GATE CE area:engineering-mathematics PYQs & Answers — Page 8

Questions 71–80 of 174. Imported answers require independent review unless marked reviewed.

The differential equation,

is solved by employing a backward difference scheme within the finite difference framework. The value of

at the

time-step, for some

, is 1.75. The corresponding time (t) is 3.14 s. Each time step is 0.01 s long. Then, the value of

is ______ (round off to three decimal places).

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A 5 cm long metal rod AB was initially at a uniform temperature of

°C. Thereafter, temperature at both the ends are maintained at 0 °C. Neglecting the heat transfer from the lateral surface of the rod, the heat transfer in the rod is governed by the one-dimensional diffusion equation

, where D is the thermal diffusivity of the metal, given as 1.0 cm²/s.

The temperature distribution in the rod is obtained as

where x is in cm measured from A to B with

at A, t is in s,

are constants in °C, T is in °C, and

is in s⁻¹.

The value of

(in s⁻¹, rounded off to three decimal places) is ____________.

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Consider the following expression:

where

, and

are variables, and

is a complex number. The partial differential equation derived from the above expression is

Your answerChoose one option.

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The function

satisfies the Laplace equation

on a circular domain of radius

with its center at point

with coordinates

. The value of this function on the circular boundary of this domain is equal to 3.

The numerical value of

is:

Your answerChoose one option.

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For the equation

the correct description is

Your answerChoose one option.

an ordinary differential equation of order 3 and degree 2.

an ordinary differential equation of order 3 and degree 3.

an ordinary differential equation of order 2 and degree 3.

an ordinary differential equation of order 3 and degree 3/2.

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is equal to

Your answerChoose one option.

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The matrix

is defined as

and has eigenvalues 5 and −2. The matrix

is formed as

Which of the following is/are the eigenvalue(s) of matrix

Your answerSelect all correct options. You can choose more than one.

−20

−30

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and

are two square matrices of the same order. Which of the following statement(s) is/are correct?

Your answerSelect all correct options. You can choose more than one.

and

are invertible, then

and

are invertible, then

and

are invertible, then

and

are not invertible, then

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Consider the following recursive iteration scheme for different values of variable

with the initial guess

For

is obtained to be 1.414, rounded-off to three decimal places. For

is obtained to be 1.732, rounded-off to three decimal places.

, the numerical value of

is _________. (round off to three decimal places)

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The Fourier cosine series of a function is given by:

For

, the numerical value of

is ______. (round off to three decimal places)

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GATE CE area:engineering-mathematics PYQs

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