Recent questions

​​​​A rotating weather system has a tangential velocity of $100 \mathrm{~m} \mathrm{~s}^{-1}$, diameter of $1 \: \mathrm{ km}$ , and located at a latitude where the Corio...

​​​The sea surface height concentric isolines ($\mathbf{L1}$ and $\mathbf{L2}$ in $\mathrm{cm}$ ) and the distance between them ( $\mathbf{d} \mathbf{x}$ in $\mathrm{km}$...

​​​​The vertical (depth) profiles for three parameters $\mathbf{P1}$, $\mathbf{P2}$, and $\mathbf{P3}$ in the northern Indian Ocean are given in the figure below. The val...

​​​​The zonal gradient of meridional current and the meridional gradient of zonal current is $-0.3 \times 10^{-3} \mathrm{~s}^{-1}$ and $0.3 \times 10^{-3} \mathrm{~s}^{-...

​​​​​The north-Atlantic deep-water is associated with $\_\_\_\_\_\_\_$low temperature and low salinityhigh temperature and high salinityhigh temperature and low salinityl...

​​​​Which of the following is the correct form of the mass divergence form of the continuity equation for a compressible fluid?[In the given equations, $\rho$ is the dens...

​​​In the figures given below, $\mathbf{L}$ and $\mathbf{H}$ indicate low and high pressure centers, respectively; $\mathbf{PGF}$, $\mathbf{CoF}$ and $\mathbf{CeF}$ indic...

One kg of dry air at $15^{\circ} \mathrm{C}$ is isothermally compressed to one-tenth of its initial volume. The work done on the system is $\_\_\_\_\_\_ \: \mathrm{kJ}$....

In hot weather, a human body cools by the evaporation of sweat from its skin. The amount of water that must evaporate to cool the body by $1^{\circ} \mathrm{C}$ is $\_\_\...

A floating hot air balloon with volume $1000 \mathrm{~m}^{3}$ and gross mass (excluding the air in the balloon) $100 \: \mathrm{kg}$ is in hydrostatic balance where the e...

The solar constant for the Earth is $1368 \mathrm{~W} \mathrm{~m}^{-2}$. Consider the planet Jupiter whose mass is $320$ times that of the Earth and distance from the Sun...

A column of air mass extending from surface to a height of $10 \:\mathrm{km}$ moving eastward along $30^{\circ} \: \mathrm{N}$ strikes a north-south oriented mountain ran...

The Sea Surface Temperature, Air Temperature and $10 \: m$ Wind Speed at the locations $\textsf{P}$ and $\textsf{Q}$ are given in the table below.[Assume the density of a...

Let\[f(x)=\left\{\begin{array}{cr}\pi+x, & -\pi \leq x<0, \\0, & 0 \leq x<\pi,\end{array}\right.\]with $f(x+2 \pi)=f(x)$. If $F(x)$ represents the Fourier series of $f(x)...

Let $y$ be a non-zero quadratic polynomial satisfying the differential equation\[\left(2+x^{2}\right) \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}-k y=0,\]where $k$ is a rea...

There are four cities, namely, $C_{1}, C_{2}, C_{3}$ and $C_{4}$. The cities are directly connected by four roads as shown in the picture given below, that is, $C_{1}$ is...

Assume that $f:[0,1] \rightarrow \mathbb{R}$ is continuous on $[0,1]$ and differentiable on $(0,1)$ such that $f(x+h)=f(x)+h f^{\prime}(x+\theta h)$ for some $0<\theta<1$...

Let $A$ be a $3 \times 3$ matrix whose eigenvalues are $2,3,4$ and let $I$ be the identity matrix of order 3 . If\[A^{-1}=\frac{1}{2 k}\left(A^{2}-9 A\right)+\frac{13}{k}...

For some integer $k$, the differential equation\[x^{2} \frac{d^{2} y}{d x^{2}}-3 x \frac{d y}{d x}+(k+2) y=0\]is transformed into $(D-2)^{2} y=0$, where $D=\frac{d}{d t}$...

