Recent activity in Engineering Mathematics

A matrix $M$ is constructed by stacking three column vectors $v_{1}, v_{2}, v_{3}$ as$$ M=\left[\begin{array}{lll} v_{1} & v_{2} & v_{3} \end{array}\right]$$Choose the se...

$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\wi...

The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightar...

The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional tox$^{-1}$x$^{2}$x$^{3}...

A $2 n \times 2 n$ matrix $A=\left[a_{i j}\right]$ has its elements as$$ a_{i j}=\begin{cases} \beta & \text { if }(i+j) \text { is odd } \\ -\beta & \text { if }(i+j) \t...

Consider a matrix$A=\left[\begin{array}{ccc}1 & 0 & 2 \\-1 & 1 & 0 \\0 & 1 & 2\end{array}\right]$Let $\boldsymbol{b}=\left[\begin{array}{l}1 \\ 3 \\ 0\end{array}\right]$ ...

A matrix $P \in \mathbb{R}^{3 \times 3}$ satisfies $P^{3}-4 P^{2}+5 P-2 I=0$ where $I$ is a $3 \times 3$ identity matrix.The set of all possible eigenvalues of matrix $P$...

The solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=9 \frac{x}{y}$ representsa hyperbolaa parabolaan ellipsea circle

The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer).$$A=\left[\begin{array}{cc}1 & 4 \\-3 &...

A $3 \times 3$ matrix $P$ with all real elements has eigenvalues $\dfrac{1}{4}, 1$, and $-2$. The value of $\mid P^{-1}\mid$ is $\_\_\_\_\_\_$ (rounded off to nearest int...

Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.

Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded ...