GATE ME year:2024 PYQs & Answers — Page 2

Questions 11–20 of 65. Imported answers require independent review unless marked reviewed.

In order to numerically solve the ordinary differential equation

for

, with an initial condition

, the following scheme is employed

Here,

is the time step and

for

This numerical scheme will yield a solution with non-physical oscillations for

. The value of

Your answerChoose one option.

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The value of the surface integral

where

is the external surface of the sphere

Your answerChoose one option.

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Let

be an analytic function, where

. If the real part of

, and the imaginary part of

is zero for

, then

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Consider the system of linear equations

The values of

and

such that there exists a non-trivial null space and the system admits infinite solutions are

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Let

be a twice differentiable function from

. If

where

is sufficiently small (here

is the Euclidean norm or distance function), then

where

is a point on the line segment joining

and

. If

is a strict local minimum of

, then which one of the following statements is TRUE?

Your answerChoose one option.

and

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The velocity field of a two-dimensional, incompressible flow is given by

where

and

denote the unit vectors in

and

directions, respectively. If

, then

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A plane, solid slab of thickness

, shown in the figure, has thermal conductivity

that varies with the spatial coordinate

, where

and

are positive constants (

). The slab walls are maintained at fixed temperatures of

and

. The slab has no internal heat sources. Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?

Diagram for Mechanical Engineering question 17

Your answerChoose one option.

Diagram for Mechanical Engineering question 17 (figure 2)

Diagram for Mechanical Engineering question 17 (figure 3)

Diagram for Mechanical Engineering question 17 (figure 4)

Diagram for Mechanical Engineering question 17 (figure 5)

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Consider incompressible laminar flow over a flat plate with freestream velocity of

. The Nusselt number corresponding to this flow velocity is

. If the freestream velocity is doubled, the Nusselt number changes to

. Choose the correct option for

Your answerChoose one option.

1.26

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Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., z direction). In the following statements,

is the temperature of the fluid,

is the wall temperature and

is the bulk mean temperature of the fluid. Which one of the following statements is TRUE?

Your answerChoose one option.

For a thermally fully developed flow,

, always.

For constant wall temperature of the duct,

Nusselt number varies linearly along the

direction for a thermally fully developed flow.

For constant wall temperature (

) of the duct,

increases exponentially with distance along

direction.

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A furnace can supply heat steadily at 1200 K at a rate of 2400 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at 300 K is

Your answerChoose one option.

300

150

1800

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GATE ME year:2024 PYQs

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20