GATE XE format:nat PYQs & Answers — Page 46

Questions 451–460 of 668. Imported answers require independent review unless marked reviewed.

Topic practice 668 questionsPage 46 of 67

Mₓ and Mᵧ represent the ocean mass transport in the x and y directions, respectively. Lₓ and Lᵧ are the corresponding east-west and north-south length scales. For a typical equatorial ocean gyre, if the ratio of zonal to meridional mass transport ≈ 10, then Lₓ ≈ ______ Lᵧ.

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Assume that pressure varies exponentially with height:

, where

is the pressure at a height

above the surface,

is the surface pressure, and the scale height

km. Under these conditions, one-fourth of the total mass of the atmosphere lies above a height (rounded off to 1 decimal place) of ______ km above the surface.

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Consider an atmospheric column of depth 300 m at the Earth’s surface with an average temperature of 300 K. If the temperature of the layer rises by ΔT = 10 °C, the layer depth

will increase by Δh. Assuming ΔT/T ≈ Δh/h, air density remains unchanged at 1 kg m⁻³ and g = 10 m s⁻², the change in surface pressure is ______ kg m⁻¹ s⁻².

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The value of

for which the system of equations

has a solution is ________ .

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The value of the line integral

, where

is the circle

oriented counter clockwise, is ________ .

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Let

and

be two linearly independent solutions of the differential equation

. If

, then

is ________ .

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The number of critical points of the function

at which there is neither maximum nor minimum is ________ .

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Let

, where

and

is the circle

oriented counter clockwise. Then, the value of

rounded off to one decimal place is ________ .

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Consider the two-dimensional laminar flow of water (

) between two infinitely long parallel plates

apart as shown in the figure below. The velocity profile at any location is given by

where

is in m. The magnitude of shear stress (in

, rounded off to 2 decimal places) acting on the bottom plate is ________

Diagram for Engineering Sciences question 7

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The maximum velocity in a fully developed laminar incompressible flow through a circular pipe of constant cross-sectional area is

. The average velocity (in m/s) of the flow is ________

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GATE XE format:nat PYQs

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