List of top Questions asked in GATE XE

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 density and \(\mathbf{V}\) the three-dimensional velocity vector of the fluid.] 
(i) \(\dfrac{\partial \rho}{\partial t} + \nabla \times (\rho \mathbf{V}) = 0\) 
(ii) \(\dfrac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{V}) = 0\) 
(iii) \(\dfrac{\partial \mathbf{v}}{\partial t} + \rho \, \nabla \cdot \mathbf{v} = 0\) 
(iv) \(\dfrac{\partial \rho}{\partial t} + \mathbf{v} \cdot \nabla \rho = 0\) 
 

A hot-air balloon (volume \(1000~\mathrm{m^3}\)) with gross mass (envelope, basket, payload; excluding the air inside) \(100~\mathrm{kg}\) is in hydrostatic balance. External air: \(T_\text{out}=10^\circ\mathrm{C}\), \(\rho_\text{out}=1~\mathrm{kg\,m^{-3}}\). The temperature of the air inside the balloon is ________ \(^\circ\mathrm{C}\). (Round off to the nearest integer)

In hot weather, a human body cools by evaporation of sweat. The amount of water that must evaporate to cool the body by \(1~^\circ\mathrm{C}\) is __________________________% of the body mass. (Round off to two decimal places) 
[Given: latent heat of vaporization of water \(L_v=2.25\times10^6~\mathrm{J\,kg^{-1}}\); specific heat capacities of body and water \(c=4.2\times10^3~\mathrm{J\,kg^{-1}\,K^{-1}}\).]

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 ______________________________________ kJ. (Round off to the nearest integer) [Use the gas constant for dry air \(R=287~\mathrm{J\,kg^{-1}\,K^{-1}}\).]

The solar constant for the Earth is \(1368~\mathrm{W\,m^{-2}}\). Consider Jupiter with mass \(=320\) times Earth and distance from the Sun \(=5.2\) times Earth’s. The solar constant for Jupiter is ______________________ \(\mathrm{W\,m^{-2}}\). (Round off to the nearest integer)
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 range. While crossing the range, the air mass acquires a relative vorticity of \(-3.65\times 10^{-5}~\mathrm{s^{-1}}\) at the top. If the air mass remains at the same latitude and conserves potential vorticity, the height of the mountain range is \(__________\) km. (Round off to the nearest integer) \textit{[Assume Earth’s angular velocity \(\Omega=7.3\times10^{-5}~\mathrm{s^{-1}}\) and initial relative vorticity is zero.]}
The Sea Surface Temperature (SST), Air Temperature and 10 m Wind Speed at the locations P and Q are given in the table. Assume the density of air, specific heat capacity, and sensible heat transfer coefficient are the same at both locations. The sensible heat (SH) fluxes at P and Q are \(\mathrm{SH}_P\) and \(\mathrm{SH}_Q\). The value of \(\left(\dfrac{\mathrm{SH}_P}{\mathrm{SH}_Q}\right)\) is \(__________\). (in integer)
The north-Atlantic deep-water is associated with ____________.
In the figures given below, L and H indicate low and high pressure centers, respectively; PGF, CoF and CeF indicate Pressure Gradient Force, Coriolis Force and Centrifugal Force, respectively; V is Velocity. [The arrows indicate only the directions but not the magnitudes of the forces and velocity.]
Which of the following is/are the correct representation(s) of the directions of various forces and velocity in the gradient wind balance in the northern hemisphere?
Accumulated rainfall is often measured in mm. If the density of rain water is \(1000~\mathrm{kg\,m^{-3}}\), then one mm of rain is equal to __________________ \(\mathrm{kg\,m^{-2}}\) of rain. (in integer)
A rotating weather system has a tangential velocity of \(100~\mathrm{m/s}\), diameter of \(1~\mathrm{km}\), and located at a latitude where the Coriolis parameter is \(10^{-4}~\mathrm{s^{-1}}\). Which one of the following statements is true about this weather system?
The sea surface height concentric isolines (\(L1\) and \(L2\) in cm) and the distance between them (\(dx\) in km) for three different eddies at the same latitude are given in the figure.
Which one of the following orders is correct about the magnitudes of the geostrophic currents within the isolines?
The zonal gradient of meridional current and the meridional gradient of zonal current is \(-0.3 \times 10^{-3}~\mathrm{s^{-1}}\) and \(0.3 \times 10^{-3}~\mathrm{s^{-1}}\), respectively, at a location P (87°E, 15°N). Which one of the following best explains the nature of the flow?
At which of the following locations in the atmosphere is the anvil of a towering cumulonimbus cloud usually located?
Which one of the following is the main reason why tropical cyclones rarely form over the Bay of Bengal during the summer monsoon season?
Which one of the following is the main cause of the land-sea temperature contrast that drives phenomena like sea breeze and the Indian summer monsoon?
The time period of the inertial oscillation at a location R is 1.5 times that of a particle moving at a speed of \(0.5~\mathrm{m/s}\) at a location S (87°E, 45°S). Which of the following is the latitude of location R? (Round off to the nearest integer)
Which of the following Period(s) correspond(s) to wind waves?
Match the following food products in Column I with their corresponding processes in Column II.
Which of the following is/are inhibitor(s) of enzymatic browning in peeled potatoes?
Match the following enzymes in Column I with their applications in Column II.
The \(F_{121}\) value of a known microorganism with \(Z\) value of \(11~^\circ\mathrm{C}\) is \(2.4\) min for \(99.9999%\) inactivation. For a \(12D\) inactivation of the said microorganism at \(143~^\circ\mathrm{C}\), the \(F\) value (in min) is \underline{\hspace{2cm}. (rounded off to 3 decimal places)}
A fruit juice is concentrated using an ultrafiltration membrane. A feed stream at \(10~\mathrm{kg/min}\) with \(6%\) total solids (by weight) is increased to \(20%\) total solids (by weight). The membrane tube has \(10~\mathrm{cm}\) inside diameter and the pressure difference across the membrane is \(2000~\mathrm{kPa}\). If the permeability constant of the membrane is \(5 \times 10^{-6}\ \mathrm{kg\ water/(m^2\ kPa\ s)\), the length of membrane tube (in m) is \underline{\hspace{2cm}}. (rounded off to 2 decimal places)}
In a typical grinding operation, \(80%\) of the feed material passes through a sieve opening of \(4.75~\mathrm{mm}\); whereas, \(80%\) of the ground product passes through \(0.5~\mathrm{mm}\) opening. If the power required to grind \(2~\mathrm{tonnes/h}\) of the feed material is \(3.8~\mathrm{kW}\), the work index of the material is \underline{\hspace{2cm}. (rounded off to 2 decimal places)}
During which of the following times of the day is the 2 m air temperature usually the lowest at a tropical location?