The approximate value $\text{(rounded off to two decimal places)}$ of the integral\[\int_{0}^{1 / 2} e^{-x^{2}} d x\]using the Trapezoidal rule with step-size $h=\frac{1}...

Consider $f(z)=e^{z}$, where $z=x+i y$ and $i=\sqrt{-1}$. Which of the following statements is correct?$f$ is periodic$f$ is not periodic$|f|=1$$\arg (f)=y \pm n \pi$ for...

Let $P$ and $Q$ be two square matrices of the same order. Then, which of the following matrices is/are necessarily equal to $(P+2 Q)^{2}$ ?$P^{2}+4 P Q+4 Q^{2}$$P(P+2 Q)+...

If\[\int_{0}^{\alpha} \int_{\sqrt{x / \alpha}}^{1} e^{y^{3}} d y d x=e-1, \quad \alpha>0,\]then the value $\text{(in integer)}$ of $\alpha$ is __________.

Consider the vector field $\vec{F}=\left(2 x+y^{2}\right) \hat{\imath}+(2 x y+3 y) \hat{\jmath}$ and $\alpha_{m}=\int_{C_{m}} \vec{F} \cdot d \vec{r}$, $m=1,2$, where $C_...

Which one of the following figures shows the CORRECT dependence of apparent viscosity $(\eta)$ on rate of shear strain $(d u / d y)$ for pseudoplastic fluids?

The locus of temporary locations of all particles that have passed through a fixed point in the flow field at a particular instant is known asstreamline.streakline.pathli...

Consider the velocities $u, v$, and $w$ in $x$-, $y$-, and $z$-directions, respectively. The vorticity expression in the $y-z$ plane is$\frac{\partial v}{\partial x}-\fra...

For the laminar, incompressible flow over a flat plate with uniform free stream velocity, the axial pressure gradient within the boundary layer isgreater than zero.less t...

Let $\vec{r}, \vec{V}$, and $m$ be position vector, velocity vector, and mass, respectively in a control mass system. Which one of the following properties is considered ...

The hydraulic diameter for a circular pipe of radius $R$ is$0.5 R$$R$$2 R$$4 R$

For incompressible, laminar, fully-developed flow through a circular pipe, Darcy friction factor and Fanning friction factor are represented as $f$ and $C_{f}$, respectiv...

For an immersed neutrally buoyant body to be in stable equilibrium, the center of gravity of the body is directlyabove the metacenter.below the metacenter.above the cente...

The absolute pressure in a chamber is measured as $400$ mm Hg at a location where the atmospheric pressure is $700$ mm Hg . A vacuum gauge connected to the chamber reads ...

A thin film of an incompressible, Newtonian liquid $\text{(density $\rho$, viscosity $\mu$)}$ with an uniform thickness $(h)$ is flowing down on a vertical plate. The flo...

A one-eighth scale model of a car is to be tested in a wind tunnel. If the air velocity over the car is $16 \mathrm{~m} / \mathrm{s}$, what should be the air velocity $\t...

A set of basic dimensions, mass, length, and time are represented by $\mathrm{M}, \mathrm{L}$, and $\text{T}$, respectively. What will be the dimensions of pressure in $\...

Consider a fluid flow around an airfoil as shown in figure.The directions of drag force and lift force, respectively are alongOA and OC.OA and OD.OB and OC .OB and OD .

A vessel which contains a volatile liquid and its vapour is connected with a mercury manometer as shown in figure. Both the liquid and vapour phases are at equilibrium. T...

The velocity in a one-dimensional flow is given by $u(x)=\frac{a}{(b-x)^{2}} \mathrm{~m} / \mathrm{s}$, where $a=8 \mathrm{~m}^{3} / \mathrm{s}$ and $b=4 \mathrm{~m}$. Th...

Consider two parallel plates separated by a distance of $1$ cm filled with a Newtonian fluid of viscosity $10^{-3} \mathrm{~Pa}$.s. The top plate is moving with a velocit...