Recent questions and answers

The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is$1$$2$$3$$4$

The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3\\ 3 & 4 & 2 & 5\\ 5 & 6 & 2 & 7\\ 7 & 8 & 2 & 9 \end{bmatrix}$ is$1$$2$$3$$4$

What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ column...

Let $y$ be a non-zero vector of size $2022 \times 1.$ Which of the following statement(s) is/are $\text{TRUE}?$$yy^{T}$ is a symmetric matrix.$y^{T}y$ is an eigenvalue of...

$\text{P}$ and $\text{Q}$ are two square matrices of the same order. Which of the following statement(s) is/are correct?If $\text{P}$ and $\text{Q}$ are invertible, then ...

For the matrix$$[A]=\left[\begin{array}{lll}1 & 2 & 3 \\3 & 2 & 1 \\3 & 1 & 2\end{array}\right]$$which of the following statements is/are TRUE?The eigenvalues of $[A]^{T}...

Two vectors $\left[\begin{array}{llll}2 & 1 & 0 & 3\end{array}\right]^{T} $ and $\left[\begin{array}{cccc}1 & 0 & 1 & 2\end{array}\right]^{T}$ belong to the null space of...

Consider two matrices $\mathbf{A}=\left[\begin{array}{lll}2 & 1 & 4 \\ 1 & 0 & 3\end{array}\right]$ and $\mathbf{B}=\left[\begin{array}{cc}-1 & 0 \\ 2 & 3 \\ 1 & 4\end{ar...

​​​​​Suppose $\lambda$ is an eigenvalue of matrix $A$ and $x$ is the corresponding eigenvector. Let $x$ also be an eigenvector of the matrix $B=A-2 I$, where $I$ is the i...

Pick the CORRECT eigen value(s) of the matrix $[A]$ from the following choices.$$[A]=\left[\begin{array}{ll} 6 & 8 \\ 4 & 2 \end{array}\right]$$$10$$4$$-2$$-10$

For the matrix $[A]$ given below, the transpose is $\_\_\_\_\_\_\_\_\_\_\_$$$[A]=\left[\begin{array}{lll} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{array}\right]$$$\left[\...

The matrix $M$ is defined as $$M = \begin{bmatrix} 1 & 3\\ 4 & 2 \end{bmatrix}$$ and has eigenvalues $5$ and $-2$. The matrix $Q$ is formed as $$Q = M^{3} - 4M^{2} - 2M$$...

​​​​​The smallest positive root of the equation\[x^{5}-5 x^{4}-10 x^{3}+50 x^{2}+9 x-45=0\]lies in the range$0 < x \leq 2$$2 < x \leq 4$$6 \leq x \leq 8$$10 \leq x \leq 1...

​​​​​The second-order differential equation in an unknown function $u: u(x, y)$ is defined as\[\frac{\partial^{2} u}{\partial x^{2}}=2\]Assuming $g: g(x), f: f(y)$, and $...

Concrete of characteristic strength $30 \mathrm{MPa}$ is required. If $40$ specimens of concrete cubes are to be tested, the minimum number of specimens having at least $...

A two lane, one-way road with radius of $50$ m is predominantly carrying lorries with wheelbase of $5$ m. The speed of lorries is restricted to be between $60$ kmph and $...

A super-elevation $e$ is provided on a circular horizontal curve such that a vehicle can be stopped on the curve without sliding. Assuming a design speed $v$ and maximum ...

A road is being designed for a speed of $110$ km/hr on a horizontal curve with a super elevation of $8 \%$. If the coefficient of side friction is $0.10$, the minimum rad...

The perception-reaction time for a vehicle travelling at $90$ km/h, given the coefficient of longitudinal friction of $0.35$ and the stopping sight distance of $170$ m (a...

The base length of the runway at the mean sea level $\text{(MSL)}$ is $1500 \; \text{m}.$ If the runway is located at an altitude of $300 \; \text{m}$ above the $\text{(M...

Consider the following statements $(\mathrm{P})$ and $(\mathrm{Q})$ :$(\mathrm{P})$ : Fly ash and ground granulated blast furnace slag can be used as mineral admixtures i...

Consider the function given below and pick one or more CORRECT statement(s) from the following choices.$$f(x)=x^{3}-\frac{15}{2} x^{2}+18 x+20$$$f(x)$ has a local minimum...

The figure shows a network diagram for a construction project. The activities $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}, \mathrm{D}, \mathrm{E}$, and $\mathrm{F}$ are repre...

If the Fore Bearing of the lines $AB$ and $BC$ are $60^{\circ}$ and $122^{\circ}$, respectively, then the interior angle $\angle \mathrm{ABC}$ (in degrees) is $\_\_\_\_\_...

​​​​​"Why do they pull down and do away with crooked streets, I wonder, which are my delight, and hurt no man living? Every day the wealthier nations are pulling down one...

​​​​​For a flowing fluid, a dimensionless combination of velocity $(V)$, length scale $(l)$, and acceleration due to gravity $(g)$ would be$\frac{V^{2}}{g l}$$\frac{V g}{...

​​​​​Fecal Coliform (FC) concentration in river water was measured as $10780 \: \: \mathrm{cfu} / 100 \mathrm{ ml}$ . The FC concentration after the conventional water tr...

Which of the following process(es) can be used for conversion of salt water into fresh water?MicrofiltrationElectrodialysisUltrafiltrationReverse osmosis

Henry's law constant for transferring $O_{2}$ from air into water, at room temperature, is $1.3 \dfrac{\text{mmol}}{\text{liter-atm}}$. Given that the partial pressure of...

In a water sample, the concentrations of $Ca^{2+}, Mg^{2+}$ and $\text{HCO}_{3}^{-}$ are $100$ $\text{mg/L}$, $36$ $\text{mg/L}$ and $122$ $\text{mg/L}$, respectively. Th...

A $2\%$ sewage sample (in distilled water) was incubated for $3$ days at $27^{\circ}C$ temperature. After incubation, a dissolved oxygen depletion of $10\:mg/L$ was recor...

A water treatment plant has a sedimentation basin of depth $3\:m$, width $5\:m$, and length $40\:m$. The water inflow rate is $500\:m^{3}/h$. The removal fraction of part...

The liquid forms of particulate air pollutants aredust and mistmist and spraysmoke and sprayfly ash and fumes

The shape of the most commonly designed highway vertical curve iscircular (single radius)circular (multiple radii)parabolicspiral

A highway designed for $\text{80 km/h}$ speed has a horizontal curve section with radius $\text{250 m}$. If the design lateral friction is assumed to develop fully, the r...

Two reservoirs are connected through a $930$ m long, $0.3$ m diameter pipe, which has a gate valve. The pipe entrance is sharp (loss coefficient $=0.5$) and the valve is ...

In a catchment, there are four rain-gauge stations, $P, Q, R$, and $S$. Normal annual precipitation values at these stations are $780$ mm, $850$ mm, $920$ mm, and $980$ m...

The $4$-hr unit hydrograph for a catchment is given in the table below. What would be the maximum ordinate of the S – curve (in $m^3/s$) derived from this hydrograph?$$\b...