Recent questions tagged numerical-answers

A radioactive isotope sample has a decay constant $\lambda= 2.31 \times 10^{-4} \text{year}^{-1}$. Initially the sample contains $8000 \times 10^{15}$ atoms. The sample d...

A fuel with composition by mass is given as $78 \%$ carbon $(\mathrm{C}), 16 \%$ hydrogen $\left(\mathrm{H}_{2}\right)$, $3.2 \%$ sulphur $(\mathrm{S}), 1.6 \%$ oxygen $\...

A $75$ $\mathrm{kWh}$ electric vehicle battery pack made of lithium-ion batteries has $4,800$ individual cells in a series-parallel combination, with $120$ cells in serie...

A nonlinear load connected to a sinusoidal voltage source (of peak value $V_{m}$ and $50$ $\mathrm{Hz}$ frequency) draws a quasi-square wave shaped current (of maximum va...

A resident has ₹ $50,000$ to purchase a $5$-star rated air conditioner with a life of $10$ years. The annual energy cost savings (in ₹) needed to recover this investment ...

A country’s annual crude oil production in the year $2024$ was $150$ million tons and that in $2022$ was $141$ million tons. The proven crude oil resources in $2024$ of t...

The useful heat gain in Watt (rounded off to one decimal place) of a solar flat plate collector using Hottel-Whillier-Bliss equation is $\_\_\_\_$.Assume:Collector heat r...

Let $y(x)$ be the solution of the initial value problem,$$\begin{array}{c}x^{2} y^{\prime \prime}+x y^{\prime}-y=0, \quad x>0, \\y(1)=0, \quad y^{\prime}(1)=2 .\end{array...

Suppose that $2$ is an eigenvalue of the matrix$$\left[\begin{array}{ccc}0 & 3 & -\alpha \\0 & 1 & 0 \\1 & -1 & 3\end{array}\right]$$Then the value of $\alpha$ is equal t...

Let $u(x, t)$ be the solution of the initial boundary value problem$$ \begin{array}{c}\frac{\partial u}{\partial t}-\frac{\partial^{2} u}{\partial x^{2}}-u=0, \quad 0< x ...

Consider, $i$ and $j$ are unit vectors along $x$ and $y$ directions of a Cartesian $(x, y)$ coordinate system, respectively and $t$ is time. Temperature ($T$) and fluid v...

Driven by a pressure gradient of $100 \mathrm{kPa} / \mathrm{m}$, a fluid of dynamic viscosity $0.1 \mathrm{~Pa.s}$ flows between two fixed infinitely large parallel plat...

An incompressible fluid is flowing between two infinitely large parallel plates separated by $5 \mathrm{mm}$ distance. The bottom plate is stationary and the top plate is...

Consider, a kite weighing $100$ grams as essentially a rigid flat plate making an angle $8^{\circ}$ with the horizontal and having a planform area of $0.045 \mathrm{~m}^{...

A fixed control volume has four one-dimensional boundary sections $(1,2,3$, and $4$). For a steady flow inside the control volume, the flow properties at each section are...

A ship is to be operated in a fluid medium with kinematic viscosity $0.032 \times 10^{-3} \mathrm{~m}^{2} / \mathrm{s}$. A one-tenth scale model of the ship is built for ...

Water flows through a pipe of diameter $20 \mathrm{cm}$ at a flow rate of $0.025 \mathrm{~m}^{3} / \mathrm{s}$. A pitotstatic tube is placed at the centre of the pipe and...

An oil of density $870 \mathrm{~kg} / \mathrm{m}^{3}$ and viscosity $0.036 \: \mathrm{Pa.s}$ flows through a straight pipe of $10 \: \mathrm{cm }$ diameter and $1.5 \: \m...

If solid tin is in equilibrium with its vapor, the degree of freedom is (answer in integer) $\_\_\_\_\_\_$

A $\textsf{GaP-GaAs}$ semiconductor $\textsf{LED}$ display has a band gap of $1.9 \: \mathrm{eV}$. The wavelength of emitted light in $\mu \mathrm{m}$ is (rounded off to ...