a_{1} \sim a_{...

Let $X$ be a random variable uniformly distributed in the interval $[1,3]$ and $Y$ be a random variable uniformly distributed in the interval $[2, 4]$. If $X$ and $Y$ are...

Let $n>1$. Consider an $n \times n$ matrix $M$ with its elements from $\mathbb{R}$. Let the vector $(0,1,0,0, \ldots, 0) \in \mathbb{R}^{n}$ be in the null space of $M$.W...

​​​​Let $X$ be a continuous random variable whose cumulative distribution function $\text{(CDF)}$ $F_{X}(x)$, for some $t$, is given as follows:\[F_{X}(x)=\left\{\begin{a...

​​​​For $x \in \mathbb{R}$, the floor function is denoted by $f(x)=\lfloor x\rfloor$ and defined as follows\[\lfloor x\rfloor=k, \quad k \leq x < k + 1,\]where $k$ is a...

Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|...

Let $\mathbf{u}$ and $\mathbf{v}$ be two mutually orthogonal unit vectors in $\mathbb{R}^n$, where $n \ge 3$. A matrix $\mathbf{A}$ is defined using outer products as:$$\...

Let $\mathrm{C}=\left(\begin{array}{ccc}\sin ^{2} \theta & 1 & \cos ^{2} \theta \\ \cos ^{2} \theta & 1 & \sin ^{2} \theta \\ -3 & 4 & 7\end{array}\right)$ Then $\operato...

The product of the non-zero eigenvalues of the matrix is ____$\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & ...

Select the correct statement(s) regarding the existence of real matrices:A) There exists a matrix whose nullspace is $\text{span}\left\{ \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 ...

According to me both are inferencing each other, please someone suggest whether D is correct or B, if B is correct please provide a valid reason I could not understand wh...

Let $A= [\mathbf{c}_1\ \mathbf{c}_2\ \mathbf{c}_3\ \mathbf{c}_4]$ be a $3 \times 4$ real matrix. The complete solution of$A\mathbf{x} = \begin{bmatrix} 2 \\ -1 \\ 3 \end{...

​GATE - 2007 EE | LINEAR ALGEBRA QUESTION    The solution I found is a bit odd. I have my own approach: first, take x common and then y common. After analyzing it, I can...

Is lambda (λ) parameter used in Poisson Distribution, Exponential Distribution the same. If say λ = 4 customers per hour, then Expected value, E(possion X) = rate = λ = 4...